THE ELEMENTS PERSPECTIVE. BY SIMEON DE WITT. ALBANY i PRINTED BY H. C. SOUTHWICK. No. 94, State-Street. 1813. DISTRICT OF NEW-YORK, or. Be it remembered, that on the first day of January, in the thirty- eighth year of the Independence of the United States of America, Simeon DeWitt , of the said District, hath deposited in this office the title of a Book, the right whereof he claims as author, in the words following^ to wit : “ THE ELEMENTS OF PERSPECTIVE. By Simeon DeWitt / 7 lu conformity to the act of Congress of the United States, entitled “ An act for the encouragement of learning, by securing the copies of maps, charts and books, to the authors and proprietors of such copies, during the time herein mentioned.” And also to an act, entitled, “ An act supplementary to an act, entitled “ An act for the encouragement of learning, by securing the copies of maps, charts and books, to the authors and proprietors of such copies, during the times therein mentioned, and extending the benefits thereof to the arts of designing, engraving and etch- ing historical and other prints.” THERON RUDD, Clerk of the District of Nerv-York . PREFACE. It will be seen by the Introduction to this Trea- tise, that the Author’s principal aim in publishing it is, to have Perspective introduced among the studies of a liberal education. His motive is a sincere convic- tion that, if this end be accomplished, he will have done a service to the community. With this view, he has taken some pains to make his subject an ob- ject of attention, by giving it an attractive appear- ance, and shewing the many respects in which it may have a wholesome influence on the morality and happiness, as well as on the usefulness of men as mem- bers of society. The style and manner, which he has purposely assumed to effect this, he leaves, as a matter of experiment, to the animadversions of critics, with a perfect indifference for the result ; for the ac- quisition of literary fame never yet entered his most chimerical dreams, and he most certainly will never put himself in pursuit of that phantom, or make an effort to seize it, how much soever he may be pleas- ed to see others in the chase or gratified by their suc- cessful exertions. His method of explaining the Art of Perspective, as it is different from that of preceding writers on the same subject, and, as he believes, better adapted to the habits of students passing through a Mathemati- cal course, he flatters himself will more effectually fix their attention to it, and enable them to acquire a IV PREFACE. knowledge of it with more ease. Prolixity, it will be observed, has been avoided as much as possible, with- out neglecting a due regard to perspicuity ; and the Examples have been limited in number to what was indispensable for illustrating the Rules: Whoever makes himself master of the Elements , will not need any more to instruct him in the drawing of objects of every kind ; and teachers will be able to multiply them at pleasure. How far the author has succeeded in his views must be left to the decision of judges more competent and less interested than himself. Aware of the false esti- mate we are prone to make of our own productions, and the extravagant value we generally set on favo- rite things, however diminutive, he is far from being sanguine that others will view his subject with the same impressions of its importance, or that this work will meet with the unqualified approbation of those who are best able to form a correct opinion of its me • rits. He is not, however, without hopes that the charms of his favorite will obtain her a permanent place in our seminaries of learning, and that she will yet be cherished as a beautiful, worthy, little sister of the sciences. If so, he will be happy to think that what was his amusement has become productive of a public benefit. As he does not calculate on any pecuniary gain from this publication, but rather the reverse, and as its limited scope, and the littleness of its subject, for- bid the surmise that he is prompted by the ambition of acquiring reputation by it, he hopes full credit will be given to the avowed integrity of Iris motive. He PREFACE. v therefore claims the right of an exemption from the suspicion of self-interest, while he calls on those who superintend the American institutions, dedicated to the Arts and Sciences , to give their patronage to works of this kind, which from the very nature of them, can be in demand with but a small portion of Readers, and which cannot therefore be brought before the public without individual sacrifice, or that patronage which can be effective. Why so few scientific works are seen as the product of America, is doubtless ow- ing to this cause, and not to a sterility of genius, or a want of adequate talents. This ordinary discourage- ment may not be a matter of serious consideration, in the present instance, with the writer of this Treatise ; but with many it would be an imperious veto against the bringing of their productions into the world, were the merit of them ever so great, or should the acqui- sition of them be ever so invaluable. This call is addressed to the Patriotism of our Country ; a country which, for many reasons, ought to be eminently proud of its Independence, and omit no opportunity of giving it a more decided and per- fect character : But this cannot be expected without having the spirit and munificence of the Maoenases and the Medici of other nations emulated in our own. V I - f f . * - Digitized by the Internet Archive in 2015 ’ \ https://archive.org/details/elementsofperspeOOdewi INTRODUCTION. EVER since I have been acquainted with Perspect- ive, that elegant and very useful little branch of the Arts, sprung from the Science of Mathematics, has appeared to me too much neglected in the education of youth. While public seminaries profess to make their pupils acquainted with the whole circle of the sci- ences, and give them the accomplishments requisite for entering the world with respectability and prospects of usefulness, this, strange as it may seem, receives generally no more notice than if it had never been discovered. Perhaps the reason is, because, few hav- ing seen it treated as an appendage to Mathematics, it is considered as belonging exclusively to the Draw- ing-Master, and therefore unbecoming a place in a learned institution, when, in fact, the Drawing-Mas- ter, although well qualified to be useful in his station, may know nothing of its principles, and therefore can- not teach it : or perhaps it is ranked among those things which serve only for idle amusement ; or it may, be because it is thought that drawing can be suf- ficiently learnt without it, as some learn the practice of Music, without knowing any thing of the Gamut or Notes. It is to remove such misconceptions and prejudices and to do justice to the merits of this art, that I have INTRODUCTION. viii been induced to unveil its countenance anew to the public, and to give it a dress different from any in which it has yet appeared. I shall, in this introduc- tion, shew its usefulness, and then explain and demon- strate its principles and the practical rules deductible from them. All that I have ever seen on the subject, has ap- peared unsatisfactory to me. I Lave, therefore, not followed the plan of any previous author, but have as- sumed a method which I conceived best calculated to explain the principles of the art, and to develope its elements by a regular mathematical process ; which, I hope, will give such a view of it as that it shall ap- pear not unworthy of being made a task even for stu- dents under the professors of a University. The little time it will take, for any young gentleman, in a regular course of education, to make himself master of it, compared with the very great use he may find in it, carries to my mind an irresistible argument for its adoption as an indispensable part of public instruc- tion. Projections of the Sphere, Conic Sections and Spherical Trigonometry, are indeed necessary step- ping-stones to the higher branches of science, but they are of little practical use to most students after their emancipation from College ; and I will venture to say, of less benefit on the whole, than this study would be, were it made equally general. It opens a path into which strong allurements invite the reasoning facul- ties. It is therefore well calculated to lead them into a cheerful submission to that extent of discipline which is held necessary for rearing them to maturity ; and this consideration alone gives it a stamp of value that INTRODUCTION. k entitles it to more than common regard. Were no other purpose contemplated — were it not even intend- ed ever to apply it to practice, still its use in this re- spect would amply justify its adoption. The Americans are an inventive people ; perhaps more so than any other existing. We have reason to think so from the number of inventions made pub- lic and applied to useful purposes within a few years : And, without arrogating to ourselves any superiori- ty of intellect, the cause may be traced to our more favorable circumstances ; especially to the facility with which a respectable education and the means of comfortable subsistence may be procured, and which leaves leisure to the mind to wander through the mysterious, unfathomable repositories of possible things ; to the boundless field of improvement be- fore us, and to the scarcity of labouring hands, which acts as a constant stimulus to resort to the mechani- cal powers, and every other attainable aid, to supply the deficiency. In aid of the inventive faculty, Perspective or rather Draw ing, of which it is the foundation, serves a twofold purpose. It creates habits of forming clear and distinct ideas of complex objects, with the rela- tive bearings of all their parts, whether such objects have been presented to the eye, or be only crea- tures of the mind, and changed to every shape and position, in order to ascertain which will best answer a meditated purpose. The imagination becomes so far improved by it, that the models it forms are as complete as those made of material substances. But its most useful office is to give substance and visibili- ty to those aerial shapes. The productions of the 2 introduction. X creative mind grow under the pencil till they result in wonderful systems, endowed with powers to pro- duce effects of incalculable benefit to man. I have no doubt that, for the want of this art, many a one, who had got on the track of some useful discovery, has lost his way in the pursuit and been necessitated to abandon it ; as the strongest mind would be oblig- ed to discontinue the investigation of some problems, without the aid of algebraic characters, that keep the whole process of his reasoning continually before his eyes, and render his progress to the conclusion practicable and easy. Without this art moreover, it would be impossible to communicate some discoveries, and make them in- telligible, even to the artists who alone can bring them into use. How often does it happen that the agriculturalist or the manufacturer requires implements or machine- ries which cannot be explained without accurate drawings ! Such agriculturalist and manufacturer may have received a liberal and even a polished education, and why cannot they give the requisite description ? It is because this art was, most undeservedly, consi- dered as too insignificant or too useless to be taught, and therefore they were left in total ignorance of the beauties and powers of its language. But the in- stances in which a knowledge of it would be found at least a convenient thing , even where it might not be wanted as a professional qualification, cannot be enu- merated. That drawing may be learnt to a certain extent, without a knowledge of perspective, is granted ; so may trigonometry, surveying and navigation be INTRODUCTION. y* learnt by committing some rules to memory. But is this a competent education? Would it be sufferable in a public seminary ? Could any student, possessed of ordinary ingenuity, undergo the drudgery of piling on his memory rules upon rules of which he knows not the reason ? Knowledge thus acquired is deserv- edly held in contempt as mere smattering, and a dis- reputable mimicry of science, and the pretenders to it considered as incapable of rising to a respectable eminence. > In drawing, through all the grades of the profes- sion, from the planner of architectural works to the historical painter, an acquaintance with perspectiVe is necessary ; and especially in those performances in which the joint powers of genius and fancy are to be displayed ; there it becomes emphatically indis- pensable.