PAPYRO-PLASTICS.W. Wilsou, Printor, 57, Skinner-Street, London.PAPYRO-PLASTICS,

OR THE

ART OF MODELLING IN PAPER;

BEING AN

Instructive Amusement

FOR

YOUNG PERSONS OF BOTH SEXES.

FROM THE GERMAN,

BY

D. BOILEAU.

SECOND EDITION,

GREATLY ENLARGED AND IMPROVED.

WITH TWENTY-TWO PLATES.

LONDON:

PRINTED FOR BOOSEY AM) SONS,

broad-street, exchange.

1825.PREFACE

On submitting- to an enlig-htened Public
a new, eleg-ant, and instructive amusement
for Children, we have first to account for its
name. We are aware that the term Plastics
is generally confined to the modelling- of
sculptors and statuaries in gypsum, clay,
wax, &c. But as the art of making cork
models of architectural monuments on a
small scale, has obtained on the Continent
the appellation of Phelloplastics, from the
Greek word	cork; we think ourselves

warranted by this analogy in denominating
the art of modelling in paper Papyro-
p/astics. \_____________This ingenious art is calculated to intro-
duce children to the most common and prac-
tical applications of geometry, in a way
which occupies their hands, and thus en-
forces their attention, without any particular
effort of their thinking powers. By a law
of our nature, our curiosity, in our earlier
years, is preferably directed to palpable ob-
jects. Abstraction is an exertion of the
mind, which is irksome even to a great many
grown up persons ; and children can hardly
be induced to exercise it, because they can-
not form an idea of the advantages resulting
from that faculty. This love of reality is
likewise the characteristic of the infancy of
nations. The Greeks had clever statuaries
long before they had able paintt rs. The
sculptor represents the object as it is, with allits angles and rotundities ; his works are
real representations, they may be touched
and handled, whilst those of the painter are
mere illusions, which vanish, as it were, at
the touch. Complete figures, by which both
the senses of seeing- and feeling- are gratified,
satisfy the infant mind better than bare out-
lines; and the study of mathematics is likely
to be prosecuted with more ardour after
young- persons have previously amused them-
selves with converting quadrangles and pa-
rellelograms into tables, chairs, houses,
churches, bridges, and ships.

But, independently of the mathematical
studies for which it prepares the youthful
mind, Papyroplastics, or the art of model-
ling in paper, has the additional advantage of
teaching manual dexterity and the knowledgeof proportions, of imparting a taste for the
arts of design, and, above all, of affording
a salutary antidote to that listless indolence,
that pernicious love of cards, or that rage of
indiscriminately reading any book at random,
which are unfortunately tolerated in many
respectable families during the long winter
evenings, and which are alike unfavourable
to the comfort and to the best interests of
young persons, as they greatly tend to ob-
struct them 011 their road to duty and hap-
piness.PREFACE

TO

THE SECOND EDITION.

The approbation which this little Essay
on Papyro-Plastics has met with, has been
so general, that the first edition was sold in
a few months. To render the work still more
deserving of the patronage of an enlightened
public, and to insure its constant success,
great pains have been taken to enlarge, im-
prove, and correct it. Many of the flat
paper figures having been found rather in-
correct upon trial, they have all been re-drawn after models furnished by an intelli-
gent correspondent, to whom we readily
pay the tribute of our best thanks. The
Ancient Tower, which faces the title-
page, has been coloured, to give young artists
some idea how to proceed in colouring; and
the Plates have been increased in number,
to furnish students with additional objects
for modelling, all from the. same ingenious
Correspondent, who has corrected the paper
figures of the original models.TABLE OF CONTENTS.

CHAPTER 1.

Page

Preliminary Requisites and Directions ............ I

, CHAPTER II.

Introductory Exercises in drawing with Compasses

and a Ruler.................................. 6

CHAPTER III.