* To the traveller this art is invaluable. With those who have ample means for the purpose, it is a lauda- ble practice to send their sons, after finishing their ordinary course of education at home, to visit diffe- rent parts of the world, in order that they may ac- quire a knowledge of it which cannot be acquired from books, and that they may see, in the displays of the human character in its varieties, in the works of art, and in the appearances and productions of na- ture, in different regions, exemplifications of what they had been taught in the retirement of study, with the view that the information thus acquired may be preserved to assist them in their future services to their country. But every reader would anticipate me, should T undertake to mention how many things there are which in a little time will grow dim on the * See note A. INTRODUCTION* xii traveller’s memory, and how many which it will be impossible for him to make known tb others, or even to preserve in his own recollection, without availing himself of this art. Without it What account would De Non have brought from Egypt ? His verbal de* scriptions of that interesting country, the cradle of the human intellect, would doubtless have been as accurate as language could make them ; but, like the descriptions of the enchanted castles of novelists, or even like the description of the Turkish seraglio, by Clarke, they would have only filled the brain w ith a confused mixture of obscure and mutilated ideas, and tortured it with painful, perplexed, unavailing efforts at distinct perception. But it w T as otherwise With our traveller. He brought back with him the perfect resemblances of what he saw, and has given us a view of the mansions, the temples and the Gods of the Pharaos’ who flourished in ages buried deep in the dark bosom of antiquity* and of a race become venerable by their affinity to the infancy of the world. He who cannot mould and group his ideas in dis- tinct vivid images, and pencil them on his fancy with the skill of a painter, must never dream of chaplets about his temples for exploits in the field of Poetry. This art is therefore important also in that depart- ment of genius. And even in prose-rhetorick, mak- ing pretensions to merit, how often do we meet w 7 ith metaphorical images of monstrous shapes and the most incongruous composition ! As such must ever be disgusting to a correct critical taste, they could never be admitted into the productions bf one ac- quainted with the rules of symmetry, and that chaste* INTRODUCTION. xiii harmonious arrangement of imagery, which perspec- tive familiarizes to the mind. In the allusions of Homer, Virgil, Shakspeare and Milton, we see things as distinctly as if they were presented to us in a finished picture. On the contra- ry, we see in much of modern composition, the fi- gures intended to be introduced scarcely emerging from a fog impervious to the utmost efforts of intel- lectual vision, or so mis-shapen, or thrown upon each other in such confusion, that they resemble the odd compound of the Zodiac, rather than those simple, plain, complete, w ell selected and well arranged ob- jects most proper to make deep, lively and agreeable impressions on the mind. Whoever will compare literary works of universally acknowledged merit, not depending on any temporary fashion of language> with those frothy productions which, by a quaintness of phraseology, a clumsy attempt at rhetorical fi- gures, a rhapsodical affectation of passion and senti- ment, or a ridiculous, studied departure from all the rules of metrical arrangement, obtain an ephemeral currency, will constantly find this difference. Nor can it be unobserved in how’ many poetic as well as prose writers, there appears too much of a disregard for that melody and forcible expressive- ness of sousd of which our language is so happilv capable ; and which, by the most celebrated orators and poets of antiquity, were evidently studied to the utmost extent of possible refinement. It is doubt- less ow ing to a long continued prevalence of this study that, w ith them, an undefinable latitude in the transposition of words, especially in the Latin tongue, became orthographically allowable. It is from the XIV INTRODUCTION, same cause that in the French orthography, some- times the adjective and sometimes the substantive is directed to be the antecedent. An art which refines the sense, that receives the harmonies which the eye transmits to the soul, cannot but have somewhat of a similar effect on the sense that receives the harmonies of which the ear is the organ of transmission ; and especially in the offices of language, by which pleasurable ideas and pleasur- able sounds are simultaneously communicated, and by a concordant impetus, produce the ultimate effect to which its powers are limited. Drawing, sculpture, music, poetry, and the poetic qualities of prose, have reciprocal effects, and act with each other as auxili- aries ; a proficiency in either of them will therefore be serviceable to attainments in some one, if not in each, of the others,* These observations are made for the consideration of those who are concerned in the instruction of youth, to assist them in judging how far that preci- sion in the delineation of objects, and that relish for the harmonies of proportion which are acquired by the practice of drawing, may be of use in forming the true taste of criticism and habits of chaste com- position. No approaches can be made to the perfection of Art, without the habit of attentively observing the attributes and operations of nature, and a perse- vering study to imitate them ; and for this perspec- tive paves the avenue and opens the gate. Those matchless specimens of taste, the Grecian columns, which have mocked the efforts of a thousand years to * See note B. INTRODUCTION. xv produce an equal, grew from observations made on the trunks of trees, and the shapes and curvatures of leaves ; and the finest ornaments of architecture are but imitations of the fruits, flowers and foliage with which nature adorns the earth. Let the orator attend to the gestures of a child, as soon as it has obtained the command of its limbs ; or to the giant of the woods, and the motions of his arms, when fencing with the winds, and they will give him instructive les- sons in the practice of his profession. In both there is that gracefulness and total absence of awkwardness which the most finished education in man can never attain. An aptitude and partiality for drawing, have a ten- dency, more powerful than any other bent of the mind, to improve that taste which qualifies us for relishing the beauties of the Fine Arts as well as the beauties of Nature, and without which, no work of excellence can ever be produced. They have a tendency also to improve the Moral Complexion of the human soul ; for there is that affinity between the beauties of nature and the beauties of morality, that he whose sensibilities are alive to the one, cannot, without hav- ing unnaturally jarring elements dominant in his make, be impassive to the other. To contemplate the wonderful works of the Cre- ator, the Magnalia Dei, is the chief purpose of our creation, and therefore are virtue and happiness so closely connected with it. I may add in illustrating the usefulness of my sub- ject, that without some acquaintance with it a MILI- TARY EDUCATION cannot become perfect. Besides serving those purposes of practical utility; Perspective drawing, as a minister of R ATIONAL INTRODUCTION. *vi AMUSEMENT, holds a high station in the gradua- tions of merit ; and may almost dispute precedency with the poetic muse. Let those who practice it, and those whose harmoniously strung feelings enable them to relish its performances, testify ; to such, any observations as proofs would be needless, and to others, they would be as vain as pourtraying the rain- bow for the entertainment of the blind. Amusements must be had— by the busy to relieve them from the lassitude of toil, and re-invigorate them for labor — by the idle, to fill up the dreadful vacuities of time : And wo ! to that man who is not furnished with harmless resources from which to draw the supply. The most pitiable object of our race is lie who is cursed with an ample patrimony, without possessing the talents and education to fit him for being usefully busy, and without the capaci- ty of being reputably and innocently amused. His malignant destiny drives him to the fraternity of gam- blers, the resorts of drunkards, or the haunts of more infamous gratifications, as refuges from the intolera- ble dreariness of a vacant life. An acquaintance with one source of diversion for his mind, such as is here recommended, might save him from ruin. And why do we see so many of the lovelier part of the human race sacrifice the best of their time, or so much of it as can be spared from other noxious re- creations, to the DEMON of ROMANCE, have their delicate, susceptible minds irremediably poison- ed by that pestiferous trash, which, under the deno- mination of Novels , is poured upon the world; and, by indiscriminately and incessantly swallowing those deleterious opiates, have their judgments deranged. INTRODUCTION. xvii and their mental appetites so utterly vitiated, as to re- volt from the natural aliment of rational souls ? It is because for their employment, selections have been made of frivolous studies, and readings calculated merely to fascinate them, or to embellish their scanty acquirements with the tinsel glitter of mock orna- ment. They have had no guide to direct their par- tialities to substantial improvements, and those acqui- sitions which give power to the lovely, unsophisticat- ed, native blandishments of the sex. They have had no friend to bend their habits to employments worthy of the rank they hold in the scale of being, and tend- ing to ennoble, as well as to sweeten, the amiable dip- ties, which it is their proud prerogative to claim as exclusively theirs ; and especially, “ Well ordered home man’s best delight to make.” When we contemplate the illimitable field which a beneficent Providence has opened for the activity of man, and the delightful incentives that press us through all its avenues, it seems incredible that any one should be found to loiter on its confines in inglo- rious indolence. And yet we behold multitudes who can scarcely find any thing to pursue to which they are not impelled by stimulants possessed in common with the brutal race. Habits suffered to acquire a spontaneous growth, the criminal neglect of early discipline in the proper duties of life, cruel indulgen- ces of a depraved propensity to idleness, and a w r ant of attention to the cultivation of those inlets of ration- al delight, so bounteously provided, for animating and cheering Us on the journey of life, bring on, with an accelerated speed, that fatal apathy, which, to the miserable sufferer, blasts all the beauties of creation. 3 INTRODUCTION. xtiii It is the destiny of man, fixed unalterably in the councils of eternal wisdom, that he must be employ- ed ; he must have some object of pursuit or be mise- rable ; and it is a wise provision in the laws of na- ture, that he has innumerable wants to coerce him in- to the road of happiness, and, like the flaming sword of paradise, drive him to fields where he must labor or die ; where corporeal toil or mental energy only can save him from the wretchedness of his doom. — The condition of one fortuitously placed above the necessity of summoning all his powers into action, is an unnatural condition, and therefore cannot be hap- py ; unless education, like a spirit from another world, rouse up in him the dormant enthusiasm that soars above the common track of human actions, and aims at nobler ends than the subservience of ordinary * wants. HAPPINESS and IDLENESS can never become associates. Alan must act or suffer. To prepare one for a happy as well as for a useful life, it is there- fore necessary to furnish him with as many as possi- ble of those means which the paternal goodness of Heaven has provided, and permitted us to use, for keeping in employ the active instinct of our nature, when not demanded by imperative duties, in gratifi- cations compatible with its dignified elevation above the level of a mere animal : And among those means, that which is now recommended, is certainly not one of inferior importance ; nay, some that have been honored with a permanent place in the systems of fashionable education, can by no means boast of equal pretensions. Perspective drawing, especially that of Landscape, INTRODUCTION. xix gives him who is made familiar with its principles and practice a new and deeper interest in the APPEARANCES of THINGS. By it he becomes habituated to discriminating views of their beauties, and thus they acquire a superior power of minister- ing to his pleasures. In the aspect of nature, where others see nothing to affect them, but look “ with brute, unconscious gaze,”* he sees the distinct my- riads of parts, wonderfully formed and put toge- ther by infinite wisdom to constitute a whole, per- fect in all the varieties of proportion, shape, co- lor, and purpose, and his sensations are absorbed and dissolve in the harmony that reigns universally among them. Delight streams into his soul from every quarter to which he turns the contemplative eye. With rapture, felt in his bosom alone, he sees, spreading over the desolation of the year and displayed in all the dazzling perfection of beauty, the infinitely diversified colorings of the groves, the fields, the orchards, and the gardens of SPRING, with their nameless multitudes of animated beings, wakened to ecstacy by the spirit of the season — the boundless luxuriance of SUMMER— the fields of HARVEST in playful motion enjoying the balmy respirations of the SOUTH — and the endless profusion of AU- TUMN pendant in its countless varieties of charm- ing, delectable appearances ; and even WINTER, at every return, to the latest period of life, rekindles the juvenile joys with which he saw its approaches, braved its storms, mingled with its wild elements, himself as wild, and exulted in its sports. With sen- sations equally charmed, he sees the beauty of the riplings of RIVULETS, and the grace and majesty * See note C. XX INTRODUCTION. of the billows of OCEAN, moving in proud, curved attitudes, or rolling and roaring before the winds that play on his bosom. With the etherealised feelings of enthusiasm, he sees “ the jocund MORN standing tipt e on the misty mountain top,” and dilating and brightening, as she mounts the blue vault, the glory of crimson lustre that radiates about her ; the SUN from his meridian throne pouring “ the vital ocean’’ round and with his lights and shades, giving his exquisite finish to the picture of every prospect, or with his inimitable tints, painting the clouds that hover over him as he sinks to his nocturnal retreat ; the MOON, like the brilliant on the forehead of fa- bled Diana, suspended among the STARS, or seated among them, as the QUEEN of NIGHT, in full splendor, beaming a pale, pensive hue on the dim, death-like visage of the SLEEPING WORLD — the ever shifting scenery of the SKIES, and all the gor- geous drapery of HEAVEN. These compose the seraphic visions of him whose faculties have be- come thus refined and expanded to their influence. When from behind the western hills, in awful form, begirt with the darkness of black conglomerat- ing clouds, rises THE TEMPEST, and comes driv- ing on, in all the pomp of terrible majesty, with an immeasurable cataract before him, lightnings in his hands, embattled HURRICANES in his rear, and the roar of Heaven’s artillery round him ; the grandeur and sublimity of the spectacle are seen, felt and enjoyed by HIM who is accustomed to look with a perspective eye. And when again, the last rumbling of the retreating THUNDER is heard in the east, and the relenting clouds hang out the celes- INTRODUCTION. xxi tial signal, the pledge of purposes benign, and men gaze at the gladdening gaudy wonder ; and the te- nants of the air, the SPIRITS OF MELODY incar- nated, in bands of millions, fill heaven’s concave with the serenade, to welcome the returning monarch of day, hushing the elements and diffusing joy over the earth; HE sees and enjoys the BEAUTY of the scene. It is not pretended that such perceptions, and the sensations they produce, are exclusively his in whom they are thus cultivated ; but, beyond all doubt, to him they become a source of pleasure to a degree , and^ in some respects, in a manner , with which others are altogether unacquainted. In those happy regions to which “ the spirits of just men made perfect” are to be translated, it is supposed that there are objects which cannot be apprehended by any of the senses belonging to man in his present stage of existence, and that new senses will be furnished* for the contemplation of such objects, as additional sources whence felicities are to be multiplied. And the supposition is not unreasonable ; for the govern- ment of the universe is conducted by means most wisely adapted to their ends, and as every thing with the Almighty is infinite, there can be no assignable limits to the number of these. Objects of which we can now have no conception, and new senses to per- ceive them, may therefore be reserved for a more ex- alted stage of existence. We know that here the sum of happiness we are capable of attaining, de- pends materially on the number and perfection of our senses, and among these, those belonging to the soul, by which we perceive harmony and beauty, are INTRODUCTION. xxii of primary consequence : But in some individuals these senses shew but the glimmerings of existence, although capable of being elicited, cultivated and re- fined, till they have power to transport almost be- yond the enjoyments allotted to this infant state of being. And thus by education may the human soul be improved in its capacity for happiness here, in a man- ner resembling that by which it is prepared for the higher regions of bliss. Need I draw the inference in favor of the improvement, in the present system of education, which it is the purpose of this treatise to recommend ? Does it not resemble the creation of a new sense, by which man mounts one step higher in his approaches to the rank of superior intelligences ? And let not the gentle sex startle at the sound of Mathematics, and suffer it to frighten away what- ever impressions may have been received by them fa- vorable to this elegant Art. Although it would be disgraceful for the graduate of a college to be unac- quainted with the mathematical foundation on which his knowledge is built, the profound ploddings neces- sary for him are not required of the female learner.— Her quick intuitive apprehensions may well dispense with such a prop. A little practice after the examples that will be giv- en, will initiate her into the mysteries of the art ; and her natural ingenuity and taste will enable her, with the assistance of a few lessons from a drawing master, and the artificial helps that will be recom- mended, to prosecute it to any height of perfection she may wish to attain. “ To train the foliage o’er the snowy lawn, to guide the pencil,” and by its magic to call up the ap- INTRODUCTION. xxiii paritions of cottages, cascades, hills and dales, green woods and flowery fields, meandering brooks and waving trees, and all the witcheries of a fairy land ; to play with the children of FANCY ; to arrest the lovely, fugitive, flitting, visionary BEAUTIES, and fix them with the permanency which the enchant- ments of this art only can impress, well becomes the delicate taste, the lily hand and fingers of the fair. And, if in such employments and in the contem- plation of such objects, their gentle spirits rise in as- pirations to that wonderful POWER, from whom all things have emanated, the all beneficent Provider of such ineffable delights, they will feel themselves^ elevated to a region of pure intellectual enjoyments, far above that in which the untutored and less favor- ed part of their species are doomed to waste their ex- istence. NOTES, Referred to in the preceding Introduction; NOTE A — (Seepage \ l.) The following observations are from an author well known and justly held in high esteem for his ingenious and scientific works : “ I need not observe how requisite it is for Paint- “ ers who put groupes of figures together, but also “ for those who draw landscapes, or figures of ma- “ chines and engines for books, to know the rules of “ perspective. The want of this branch of know- “ ledge is the reason why we see not only very bad cc and distorted figures of machines and engines “ in printed books, but also why we see many histo- “ rical paintings, in which the different figures of “ men, women, hills, houses, birds and beasts are put “ together without any regard to what painters call “keeping; which is the same thing as representing “ objects in the same manner that they appear to the “ eye at different distances from it. “ I shall only mention two instances in the w ork “ of one of the greatest painters that ever existed ; I “ mean the celebrated Raphael Urbin. “ Every man is sensible, that, if he should stand by “ the sea-side, and look at a boat with men in it at “ some distance, he could not distinctly see the fea- “ tures of those men, much less the wrinkles and “ marks of the muscles in their faces or bare arms. NOTES. xxv And if he were in a boat at some distance from “ the land, he could not perceive the eyes and beaks €< of fowls on the shore. M Yet so it is, that in one of the famous Cartoons c< of Raphael, representing the miraculous draught “ of fishes, the men in each of the two boats appear “ of full size, the features of their faces strongly “ marked ; and the boats are represented so small, “ and the men so big, that any one of them appears u sufficient to sink either of the boats by his own bare “ weight ; and the fowls on the shore are likewise “ drawn so big as to seem very near the eye of the “ observer, who could not possibly in that case dkn “ tinguish the features of the men in the distant boats ; “ or supposing the observer to be in either of the “ boats, he could not see the eyes or beaks of the “ fowls on shore. “ The other instance is a very capital mistake “ in Raphael’s historical picture of our Saviour’s <( Transfiguration on the Mount ; where he is re- “ presented with those who were there with him, ab “ most as large as the rest of his disciples at the foot “ of the Mount, with the father and mother of the “ boy whom they brought to be cured, and the mo- “ ther, though on her knees, is more than half as tall a as the Mount is high. So that the Mount appears “ only of the size of a little hay-rick, with a few peo- “ pie on its top, and a great multitude at its bottom “ on the ground, in which case a spectator at a little “ distance, could as well distinguish the features of “ those on the top as those on the ground. But upon “ any large eminence^ deserving the name of a Mount, c< that would be quite impossible. My only reason 4 XXVI NOTES. “ for mentioning these extraordinary particulars, is “ to shew how necessary it is for painters to be well “ acquainted with the Rules of Perspective.” FERGUSON. NOTE B. — ( see page 14.) Doubtful whether my meaning, in what I have said about the sound of language , will be fully com- prehended, I am tempted to make a few critical re- marks to explain it ; and to this I am the more readi- ly induced by the consideration that it may be of some use, in other respects, to the student, for whose hands this work is principally intended. For this purpose* I shall take an ordinary passage from Virgil, where, in enumerating the objects of the husband- man's care, he has occasion to mention the class of vegetables, distinguished by the name of pulse , called by Botanists, the pod-bearing or leguminous plants. This he does in such a manner that the expression is in itself musical, or agreeable to the ear ; that it re- sembles in its sound what is intended to be express- ed, and, that it excites other pleasing ideas. The passage to which I allude is this : Latum quassante siliqua legumen. Which I would translate, The leguminous plant pleased with the rattling of its pod. Whether this, in the original, is not musical, can be determined only by an appeal to the ear ; and, un- less I am much mistaken, there is something in quas - sante. siliqua resembling that soft sound which is NOTES. xxv ii heard from pods, ripe for gathering, shaken by the wind. To me it seems not inferior, in this respect, to Homer’s y***r of Apollo’s bow, his of the terrified Pluto, or his *?