Modelling with Cut Paper Figures

Preliminary Observations.........................   38

A Die or Cube  ................................   40

A Chair....................................................................................... 42

A Table........................................   46

A Chest of	Drawers............................... 49xii	CONTENTS.

Page

A Sentry-box ..........................................  51

A Thatched-house......................................   54

A Pigeon-house.......................................... 50

An Inkstand *........................................   0()

A German Stove ......................................... 02

A Watch-stand........................................... 05

A Pair of Steps......................................... 67

A Small House with Gable Poof........................... 70

A Cottage............................................... 74

A Barn and Stable ...................................... 75

A Paling, or a Palisade................................. 76

A Small House with a Sloping Itoof ..................... 76

A Monument............................................   79

A Town House ........................................... 80

A House with a Gable Elevation in front................. 80

A Court or Garden Gate ................................. 82

A Bridge .............................................   82

An ancient Tower........................................ 84

A Boat.................................................. 88

A Sledge  .............................................. 90

A Ship.................................................. 92

A Church................................................ 94cohtims.	xiii

Page

A Round Hut ......................................    96

A Windmill ........................................   97

An Arm Chair........................................ 98

A Small Basket ..................................... 98

A Chiffonni&re ....................................   99

A Sofa............................................. 190

A Wheel Barrow .................................... 101

APPENDIX.—The five regular Geometrical

Figures .......................................   102

ABBREVIATIONS.

Fig. for Figure. Prop, for Proposition.DIRECTIONS FOR MODELLING

WITH

CUT PAPER FIGURES.DIRECTIONS FOR MODELLING

WITH

CUT PAPER FIGURES.

CHAPTER I.

PRELIMINARY REQUISITES AND DIRECTIONS.

To make neat representations in paper of any
given object on a small scale, is an occupation
as agreeable as useful. It consists chiefly in
drawing, cutting, folding, joining and painting.

1.	The drawing regulates the cutting and fold-
ing. It is most easily performed by means of a
pair of compasses, a common ruler, and a ruler

either of brass or wood, Fig. 10, Plate I. in the

\

See also the Second Chapter on the introductory Exercises in
Drawing.shape of a triangle, a representation of which
is given.

2. The culling is performed either with scissars
or with a penknife. When the latter is used,
the paper should be laid on a small board of soft
wood or pasteboard ; and whether the paper be
cut with scissars or with a penknife, margins
must be left on the cut paper figures for the pur-
pose of glueing them together.

3. In folding, particular attention is to be paid
to its being done in a straight line.

4. The joining may be effected with glue, gum
arabic, paste, or wafers, the latter being easily
converted into a kind of paste when properly
wetted. Care however must be had to glue only
the edges or margins left for that purpose in each
cut paper figure; and in some cases recourse
must be had to cording or fastening with small
slips of tin, until the parts glued be properly
joined and perfectly dry.

5. Of the articles used for joining,, the gluemust be in such a state of thickness as to be like
the white of an egg, or pretty thick oil, when suf-
fered to drop from the vessel in which it is made:
the gum arabic is to be dissolved in water so as
to have the same consistency with glue; paste is
best when made of starch or fine wheat flour ; it
is much cleaner than glue, but any brush or stick
left in it, will cause it to ferment and render it
too watery.

6. The painting is performed in the usual way
with different colours or mixtures of colours, and
with brushes proportioned to the size of the cut
paper figures to which the painting is to be ap-
plied.

But every thing depends on the goodness of
the paper, which should be strong, stiff, and very
smooth. Laid royal, or drawing paper, Bristol
board of moderate thickness, is the best. A thin-
ner sort of paper may be employed, whenever it
is to be used double; and in this case, both sheets
of paper are to be done over on one side with
b 2glue or paste, but one of them so sparingly as
only to become moist; they then should quickly
be laid one upon the other, covered with a dry
sheet of paper, smoothed in an uniform direction
on a hard, even surface, and pressed between two
boards or in an old book until they are perfectly
dry.