***** nctx'evB* x*< the horses of .Eneas; and in sweetness of tone, if not fe- licity of expression, equal to his &*h V * £V v ******* of Andromache. Besides, one can hardly read this line without having raised in his mind one of the most agreeable sights in nature, a child happy in the pos- session of a toy, or a mother amused with the sports of her children. It is in exciting pleasing ideas to associate with* those primarily intended to be communicated, that the chief art of poetry consists. Here the poet gives perception and affection, properties of animated be- ings, to the vegetable, and thus furnishes a handsome specimen of the prosopopeia. Davidson’s translation is, A joyful crop of pulse rvilh rattling pods. Now, to my ears and to my understanding, this is far from being a true representative of the original. And thus it is that the classics are ordinarily taught. Their melody is personated by discord. The delight- ful associated and secondary ideas, that croud about their principals, are totally lost ; and a body the most beautiful, and full of soul and animation, such as a Georgic or an Enead, is exhibited as a mass destitute of every attractive quality, excepting per- haps so much of the ingenuity of the original as can- not be disguised, or the interesting matter of the sto- ries it relates. To mistake the obvious meaning of an author, is unpardonable in a translator ; not to do justice to his NOTES. xxviii style may be excusable ; for the fact is, that no man's, style can partake fully of the melody of language, unless he has an ear that can detect the slightest touches of discord in a sentence, and a taste that will direct him to the true medium between a tedious mo- notony and too excessive a variety of measure, whe- ther prose or poetry be the manner of his writing. These discriminating faculties in regard to the me- lody of language, are what I have supposed may be favorably affected by that taste for the kindred har- monies, which the study of perspective and the prac- tice of drawing are calculated more immediately to improve. When I read Horace, Virgil or Homer, I see, with- out an interposed veil of obscure diction, the most beautiful images moving to the most melodious mu- sic. The sound of Cicero’s language, little less than the matter it conveys, is an instrument of delight, and both combined have produced that wonderful effect in which subsequent ages have in vain attempted to rival him. These writers never insulted their cotem- poraries by offering for their admiration, the uncouth dialects and barbarous phrases current in the days of Theseus and Romulus. The polished Grecians and Romans were not to be duped by such literary cun- ning ; they did not complain that their language was enervated by a departure from the rough jargon of their ancestors, or poisoned by borrowing sweetness from neighboring nations ; although there might have been some then, as there are critics now, disposed to plead for a recurrence to the days of VORE. NOTES. xxrx NOTE C— (Seepage 19.J As coincident with several of the sentiments ad- vanced in this treatise, the following passage is trans- cribed from the works of one of the most eminent and most amiable of moral philosophers : — “ It is strange to observe the callousness of some “ men, before whom all the glories of Heaven and “ earth pass in daily succession, without touching “ their hearts, elevating their fancy, or leaving any “ durable remembrance. Even of those who pie- ‘‘ tend to sensibility, how many are there to whom the lustre of the rising or setting sun ; the sparkling concave of the midnight sky ; the mountain-forest “ tossing and roaring to the storm, or warbling with ■ c all the melody of a summer-evening ; the sweet in- “ terchange of hill and dale, shade and sunshine, “ grove, lawn, and water, which an extensive land- “ scape offers to the view ; the scenery of the ocean, “ so lovely, so majestic, and so tremendous ; and “ the many pleasing varieties of the animal and ve- “ getable kingdom, could never afford so much real “ satisfaction, as the steams and noise of a ball-room, “ the insipid fiddling and squeaking of an opera, or “ the vexations and wranglings of a card-table.” “ But some minds there are of a different make ; “ who, even in the early part of life, receive from “ the contemplation of nature a species of delight “ which they would hardly exchange for any other. “ Such minds have always in them the seeds of true “ taste, and frequently of imitative genius. At least, “ though their enthusiastic or visionary turn of mind “ (as the man of the world would call it) should not “ always incline them to practice poetry or painting, XXX NOTES. “ we need not scruple to affirm, that without some “ portion of this enthusiasm, no person ever became “ a true poet or painter. For he who would imitate “ the works of nature, must first accurately observe “ them ; and accurate observation is to be expected “ from those only who take great pleasure in it. “ Toa mind thus disposed, no part of creation is “ indifferent. In the crouded city and howling wil- “ derness ; in the cultivated province and solitary “ isle ; in the flowery lawn, and craggy mountain ; “ in the murmuring of the rivulet, and uproar of the “ ocean ; in the radiance of summer, and gloom of n . . •' " ‘ ■ i A j If fM j| { j ,) .j. » : : > r. • ■ L i . ) J .i J. . * irriAaa ■ ‘ . r •- ■ • . ELEMENTS OF PERSPECTIVE. DEFINITIONS. Perspective is the art of finding on a plane, * placed between the eye and an object, the several points through which straight lines, drawn from any given points in the object to the eye, will pass; for the purpose of making a representation of such object on such plane ; the position of the eye, the plane, and object, being given. The plane on which objects are so to be represent- ed extended indefinitely each way, is called the Plane of the Picture ; and is generally placed perpendicu- lar (or at right angles) to the horizon. That point in the plane of the picture, to which the eye is supposed to be perpendicular, is called the point of sight. A line drawn on the plane of the picture, through the point of sight parallel to the horizon, is called the horizon line . A point in the horizon line at a distance from the point of sight, equal to the distance between the sup- posed place of the eye and the plane of the picture, is called the point of distance . 5 34 ELEMENTS of A horizontal plane intersecting the plane of the picture at any distance below the horizon line on which the objects to be drawn are first to be Ortho- graphically projected, is called the j undam enlal plane. The line of intersection between the plane of the pict ure and the fundamental plane, is called the Fun- damental or Base line. If, from any number of points in an object, straight lines be drawn perpendicular to the fundamental plane, such points are said to be orthographically projected on the plane, where it is met by such per- pendiculars. The heighth to which the perspective representa- tion of an object is raised above the base line in the plane of the picture, is called the perspective elevation . The perspective representation of the heighth of an object above the fundamental plane, is called theper- spective altitude. The angle, by which any straight line deviates from a vertical plane supposed to be placed at right an- gles to the plane of the picture, is called the angle of inclination. The angle by which any straight line deviates from a horizontal plane, is called the angle of declination. PROPOSITION 1st .—Fig. 1. If, from any given point in an object, a straight line be drawn at right angles to the plane of the pic- ture till it meets it, and from thence another straight line be drawn on the plane of the picture to the point of sight, the given point will then be represented some where in this line. DEMONSTRATION. Let GH be the plane of the picture, E the point PERSPECTIVE. 35 of sight, F the given point in the object, FI the line drawn from it, at right angles to the plane of the pic- ture, meeting it in I ; and IE the line drawn thence to the point of sight. Continue FI to C & D, through E draw AB parallel to CD ; also draw AC and BD ; then ABCD will be a plane intersecting the plane of the picture in the line IE. Suppose B the place of the eye, and FB a straight line drawn from the given point to the eye. It is evident that the line FB will be in the plane ABCD, and therefore will inter- , - 'A sect the plane of the picture somewhere in the line IE. Q. E. D. PROPOSITION 2d. — Fig. 2. If EB be the line drawn by Proposition 1st. some- where in which the given point in the object will be represented, B being the point of sight, A the point of distance, and EG parallel to AB. Then if EH laid off in a direction contrary to that from B to A be equal to the distance of the object from the plane of the picture ; and AH be drawn : the point C where it intersects the first mentioned line, will represent the given point, or CL will re pr esent, its perspective elevation. DEMONSTRATION. Let BF be the profile of the plane of the picture, G the given point, and a straight line be draw n from it to the eye at A ; it is evident that DF, (the dist- ance between the place where it intersects the plane of the picture and the line EG,) will be its elevation; and this line DF is equal to CL, or CD is parallel to EG ; for if it be not, make Cl parallel to EG, and through I draw AK. Then, from the properties of similar triangles it will be ; 36 ELEMENTS OF In the Triangles ACI,AHK ; Cl: HK : : AI : AK ) W In the Triangles ABI,KFI ; AI : AK : : BI : BF > ^ In the Triangles BIC,BFE ; BI : BF : : Cl : EF ) p Therefore, Cl : HK : : Cl : EF. (E. 11, 5.) And Therefore, HK-EF. (E. 9, 5.) But HG is equal to EF, for EH was made equal to FG, wherefore HK is not equal to EF, neither, therefore, is Cl parallel to EJG. In the same manner it may be demonstrated that no other line drawn from C to BF, but CD is parallel to EG, wherefore CD is parallel to EG, and of consequence CL is equal to DF, the perspective elevation of the given point. Q.E.D. PROPOSITION 3d. — Fig. 3. If K on the plane of the picture be the perspective representation of a given point on the fundamental plane, and it be required to represent another given point above it of the lieighth EF, take any point in the horizon line as A, draw AE, and AF ; through K draw KG parallel to the horizon line, till it meet AF in G, and from G draw the perpendicular line GC, till it meet AE, make MK equal and parallel to GC ; M will then represent the other given point, and MK will be its perspective altitude. DEMONSTRATION. Let LI be the profile of the plane of the Picture, F a point in the fundamental plane, E another point above it, and B the place of the eye ; complete the figure by drawing the lines BF, and BE, PI and K being of equal elevation. It is evident that D and H, where these lines intersect the plane of the pic- PERSPECTIVE. £/f- c 37 ture, will be the perspective elevations respectively of E and F, or DH will be the perpendicular dis- tance between the points on the plane of the picture representing E and F. But, CG is equal to DH, for, from the properties of equiangular Triangles, it will be : In the Triangles AEF,ACG; FE : GC : : FA : GA ) t*j In the Triangles FAB, FGH; FA : GA: : FB : HB > IritheTrianglesBEF,BDH ; FB : HB : : FE :HD ) P Therefore, FE : GC : : FE : HD. (E. 11 . 5.) Wherefore, GC=HD. E. 9. 5. But MK was made equal to GC, therefore MK will also be equal to HD, which is the perspective altitude of the point E. Q,. E. D. These propositions furnish rules by which all ob- jects may be represented perspectively ; and in their application to practice, observe the following GENERAL DIRECTIONS. On the fundamental plane project orthographi- cally all the points in the object to be represented that may be considered necessary for delineating its outlines: From these points, (by proposition 1st) draw straight lines perpendicular to the fundamental or base line, and from the points where they intersect it draw straight lines to the point of sight; in these lines, (by proposition 2d) find the Perspective eleva- tion of the several points to be represented, then (by proposition 3d) draw r the perspective altitudes of the several points according to their respective heights ; and finally connect the several points in the repre- sentation, as they are in the outlines of the objects. 38 ELEMENTS OF Besides these, some auxiliary rules may be deduc- ed from the same principles, as the following propo- sitions will indicate. PROPOSITION 4th. If a line on the fundamental plane be neither at right angles, nor parallel, to the pfcwe of the picture or base line, and that line be continued to the plane of the picture or base line, and a line be drawn thence, on the plane of the picture, to a point in the horizon line, distant from the point of sight by the tangent of the angle of inclination, (the distance of the eye from the plane of the picture being radius) then will the first mentioned line be represented in the line so drawn on the plane of the picture. DEMONSTRATION.— Fig. 1. Suppose FI and BE not at right angles to the plane of the picture GH, then draw BK at right an- gles to the plane of the picture ; K will then be the point of sight, and E may be called a casual point of sight, whose distance EK from the point of sight will be the tangent (to the radius BK) of the angle of in- clination KBE, and (by proposition 1st) FI is repre- sented in the line EL ft. E. D, For the same reason, lines in objects declining up- wards or downwards from a horizontal plane, will have their casual points of sight below or above the horizon line by the tangent of the angle of declina- tion, to the same radius, if there be no horizontal in- clination ; otherwise to a radius which shall be the se- cant of the angle of such inclination : For EL is the tangent of the angle of declination EBL to the radius BE which is the secant of the angle of inclination EBK. If the inclination be to the right, the casual PERSPECTIVE. 39 point must be laid off to the left of the point of sight ; if the declination be upwards, the casual point must be laid downwards from the horizon line, and vice versa . The casual point may be found in the following manner : (Fig. 4th.) S If HO be the horizon line, BA the base line, S the point of sight, D the point of distance, and IKLM a parallelogram on the fundamental plane to be drawn perspectively. Continue LK and LM to U and F ; draw LY at right angles to the base line and equal to SD ; through Y draw EG parallel to the base line till it meet LU and LF in E and G ; make GS % equal to GY, and SP to EY ; then will C be the casual point for LM and all lines parallel to it ; for, CS, or GY which w r as made equal to it, is the tan- gent of the angle of inclination YLG of the line LM, to the radius LY, which is equal to SD the distance between the eye and the plane of the picture. For the same reason P is the casual point for LK, and all lines parallel to it : Wherefore, CF, CX, PU and PW being drawn, their points of intersection, i.LLm. will be the perspective of I.K.L.M. Suppose now that the end IK of the parallelogram be raised above the fundamental plane to the height qa> then through a draw LT, making ET at right angles to LU, and from P lay off P p at right angles to HO and equal to ET ; p will then be the casual point for LK and MI raised as aforesaid: For P 'p % which is equal to ET, is the tangent of the angle of declination ELT to the radius EL, which is the se- cant of the angle of inclination ELY, and in this case the perspective of KL and IM will be in the line drawn from p through l and in. 40 ELEMENTS OF Since aq is supposed the perpendicular drawn to the fundamental plane from K elevated to a, the point q will be the orthographic projection of K so elevated, and qt of the line IK ; qt continued will strike the base line at b, and IK, so elevated, conti- nued, will strike above it a distance equal to qa to wit, at v y wherefore K and I will then be found in a line drawn from V to the casual point C, to w it, at tv and s, where it is intersected by pm and ps ; lm,rvs w 7 ill then be the perspective of IM,LK, so elevated. If IK remaining on the fundamental plane ; ML had been elevated to the height aq, then would c in- stead of p have been the casual point of si^ht for IM and KL. If the perpendicular S D be made equal to SD=* LY and lines be drawn from D parallel to LK and LM, they will intersect HO in C and P because the triangles ELY and YLG are similar and equal to PjDS and SZ)C ; the casual points C and P may therefore be found in this as the easiest manner. — Now if a line be draw r n from L to D , intersecting EG in 8 and HO in 7, S 7 will be equal to Y 8, and, as before shew n, a distance equal to Y 8, laid off from S on HO will give the casual point for the line L 8 ; wherefore 7 will be the casual point for L 8, and L 8 continued to the base line and thence to 7 will be re- presented in such continuation ; whence it follows, that w here a straight line drawn from L to D inter- sects either UP or FC, (in which LK and LM are re- presented) to wit at Z, will be the perspective repre- sentation of L. In the same manner lines drawn from M, I and K, to J3 will, at their intersections with CF, CX, PYV and PL T give the points representing M, I and K. PERSPECTIVE. 41 Henfce we have still an easier method of drawing the perspectives of lines inclined to the plane of the picture, thus : If it be required to draw the perspec- tive of 9, 10, continue that line to the base line at 1 1, from D draw DC , parallel to it ; draw 1 1 C, D 10 and D 9 and the points of intersection if, 12 and 13 will represent 10 and 9. ^ Thus also, by making PZ>^ equal to ELT, or the angle of declination, and drawing P 14 at right an- gles to P D and making P p and Pc equal to P 14 may p and c be found, or the casual points of LK and MI declining upwards or downwards as aforesaid. From this proposition, and from proposition 1, it follows, that all lines parallel to each other, and not parallel to the plane of the picture, will be repre- sented in lines meeting in one point, those which are at right angles to the plane of the picture will be re- presented in lines meeting in the point of sight ; and those which are inclined to the plane of the picture, will be represented in lines meeting in some casual point. PROPOSITION 5th. All lines parallel to the plane of the picture, and equi-distant from it, will be represented by lines parallel to them, and having the same proportions to each other ; and hence any figures whose parts are equi-distant from the plane of the picture will be re- represented by similar figures ; that is, squares will be represented by squares, circles by circles, &c. &c. DEMONSTRATION. — Fig. 5. Let AB be a section of the plane of the picture, C the eye, DE and FG two lines parallel to AB, and equi-distant from it ; and HI and KL the lines re- 6 42 ELEMENTS OF spectively representing them. Then will HI be to KL as HE is to FG. Join E,F; DG will then be one line parallel to AB. Then from the properties of similar triangles, it will be, In Triangles CGD,CLH ; CG : CL : : DG : HL \ H In Triangles CGE,CLI;CG: CL r.EG .lL ] & Therefore DG :HL. : EG : IL (El 1,5) and DG : HL : : DE : HI(E 1 9,5) and for the same reason DG : HL : : FG : KL Wherefore DE : FG : : HI :KL(El 1,5) £ PROPOSITION 6th. The diagonals of squares having two sides parallel andi two sides at right angles to the plane of the pic- ture, will have their casual points of sight in the point of distance laid off either way from the pointof sight on the horizon line. DEMONSTRATION.— Fig. 6. The diagonals of squares so situated will incline to the plane of the picture under angles of 45°, the tan- gents of which are equal to radius, (and by proposi- tion 4th) the distance of the casual points from the point of sight is equal to the tangent of the angle of inclination (the distance of the eye from the plane of the picture being radius) ; wherefore, the casual point of sight of every such diagonal will be in the point of distance laid off either way from the point of sight in the horizon line. Q.E.D. Hence we have a convenient substitute for the rule deduced from propositions 1st and 2d to find the perspective of points given on the fundamental plane ; for if from any such point a line be drawn to . the right, and another to the left, meeting tlte! base line under angles of 45°, and lines be thence drawndo PERSPECTIVE. 43 the casual points of sight (which will be the same as for the diagonals above mentioned, that is in the points of distance) where the last mentioned lines intersect each other will be the perspective of the gi- ven point: Thus, Figure 6. If A be the point of sight, B and C the points of distance^ then C and B will be the casual points of sight for the diagonals of the squares DOEG and EGFH, and also for all lines meeting the base line JDN under angles of 45°. If, therefore, any point, as L, is to be drawn perspectively, draw LM and LN to fall on DN under angles of 45° and draw MB „ and NC ; the point of intersection l will then be the perspective of L. Figure 7, Shews the perspective of a cube, the bottom and top of which are made by drawing the diagonals as in tig. 6 : thus, make GF equal to DG ; draw' DB and FC, and from the point of intersection o draw T to pa- rallel to DG, and from e where it intersects CG draw r eD ; DGo? w ill then be the bottom of the cube. — Having made the square DG(/g for the front side of the cube, from dg draw' the top in the same manner as the bottom was drawn from DG, and connect the several corners. The foregoing propositions shew the several ways in which objects may be perspectively represented. The practitioner w ill use such of them as he will find most convenient for his occasion. A few examples of those different methods will now be given. In the succeeding figures HO will denote the ho- rizon line ; BA the base line ; S the point of sight ; 44 ELEMENTS OF D the point of distance, and C and P the casual points of sight. The pla ee immediately below the base line is considered as the fundamental plane, and the place of the eye to be on the opposite side of the plane of the picture. It is here proper to apprise the reader, that for the sake of adapting the figures to the size of the book, they are, in the following examples, necessarily made too small to serve as precedents, in point of size, for practical drawing, in which the point of distance from the point of sight ought never to be less than eight inches, that being the least distance at which the human eye generally can distinctly discern objects ; and the greater the point of distance is taken, and the less, in proportion, the field of the picture, the less will that distortion appear which is observed in objects represented remotely to the right or left of the centre of the picture. It has been assumed, by some waiters on perspective, as a general rule, that the horizontal extent of the picture should not ex- ceed the side of an equilateral triangle, in the oppo- site angle of which the eye is supposed to be placed ; or that no object ought to be taken into a picture which is seen at a greater distance than thirty de- grees to the right or left of the point of sight. Al- though this, as it regards the precise angle, is an ar- bitrary rule, it will be well to observe it. It may not be amiss to remark here also, that to view a drawing to the best advantage, the eye should be placed exactly in that point where it was suppos- ed to be, that is, in the point of distance directly op- posite to the point of sight. PERSPECTIVE. 