Lastly, objects ought not to be represented on
too large or on too small a scale, [n the former
case, or when the objects are complicated and
composed of too many parts, the surface of the
paper seldom proves sufficiently stretched and
even, and both the beauty and durability of the
model are impaired. And when the scale is too
small, it frequently occasions a waste of time and
labour, and too diminutive models rarely succeed
after all.

Neither should such objects be attempted
which cannot well be represented in paper. A
certain facility in modelling easy objects must
have been previously acquired, before one mayventure upon more difficult ones. The models
mentioned in the following Directions should not
be altered, nor should new ones be undertaken,
but after they have been repeatedly and success-
fully executed. The transition from what is easy
to what is more difficult, is as indispensable in
this, as in any other art or science.INTRODUCTORY EXERCISES IN DRAWING WITH
COMPASSES AND A RULER.

The first and second plate refer to these exercises. The points,
lineri, and surfaces, are designated by letters.

I.	To draw a right or straight line.

Have a very sharp pointed black lead pencil,
and keep uniformly close to the ruler in drawing
the line, taking care to have it very fine and al-
most imperceptible, for a line is that which has
length without breadth.

II.	To lake the length of a line with the
compasses.

The compasses must be opened so wide that
the ends of the two legs may exactly touch the
two extremities, or the beginning and termina-ting points of a line. The place where a line
commences or ends, or where two lines pass
through, or intersect each other, is a point.

III. To take the length of a long line in order to
make another exactly similar, as for instance of
a line longer than a common size sheet of 'paper.

Divide the given line, by dots, into several
parts, at pleasure ; then set off each part succes-
sively with the compasses.

IV. To mark the exact division of a given line on

another line.

Whenever the given line is not very long

r	*....*	" f

as for instance, the line b, ~ ; 7 g,

this is most accurately done by measuring not the
intermediate successive lengths, but. by taking
the spaces, be, bd> bf} or gf, gd, gc, beginning al-
ways with b or g.

But when the line is of considerable length, a8

common ruler or a straight slip of paper may be
held against it, and the divisions may be marked
on the same.

Proposition III. may also be done in a similar
manner.

V.	To give the distance of a point from an opposite
line, as, for instance, the distance of the point h
from the line cd. (See plate I. fig. 1.)

One end of a pair of compasses, that have been
previously opened nearly as wide as is the dis-
tance of the point b from the line c d, is placed
on this point b, and the other end is made to
describe an arc which touches the line, but does
not intersect it. In this case the distance is
given by the width between the two ends of the
compasses.VI.	To divide a given line into two equal parts
with the compasses, as, for instance, the line f g,
or Im (fig. 2, or 3, plate I.)

Set one point of the compasses in k as near
the middle of the line as possible, then open
the compasses to g, and keeping one point fixed
in k, turn the other towards f. Then if there
be any part of the line left, as fh (fig. 2), one
point of the compasses is kept steady on k, and
the other is carried by guess to the middle of
f h. Should there now be too much, as the dis-
tance I p, (fig. 3), one point of the compasses is
kept steady on n, and the other is carried to about
the middle of / p nearer the other point of the
compasses.

If on examination the line is not yet divided
into two equal parts, the same process must be
repeated until the two parts are of equal length.
Or it may be done thus:To diride the line fg into two equal parts.

1. From the points f and g, as centres, with any opening of the
compasses greater than half fg, describe arcs cutting each other*
in a and b.

2. Draw the line ab, and the point e, where it cuts fg, will be
the middle of the line required*

VII. To divide a line into more than tzco equal
parts, as, for instance, the line q r (fig. 4, pi. I.)
or the line v w (fig. 5, pi. I.) into three.

Take, by guess, as near a third part of the line as
possible, then after having set off three equal parts
on the line r q\ should there be a remainder, as
q s (Fig. 4), one point of the compasses must be
kept steady on t, and one-third of q s must be
taken by the other. But if, by turning over the
compasses three times, the point should fallbeyond the line,*as v z (fig. 5), one point of the
compasses must be kept steady on or, and the
other must be brought one-third of z v, nearer
to v.