45 EXAMPLE 1st. To draw the shape of a house, the body of which is a parallelapiped, and the roof a prism, in a posi- tion oblique to the plane of picture. Figure ^ Let 1KLM be the base of the figure on the funda- mental plane, BV the heighth of its perpendicular side, NR the orthographic projection of the upper edge of the roof or prism, and BQ, its height. From IKLM, according to proposition 1st, draw the perpendiculars la, K6, Lc, Me?, and from a, b , c, d , draw straight lines to the point of sight S. Then, according to proposition 2d, lay off ac , bf \ eg and dh , equal to la, K£>, L c and Me?, respectively, and from e,/, g, h, draw straight lines to the point of distance D ; connect the points i, k , /, m, where the lines, so drawn from a, b , c, d, and e , /, g , h, intersect each other ; then will i } k, l, m be the perspective of IKLM. In the next place, according to proposition 3d, on i, k, 1, m raise the perspective altitude of BV, thus : take any point, as T, in the horizon line, and draw TB and TV ; from i, k, /, m draw horizontal lines to TB, and from the several points t, u y v, w y where they intersect it, draw perpendiculars to TV. On i, k y /, m 9 raise perpendiculars respectively equal to those on ty Uy v, Wy and connect 1, 2, 3, 4, their upper ends, by straight lines as in the figure, which will then be the upper side of the parallelapiped as seen from below, for in this case it is above the point of sight. To draw the roof or prism : from N draw the per- pendicular Np and from p draw pS 9 then will n, where this line intersects ik, be the perspective of N ; in the same manner find r, the perspective of R ; draw TO ; from n and r draw horizontal lines to BI, and, 46 ELEMENTS OF from the points where they strike it, draw perpendi- culars TO, and equal to them make the perpendicu- lars n 5 and r 6, draw 1, 5 — 2, 5 — 3, 6 — 4, 6 and 5, 6, which will give the perspective of the roof or prism. In perspective, all the parts are commonly first drawn as if the figures were transparent ; but, in finishing, those parts only are drawn which are not hid from the eye by others, as ki, im, k2 , il, mi, 2, 5 — 1 , 5 — 5, 6 and 6, 4. — ( See W.) The perspectives of two oblique parallel lines pro- duced will meet in their casual point of sight ; which may therefore thus be found, as a substitute for the method directed under proposition 4th : kl and im produced will meet in P, to which 2,3 — 1,4 and 5, 6 are also drawn — ik and ml produced will meet in C, to which 1, 2 and 3, 4 are also drawn. If then, any number of oblique parallel lines are to be drawn (as for example the boarding of the side of a house) it is a convenient method, first to find their casual point of sight in this manner, in order to show the direction in which they are to be drawn, as ex- emplified at W. EXAMPLE 2d, Shewing a different method of drawing perspec* live altitudes. Figure 9. Draw the perspective of IKLM, as in the preced- ing example, or according to the method described in the latter part of proposition 4, which is here ex- emplified : — Thus, Make the perpendicular SZ>, equal to SD, make DP parallel to KL and IM ; continue KL and IM to X and W ; draw PX and PW> draw straight lines PERSPECTIVE. 47 also from D to I, K,L and M, and where these in- tersect PX and PW, to wit : at i, k , l, m, will he the perspective representation of I,K,L,M. Draw VU and QT parallel to the horizon ; con- tinue la, K6, L c and M d to VU ; then will the se- veral points, where these lines intersect VU, be the points where lines at right angles to the plan of the picture, drawn from IKLM raised to the height V, w ould strike it ; and by proposition 2d, w here lines drawn thence to the point of sight S, intersect perpendiculars raised on i, /, k , m, will be found the perspective of IKLM raised as aforesaid, as at 1, 2, 3, 4. Thus the perpendicular from K, being continued to u, the line drawn thence to the point of sight S intersects the perpendicular raised on A:, at 2 ; 2 will therefore be the perspective of K, raised to the heighth V, and so with the rest. Again, because NR is to be raised to the height Q, continue N p and R# to QT, and from the points v and y , where they strike it, draw straight lines to S, intersecting the per- pendiculars raised on n and r, at 5 and (5, which will therefore be the perspectives of N and R, raised to the height Q. EXAMPLE 3d. To draw perspective altitudes by the casual points of sight. Figure #. Having drawn the perspective of IKLM accord- ing to the directions under proposition 4th, from U raise a perpendicular to VZ, and x , the point where it strikes it, will be the point where KL, raised to the height V, and produced, w ill strike the plane of the picture; then, in the line drawn thence to the 43 ELEMENTS OF casual point P, will be found the perspective of KL so raised, (according to proposition 4th) and the points 2 and 3, where it intersects the perpendiculars raised on k and 7, will be the perspective of E and L, raised as aforesaid. In the same manner, by raising a perpendicular from W to VZ, and drawing a line thence to P, intersecting perpendiculars raised on im , we find the points 1, 4, for the perspective of IM. — Instead of P, the casual point C might have been used, working from KI and LM, instead of KL and IM. To find the perspective of NR, produce it till 4 it meet BA, thence draw a perpendicular to y , the height of Q,, thence draw yV, and where it intersects perpendiculars raised on n, r, to wit : at 5 and 6, will be the perspective of NR, raised to the height Q,. In drawing the perspective altitudes of horizontal parallelograms, after having found that of one of the corners, the next may be found by the intersection of a line drawn thence to the casual point, with the corresponding perpendicular ; and this being found the next is found in the same way, and so on : Thus, having found 1, a line drawn thence to C, will give 2 a line drawn thence to P will give 3, and a line drawn from C, through 3, will give 4. For if two lines intersecting each other, be drawn perspectively, their point of intersection will be represented by the point of intersection in the perspective. EXAMPLE 4th. To draw the same by angles of forty-five degrees. Figure 10. From K draw KW and KX, meeting the base line under angles of forty-five degrees ; from W draw a straight line to D on the right ; and from X draw a PERSPECTIVE. 49 Straight line to D on the left ; and the point k , where these two lines meet, will (by proposition 6th) be the perspective of K. In the same manner find i, /, m, n, r, the perspective of ILMNR ; from W raise a perpendicular to Y, making WY equal to BV, draw a straight line from Y, to D on the right, and on k, raise a perpendicular till it meet it at 2 ; then will 2 be the perspective of K, raised to the height V ; and proceed in the same manner to find the perspective altitudes of all the other points in the figure. In order to practice in this manner, it will be ne- cessary to have a thin board, in the shape of a right angled triangle, having the two legs exactly equal to each other ; then by laying a ruler parallel to the base line below the figure to be drawn, and applying to it the hypothenuse of the triangle, if one of the legs be made to touch any of the points in the figure* a line drawn along that leg will meet the base line under an angle of forty-five degrees ; the other leg is used to draw the contrary way. In many sided figures, where there are few paral- lel lines, this is perhaps the most expeditious, as well as the neatest way of perspective drawing ; but where there are many oblique parallel lines, it will be easi- er to draw from the casual points, as shewn in the 3d example ; either of these methods however need not be adopted, in complex drawings, to the exclusion of others ; but sometimes the one, and sometimes the other, may be chosen as the practitioner shall find best for his purpose. 7 50 ELEMENTS OF EXAMPLE 5th. — Fig. 11. To draw Curvilinear Figures . First circumscribe them with the simplest rectili- neal figures* of which draw the perspective ; and in the same, draw the perspective of the given figure, as correct as can be judged by the eye. Circles are best inscribed in squares, having their sides parallel and perpendicular to the base line. Thus, if it be re- quired to draw a figure in the shape of a churn, or frustum of a cone, having its bottom equal to the cir- cle N, and its top equal to C ; round them circum- scribe the squares EFPG and IKML* having their sides parallel and perpendicular to the base line. Continue the perpendicular sides to the base line, and draw straight lines thence to the point of sight; and from Q and T, where the diagonals produced strike the base line, draw straight lines to the points of dis- tance as in the figure. Then will the points of inter- section c,fg, p , be the perspectives of E, F, G, P, and i, k , l, m, will be the perspectives of I, K, L, M, the orthographic projection of the square circumscribed about the top of the frustum to be drawn. On (1, and T raise the perpendiculars Q,R, and TV, equal to the heighth of the frustum. From R, and V, draw straight lines to the points of distance ; and 1, 2, 3, 4, where these intersect perpendiculars raised on i, k, l, m, will be the perspective altitudes of i, k, l, m : Then in efg h and 1, 2, 3, 4, draw, for the perspectives of the bottom and top of the frustum, the curved figures touching the perspectives of the middle of the sides of the circumscribed squares, and crossing the per- spectives of the diagonals in points found thus ; from 5 and 6, where the circle N intersects the diagonals PERSPECTIVE. 51 of the circumscribing square, draw perpendiculars to the base line, and from the points 7, 8, where they meet it, draw lines to the point of sight : where these lines intersect the perspectives of the diagonals, the perspective of the circle must cross them. And last- ly, draw straight lines for the sides of the frustum, touching the perspectives of the two ends. This shews an oblique view of the object, and gives it somewhat of a distorted appearance, which is una- voidable in groups ; but where a drawing is required * of a single object, especially of cones and cylinders, it will be adviseable to take a front view, or as near- ly so as may be. The base of the frustum in the example, will then assume the shape represented at W, and the whole figure be like that at Y. X is the perspective of a cylinder whose sides are perpendicular to the plane of the picture, and the ends parallel to it ; in which case, according to propo- sition 5th, the perspectives of the ends will be cir- cles, and by proposition 1st, the sides will appear in lines drawn to the point of sight : Z is the drawing of it completed. EXAMPLE 6th. — Fig. 12. To draw the perspective of lines divided into equal parts — - If a line be parallel to the plane of the picture, its equal divisions will be represented by equal divisions in the perspective. No particular directions need therefore be given for the operation. If a line at right angles to the plane of the picture, be divided into equal parts, as EF divided at a and b ; make E a, E b, E/, equal to Ea, Eb, EF respectively : Draw ES, also draw Da, D6, Df \ Ee will then be 52 ELEMENTS OP the perspective of EF and c and d the perspectives of a and b. Again, If a line inclining to the plane of the picture, be divided into equal parts, as GI divided at c, d, e ; con- tinue IG to K ; make the perpendicular S D equal to SD ; draw LJP parallel to KI ; join KP ; draw straight lines from D to G, c, d, e, I ; then will these points be represented by the intersections g, li, i , k , l. Another method is this. If EL, aM, bN be squares, draw ES and aS ; also draw «D ; then from c draw cm parallel to E a, next draw mD, and from d draw the parallel dn ; then from n draw nl ), and from e draw the parallel co ; E m, cn , do, will then represent the squares EL, aM, bN, and the equal divisions of EF, will be represented at c, d and e. Thus a row of squares, and consequently of lines divided into equal parts, continued to any extent, may be repre- sented in perspective, without first projecting them on the fundamental plane. In like manner, the ob- lique row of squares ITT Q,R, may be drawn per* spectively, thus, continue TIT and RQ, to the base line, and from where they meet it draw straight lines to the casual point P ; draw Dp parallel to the diago- nals of the squares ; then will p be the casual point for those diagonals : also draw DC parallel to Q,U, and the other sides of the squares crossing the row ; then will C be the casual point for those sides ; con- tinue WQ to Y, and draw Vp ; and draw successive- ly qC, qp , Crs, sp, Clu, up, Cvw, wp and C xy ; you will then have ss, ru, tw, vy, representing the several squares in the given row, and giving, of course, the perspectives of the equal divisions of the sides of the row. In this manner the perspective of a row of PERSPECTIVE. 53 squares, or of a line inclined to the plane of the pic- ture, and divided into equal parts, may be indefi- nitely extended. This method has this further con- venience, that a row of squares of any given dimen- sions, and of consequence any given division of a line, whether at right angles or inclined to the plane of the picture, may by it, be perspectively drawn on any part of the picture* or with any perspective ele- vation, without first projecting it on the fundamental plane, as shewn at m and n. Where st-aight rows of posts, trees, or any other objects equi-distant from each other, or houses with * equal or proportional fronts, as at XX, (which shews a row of posts of the heighth KX,) are to be drawn, to be familiar with these rules will be found verv useful in practice. EXAMPLE 7.— Fig. 13. This example is intended to shew how the rules of perspective are applied to landscape-drawing, and represents a row of houses thirty feet high, having their gable ends for fronts of 20 feet each, with a row’ of posts before them, 6 feet high and 10 feet apart from each other ; also a row* of trees, 70 feet from the row T of houses, and parallel to them, 20 feet from each other, and 50 feet high. The base line is divided into equal parts, each to represent 10 feet, and from these divisions, lines are drawn to the points of distance and the point of sight, to find the places of the corners of the houses, the posts and the trees, the perspective altitudes of which are found by erecting perpendiculars on the base line, equal to their respective heights, and drawing lines from their summits to the point of sight. C 54 ELEMENTS OF and P are casual points for rafters of the houses, and are thus found: Make Ea equal to the height of the ridge of the roof ; from a draw a line to S, and the point b, where it intersects a perpendicular raised on k, will be the upper point of the gable ; and a line drawn from thence to e will shew one of the. gable rafters. Continue e b to C, where it intersects a : per- pendicular raised on S ; C will then be the casual point of sight for eb, and all lines parallel to it, that is, of all the rafters on the sides of the houses next to •the spectator: Continue CS to P, and make SP equal to it. P will then be the casual point for all the raft- ers on the opposite side of the houses. The posts are about the height of a man ; if therefore there are several men shewn at different distances, as at f, g and h, their perspective altitudes will be nearly equal to those of the posts opposite to which they respec- tively stand. — It is needless to explain the manner in which the trees are drawn, as that will be readily seen by the figure. This representation supposes all the objects to stand on a horizontal plane ; but should the ground be un- even, an object on it, at any distance, would appear of the same size as here represented, but placed high- er or lower, as the ground, on which it is placed, is higher or lower than the plane. In this example, the rows of houses, trees and posts, are supposed to be at right angle to the plane of the picture : If any of them had. been inclined to it, the lines which are here drawn to the point of sight, would have been drawn to the casual points found, as shewn in former examples. PERSPECTIVE. 55 EXAMPLE 8th— Kg. 14. This shews a method of drawing which is some- times used for planning buildings in a perspective view. The plane on which the objects stand is di- vided into squares of given dimension and these thrown into perspective, thus : divide BA into equal parts, each to represent 1, 10 or any number of feet that will best suit the intended purposes. Here each is supposed to be 10 feet. From these several divi- sions draw lines to S, and from B and A draw lines to D and D, and through the several points where these lines intersect the lines so drawn to S, draw lines parallel to BA ; you will then have the per- spective of the fundamental plane, divided into squares of the dimensions proposed. Should it be considered necessary to continue the divisions fur- ther to the right and left of the picture, continue the divisions now found, of the highest line drawn paral- lel to BA, as from a to b, and through them draw r lines from S to the extent of the picture, and do the same on the opposite side. The squares then serve as scales by which to lay off objects in every part of the picture, thus : E, F and G are cubes of ten feet, each occupying a square. K is a house of 20 feet square and 20 feet high to the roof. L is a wing to it, 10 feet square and 10 feet high ; and M is a column 5 feet square and 35 feet high. Observe, that for every perspective altitude, in every part of the picture, the divisions on the hori- zontal line at that place, is the proper scale ; thus ef is made equal to eg, 20 feet; kl is equal to km, the same number of feet ; and nt is equal to nF 35 feet. From this explanation, it is presumed this method of drawing w ill be perfectly understood. 5(3 ELEMENTS OB' DRAWING IN PERSPECTIVE MECHANICALLY. Adams, in bis Geometrical and Graphical Essays , justly observes, that “there is no artist who will be “ hardy enough to say that he can delineate by the cy€ “ the same object twice with exactness, and preserve “ a just and similar proportion of parts in each. In “ one of the figures we shall find some of the parts “ larger than in the other ; both cannot be right ; yet “ supposing them perfectly the same, neither may be “ conformable to nature. Add to this, many situa-* “ tions of an object occur, which no eye, however ha- “ bituated, can represent with accuracy.” This difficulty of making true representations of objects by drawing by the eye , has given rise to a num- ber of contrivances to effect the same purpose with greater exactness and ease. Among these, one of the simplest is to make a frame in the shape of a pa- rallellogram and divide the space inclosed by it into small squares, by stretching threads across it ; and to divide the paper, on which the drawing is to be made, with pencil lines, into similar squares, num- bering the ranges of squares on the frame and those on the paper in the same manner. The frame is then set up perpendicular, between the eye and the ob- jects, with a fixed sight at some distance before it through which the objects are observed, and what is seen through any square of the frame is drawn on the corresponding square on the paper ; this being done through all the squares will give a representa- tion on the paper, corresponding, in all its propor- tions, to the objects intended to be drawn. PERSPECTIVE. 57 In order to acquire an expertness in this manner of drawing, it will be of use for the learner to exer- cise himself in copying pictures, by dividing them into squares with pencil lines, as also the paper on which the copy is to be taken, and then, by the eye , copying whatever is seen in each square of the pic- ture on the corresponding square of his paper: As a substitute for the frame just described, and with the View of having something to answer the same purpose, as portable as cduld be made, I have constructed an instrument of the following descrip- tion, which I call a DIORASCOPE, to distinguish it from one I have called a DIORAGRAPH, that will be described afterwards, and which draws the outlines of pictures mechanically , whereas this and the frame, only guide the eye in making the drawing. Figure 15, is a representation of this instrument drawn in military perspective . THE DIORASCOPE. A,B,C,D, are pieces of mahogany, or other proper material, the dimensions of which may be measured by the scale. The limbs B and D are joined to C by binges, so as to permit them to fold down towards each other, and are kept in an upright position by the braces E,E, which move at their lower ends on pins, so that they can be folded down into the cavi- ties F,F. A is made in the form of a frame, divided by fine threads or wires into two rows of squares, each square being half an inch. The inner edges of the frame are bevelled to the middle* and perforated with holes, to receive the dividing threads. This piece is attached to B, by slipping it on two iron pins, fastened into the top of B, at 10, 11 $ entering into 8 £8 ELEMENTS OF corresponding holes in the lower part of the frafne D is perforated along its middle, with sight holes, half an inch apart from each other, countersunk on the inner side, and numbered. G is a screw packed in its place and held down at the point by a small wire staple, and at the other end, by one end of A, resting on it, when the instrument is folded up ; which is thus to be done : — Turn the braces E,E, into the cavities F,F ; take off A, and place it on C, so that the pins b , b 9 enter into the holes a, a ; next turn down B and D, which are of such lengths that their ends * will exactly meet, and the pins at 10, 11, lie in the notches at d \ D, when set up, has its middle nearly level with A . H shews the instrument folded up.— The one from which this drawing is taken measures then one inch in thickness, an inch and a half in breadth, and thirteen inches and a half in length* made of mahogany. I do not know of any thing contrived for a simi- lar purpose, so portable and simple in its construction. Gentlemen inclined to amuse themselves with land- scape drawing, will find it an agreeable and not cum- bersome companion. The method of using it is this : Set up the instrument as in the drawing ; then, with .a gimlet of suitable size, make a hole on the head of a post or stout stake, driven into the ground, or any other proper firm supporter, and passing the screw’ through the hole in the middle of C, into the hole on the supporter, screw the instrument firmly to it in a horizontal position. The paper on which the draw- ing is to be taken, must be ruled with pencil lines in- to a proper number of squares, and the ranges num- bered from left to right, and from top to bottom, in TERSPECTIYE. numerical order : then, lookingthrough the sight hole marked 1, 2, draw the objects seen through the squares of A, on the corresponding squares of the two uppermost ranges on the paper ; next, looking through the sight hole 2, 3, draw, on the third range, the objects seen through the corresponding squares on the lower range of A, connecting them with what was before drawn on the second range ; and so on, shifting the eye successively to all the sight holes, till the outlines of the picture are completed, when it is to be finished in the usual way. It is here proper to observe, that the shifting of the eye from one sight hole to another will have an effect on the drawing that will make it somewhat different from a perspective perfectly accurate. This difference, however, will only affect drawings of very near objects, but in drawings of those that are at any considerable distance, it will be altogether imper- ceptible, and can be no objection to the general utili- ty of the instrument. Asa cheap, convenient and ready assistant to a person whose taste may lead him to the use of such instruments, this has its merits, which those who try it w ill duly appreciate ; but I have never seen a de- scription of any which can so completely serve the purpose of drawing in perspective mechanically as the one of which I shall now give the description. THE DIOR AGR APH.— ( Fig. 1 6. J ! A is a drawing board dropped into the surroundr ing frame, which is here represented in the form of a box, to receive the other parts of the instrument when not in use ; l, c, c y is made in the form of the letter T, and is so called ; d , d , are two pieces screwr 60 ELEMENTS OF ed on to the back of the frame, so that their ends join in the middle, and their upper edges form one straight line ; these are then called the rail. To the bottom of the T, near its ends, where the letters c , c, b , are placed, wheels are fixed to facilitate a la- teral motion : The wheels at c, c , run in a groove on the rail, apd the wheel at b on the front edge of the frame, e is a piece called the port-pencil, with two wheels to its bottom, moving in the grooves r, r. — From the port-pencil a piece is extended to /*, called the rod, in the under part of w 7 hich is a groove, to receive the edge of a w heel fixed on the T, where the leg joins the crossing part ; and immediately above are two pullies, one diameter apart from each other, sinking a little into a groove on the upper edge of the rod. To the right side of the port-pencil is fixed a flat piece of brass, w T ith the two ends bent ho- rizontally, having holes in them exactly over each other, through w hich the tube, or case that holds the pencil, is to slide, w ith little or no friction. On the top of the pencil is placed a socket, S, from w hich rises a pin ; circular pieces of metal, to serve as weights to give a due pressure to the pencil on the paper, with holes in the centres are slipped on the pin and taken off, according to the degree of pressure required. At e there is a button with a w ire pin de- scending from it, bearing on a small concealed lever, which, when pressed down, raises the pencil from the paper. This button is pressed by a finger whenever the pencil is to be moved, w ithout marking the paper. g, called the gallo w r s, is made in the form as repre- sented in the draw ing, and fastened by pressing it in- to a socket on the T. Its height should be at least PERSPECTIVE. 