The same is to he observed when the line is
to be divided into 4, 5, or more equal parts, with
this difference, that whatever remains inay always
be subdivided; as, for instance, when the ques-
tion is of six parts, into six. And whenever such
parts are many, they may first be divided into a
smaller number of parts, and then each part
again separately; as, for instance, when the
question is of six parts, twice 3 or three times 2
is equal to six, therefore the given line may be
first divided into two parts, and every part again
into three; or first into three parts, and every
part again into two.

Or may be done thus:

To divide a given line as the following A B, into any proposed
number of equal parts, as, for instance, the line A B into five.n

1. With one point of the compasses in A, and the other in B,
describe the arc B«, also with the same opening of the com-
passes, and one point in B, describe the arc An; or with a
parallelnder, draw Be parallel to Ac.

2. From one end A, of the line, draw Ac, to any point, as c, in
the arc Bm, then take the arc Be in the compasses, and set off an
equal arc on An, i. e. Ae, then draw the line Be.

3- In each of the lines Ac, Be, commencing at A and B; set
off as many equal parts of any convenient length, as A B is to be
divided into.

4. Join the points A, 5; 1,4; 2, 3; 3, 2; 4, 1; 5, B; and
A B will then be divided into five equal parts as was required.

VIII.	To place the length of a given line exactly
in the middle of another line, as, for instance, the
line h c (fig. 6, pi. I.) on the line d f.

Setoff the shorter line and the longer one from d
to g, and divide the remainder gf into two equalparts. Each of these parts is the distance at
which the extremities of the shorter line are to
be from the extremitiesof the longer, if the shorter
line is to be precisely on the middle of the long
one. When therefore the distance is taken from
the beginning, as d a, and terminating point, as
f e, towards the centre of the longer line, the
middle space between (viz. a e) is the length of
the shorter line.

Supposing the line to be placed in the middle
be the width of a door, and the longer one be the
length of a small building, the door by this pro-
cess would be placed exactly in the middle of the
building.

IX.	To set off a line more than once upon another
longer one, so that the intervals be equal; as,
for instance, the line h k (fig- 7> pi. I.) three

times on the line I m.	.

The length of the shorter line must be set off
upon the longer, either from the beginning orterminating point, as often as required; here, of
course, three times. The remainder n m must
then be divided into as many equal parts as the
number of times the line is to be set off upon the
other, less one; here therefore into two parts.
After which, first take the shorter line and then
one of the two equal parts, as intermediate spaces,
beginning precisely at one of the extremities of
the longer line.

And the same manner of proceeding takes
place when the line is to be set off four, five, six,
&c. times.

X.	To set off a line several limes upon a longer one
and so that there be not only equal intervals
but that the line may be at an equal distance from
both extremities of the greater line; as, for in-
stance, the line p q (fig. 8. pi. 1.) three times on
the line r s.

The shorter line p q, as in the preceding case,
is to be placed on the longer one r s three timesfrom r to s: the remainder t s is then divided into
as many equal parts as the shorter line is to be
placed on the longer, and one more: consequently
here into four parts. Each of these four parts is
the required distance, and at the same time the
intermediate space.

It is in this way that the proper place is assign-
ed to doors or windows in a building.

XI.	To make two lines meet exactly like two
others, as for instances, omitting the dotted arc
(fig. 9. pi. 1-) the lines z c and z h} like the lines
vx and v w.

Draw the line z c, if it be not already drawn,
and with the same opening of the compasses des-
cribe from the points where they are to meet, as
herefrom v and s, two small arcs; set off the
length of the arc between the aforesaid lines,
viz. x w, from c to b, and draw a line from z
to 6, and it will meet the line z c, as required.Such a meeting of two lines in one point is
called an angle. Whenever a line meets an-
other without having any inclination, it is a right
angle, and the line itself in this case is said to be
standing right angularly, or perpendicularly, or
straight upon the other.