61 equal to the breadth of the drawing board. At h a pulley is suspended from it directly over the space between the two pullies on the T. i is a piece to slide into and out of the frame, and fastened in the inside by a wedge, k is an upright cylindrical piece, pressed into a hole near the end of i. I is a horizon- tal piece made to slide up and down on A;, and fasten- ed to it at any height, by the screw m. n is a flat piece of brass with the sight-hole in it, and will be the better if a ring be fastened to each side of it to ex- clude the light. At o is a weak wire spring rising from a cavity in the rod ; to this spring is fastened a fine smooth thread which is carried thence, through ' the groove on the rod, to, and under the first pulley on the T, thence up, to and over the pulley on the gallows ; thence down, under and beyond the second pulley on the T, to the end of the rod, where it is fastened, bearing a little on the spring at o. p is a mark on the thread, which may be either a small Conical bead, or the knot of a differently coloured thread. In the inside of the box there are apartments for the various utensils of drawing, besides the pails of the instrument to be packed up in it. There is also a lid or top-piece to be laid on it and secured by a lock. From the construction of this instrument it is evi- dent that as the pencil, with the port-pencil and rod, is moved forward, the mark on the thread will move upwards and vice versa j and as the pencil with the T moves to the right or left, so will the mark. All these movements being on wheels and pullies the friction will be very little and cause no perceptible 62 ELEMENTS OF impediment to the movements of the pencil in all di- rections. The DIORAGRAPH is thus used : Fix it in a horizontal position, with a proper bear- ing on the objects to be drawn ; which may be done by laying it on a table and fastening it with clamps, or by any other means, to prevent it from shifting. Have the drawing board prepared with paper in the usual manner ; drop it into its place, which should be so adjusted that the upper surface of the drawing board be a little lower than the upper surface of the frame ; then put on the T with its appenda- ges, so that the wheels, on the cross part of it* be in the groove on the rail ; adjust the sight and mark on the thread; prepare a pencil, with the point so sharpened, that it be as nearly as may be in the direction of its axis ; slide it into the pencil case (which it should tightly fit) until the point project a little out of it ; drop the pencil case, with the point of the pencil downwards, into its place on the port pencil : then, looking through the sight hole, move the port pencil so that the mark on the thread appears to move along the lines of the ob- jects to be drawn, and the pencil will then mark on the drawing board a true perspective representation of them. The T, with its appendages, is then removed, the drawing board taken out, the irregularities of the pencil lines corrected, and the drawing finished in the usual manner. Thus may true perspective draw- ings of any objects be made, w ith nearly as much fa- cility as copies of pictures are taken, by laying pa- per on them and tracing on it the lines of the ori- ginal, seen through it wdien held up to the light. PERSPECTIVE. 63 ' At first some awkwardness will be experienced in moving the pencil, so that the mark shall follow the lines to be drawn ; but, after a little practice, it will be as easy as to follow the lines of a picture laid on a table before you, and can be done with equal ex- pedition. Although I would by no means recommend it as a proper practice, to attempt drawing, without first obtaining a complete knowledge of the elements of perspective, still as there may be many, and espe- cially among the young ladies to whom every polite accomplishment is intended to be given, who may not find it convenient to pass this ordeal, I know of % no better assistant for them than this instrument. They will find, in the use of it, the most ready means of obtaining the outlines, in perspective, per- fectly accurate, not only of landscape views, but also of many other things, in the drawing of which they will find much amusement ; and receive much grati- fication from seeing and exhibiting what they have performed by means of it, as resemblances more per feet than w T hat are generally produced. The furni- ture of rooms, such as chairs, tables, sophas, side- boards, and also articles of dress, such as hats, caps, and any thing else that can be placed stationary be- fore the instrument, may have their outlines drawn by it in the most correct perspective, and with the greatest facilitv i f r«*: "> ; 'i S.U1 t E; v, *. > ! , ; v .. ' > * i-*‘ > / \ i r* ■ . i , / „ »•' • : : ■ i T 'V ' • */’ * . . ’i ■ . iviv> • -. 11 . , 'J: ■ i.J.1 U .! . '■ ri ■ . -■*: : t *i- ? r, • « .. 1 : i • • - * i : > . . ■ T ' • ■" <• f I- ;•!?' * . • -- ■ FT Military Perspective. This is a peculiar kind of perspective which d& serves attention, though seldom noticed in treatises of this nature. It does not indeed represent things exactly as they appear to the eye, but is better cal- culated than any other method of drawing, to give true ideas of the positions and proportions of objects. It is a species of Orthographic, called Military Per- spective ; because it has been most advantageously employed to represent Fortifications, with their va- rious structures, and especially fortified towns. For- merly it Was more common than it is now, and the reason why it is so much neglected at present, I be- lieve to be, that it is considered as having been used only by those who were ignorant of the general rules of perspective. The fact* however, is othei^ wise. It was chosen as the best kind, founded on scientific principles, for the purposes to which it was applied. The principles of Military Perspective, are these, which, together w itb the practical rules deducible from them, will be perfectly understood from a bare statement. The fundamental plane is horizontal ; the plane of the picture perpendicular, and the eye is supposed to be in front of it, elevated to an angle of 45 degrees, 9 66 ELEMENTS OP and at an infinite distance from it ; whence it follows, that all lines drawn from objects to the eye, will be parallel to each other* and make vertical angles of 45 degrees with the plane of the picture, as well as with the fundamental plane; and hence it further follows, that all figures parallel to the fundamental plane, or to the plane of the picture, will be repre- sented by equal and similar figures, and all horizon- tal and perpendicular lines will be represented by lines bearing the same proportions to each other, and may, therefore, in the drawing, be measured by a scale. A single example will be sufficient to teach this method of drawing. Let it be required to represent a house 40 by 28 feet, the elevation of the front 20 feet, and the ridge of the roof 35 feet high, with a court-yard 128 by 90 feet, inclosed by a fence of posts 10 feet high* and 7 feet apart from each other. Figure 17. Draw the ground plot of the house and yard by a scale of equal parts. Let a b c d be the plot of the house, from the corners of which raise the perpendiculars ae, bf, eg, dh, each 20 feet high ; from the middle of ab and cd raise perpendiculars to i and k 35 feet, and draw the connecting lines as in the figure : The house will then be represented in mili- tary perspective ; to which, by the same rules, may be added doors, windows, chimnies, &c. Next di- vide the sides of the plot of the court-yard into parts of 7 feet, and on the several divisions raise perpen- diculars of 10 feet for the posts. Add rails, gates, &c. and give a proper shading to the whole. PERSPECTIVE. 67 To represent circles : first draw the perspectives of the circumscribing squares by the preceding di- rections, and then draw in them, by the eye, the re- presentations of the circles, touching the sides of the squares at their middle divisions, and intersecting the diagonals at seven-tenths of the distance from the cen- ter to their ends, as exemplified at A ; which shows a pair of vertical wheels, standing parallel to the fence of the court-yard ; or more distinctly at C, where tuvw is the perspective of the square circum- scribing the circle. If C be the end of the Cylinder, /^c as Xy, will be at right angles to u y and t w. The perspectives of horizontal circles and circles parallel to the plane of the picture, will be circles, as shewn by the ends of the upright cylinder B, and horizontal cylinder D ? If a drawing of this kind be placed against a wall, and viewed at some distance from above, under an angle of 45 degrees, it will exhibit nearly a true apr pearance of the objects represented ; or if the draw- ing be laid on a table, at some distance before you, and viewed in that manner under an angle of 45 de- grees, the appearance will be the same ; because, if in making the drawing, the plane of the picture had been supposed horizontal instead of perpendicular^ there would be no difference in the result. If you look, in either case, through a small aperture, con- fining the view exclusively to the drawing, the ap- pearance will strike as a still more perfect resem- blance of the objects. This method of drawing will be found particular- ly useful for shewing the shapes, as well as situations. 68 ELEMENTS OF of buildings, on maps Of farms, or of gentlemen’s country seats, and also public edifices of diversified parts so situated that they cannot be seen from the points of view usually taken in ordinary perspective. I think it will also be found the most eligible for drawings to accompany the descriptions of machines, and ought therefore to be preferred in applications for patents, or communications for public informa- tion; an example of which may be seen in the de- scription of the Diorascope, figure 15. The circumstances which, in the estimation of some, may lessen the merits of this species of perspec- tive, will, in the opinion of others, and I think justly, enhance it : They are its simplicity, the facility with which a perfect knowledge of it may be acquired, and the little trouble that attends the practice of it. Nor can its inelegance be alleged against it. I have met with some beautiful specimens of it. There is now before me a superb work, in the Dutch lan- guage, printed in 1760, giving a description of Am- sterdam ; illustrated by a great variety of the finest copperplate prints, and among them, several in mili- tary perspective ; one of which represents the cele- brated BEURS or Exchange of that city, and gives an idea of it more perfect than could possibly be giv- en by drawings of any other kind. It must, however, be confessed, that in too many in- stances there are evidences of a want of acquaintance with the rules of this species of drawing. There are two other species of orthographic per- spective which it may not be improper to mention. One supposes the eye at an infinite distance, looking horizontally at objects, through the plane of the pic- PERSPECTIVE. 69 lure, placed perpendicular to the horizon. This is that by which architects draw the elevations of build- ings, and may therefore be called ARCHITEC- TURAL PERSPECTIVE. The other supposes the plane of the picture paral- lel to the horizon, and the eye at an infinite distance perpendicularly above it : Thisis generally called the BIRDS-EYE-VIEW, and is that by which charts or maps commonly shew the shape of the surface of the earth : Although not warranted by precedent, I shall venture to call this GEOGRAPHIC PER- SPECTIVE. The objects drawn in the examples given for illus» trating the rules of perspective, have been chosen as the simplest that could be devised, composed of lines placed in every position, horizontal, inclining, de- clining, perpendicular and parallel to the plane of the picture . They furnish therefore sufficient sam- ples for the drawing of objects of every possible shape. More w ould have needlessly swelled the size of the book. • i ■ • ■ • ► * . i • • ■ / j i. . •' .'lir; ’ ■' '» .. ; r ; . • 7 i i ‘iii.i . i-M ■ ; • • ■ 'j r '>'y ro . • r ;■ • : . . - - ■ * -• T - J '•< , f - ■ > ■ > ■ . ; DIORAGRAPHS MAT BE HAD OF Mr. Abraham Handel, C abinet- Maker, Albany, WHO HAS THE RIGHT OF MAKING AND TENDING THEM. j/anx OTtititfar azA or. */;s ; . aoir: a; . * ow PI. I. p ri s .2. £ ] L L A H Kl G B | M K r n 1 * 1 . 2 . PI. A Fig: ft . PI. 7. Kg. 13. PI. 10. Drawn in Military Perspective J Mil i tahy PeHSEEC TIVE PI. 1 2.