When the lines are more inclined to one an-
other than the quantity of a right angle, it is
called an acute angle; but when they are less
inclined to one another than a right angle, it is
an obtuse angle. Whenever a line is not per-
pendicular upon another, it is inclined.

To describe an arc from a given point, place
one end of the compasses on that point, and de-
scribe the arc with the other end.

XII.	To draw a perpendicular line upon another,
as, for instance, the line g f upon the line d f
(fig. 10. pi. 1).

This is best done with a triangular ruler. Put
the common ruler against the line on which theother line is to be placed, as here the line <//;
and bring upon this ruler one of the short sides
of the triangular ruler, then holding both rulers
firm one against the other, draw the required
line along the other side of the triangular ruler.

And to try this ruler, draw in the aforesaid
manner a line at right angles to another, and
holding the common ruler firmly, turn the trian-
gular ruler upon the right angular line just
drawn, and move it on the common ruler exactly
against this line. If the edge of the ruler and
the line meet again accurately, the triangular
ruler is correct.

XIII, To draw from a given point a line at right
angles to another line, without the triangular
ruler, as, for instance, from the point h (fig. 11.
pi. 1), a line perpendicular to k I.

Describe from the points of intersection k and
/, and draw two other arcs intersecting eachother at m. Then placing the ruler against the
points h and m, draw a line from the point h to
the line k I, and it will be at right angles to k I.

When small arcs like those (fig. 11) are
described, both above and under a line from the
two extreme points or of the same; and when
the said line is intersected by placing the ruler
on the two points where the arcs meet, that line
will be divided exactly into two equal parts.

XIV.	To draw, but without the triangular ruler,
another line at right angles, on a given point of a
line, as, for instance, the line r n on the point n
of the line p q (fig. 12. pi. 1).

Place one end of the compasses on the given
point n, and describe with the other small arc#
intersecting the line, as here at p and q. De-
scribe again small arcs from these points p and
q, intersecting each other above the line, as hereat r, and then draw the required line by holding
the common ruler against the points r and n.

XV. To draw, without the triangular ruler, an-
other line at right angles at the end of a given
line, as, for instance, the line h upon the line f
(fig. 20, plate 2).

The point f may be taken at pleasure; but de-
scribe, with the same opening of the compasses,
from this point/and the terminating point of the
line, two arcs intersecting each other as here at g.
Afterwards draw a line through the points/ and
g, then make g h equal to g/, and draw a line
from the point h to the aforesaid terminating
point.

XVI. To divide an angle into several equal parts,
as, for instance, the angle t s v (fig. 13. plate 1.)
into four equal parts.

Describe with the compasses, from the angularpoint s, an arc meeting both the lines that in-
close the angle or its sides, as here at t, and v.
Afterwards divide the arc between the two lines
of that angle into as many equal parts as the an-
gle is to be divided into, in this case of course
into four; and then draw lines through these
points of subdivision to the angular point s.

The larger or smaller the arc t v is, in case
of similar distances, asst?, which however may
be more or less considerable, the larger or smaller
is the angle itself. The length of the lines has
no effect on the magnitude of the angle, which
varies only aocording to the inclination of the
lines towards each other.

XVII.	To draw a line to be every where equidis-
tant from another, or parallel to another line; as,
for instance, the line w x (fig. 14, pi. 2,) pa-
rallel to the line z b.

From any two points, at pleasure, as ac, in the
line z b, with an opening of the compasses equalto the required distance, describe the arcs n m,
and placing the ruler upon the upper extremities
of these arcs, draw a line (without cutting
them) to touch the two arcs.

Equidistant or parallel lines may be seen, for
instance, in the side walls of houses, in doors,
windows, and other objects:

XVIII.	Another say of drawing one line parallel
to another; as, fur instance, the line c d to the
li"efg (fig- P^te 2).

Draw on the given line,/g, if possible at a good
distance, two lines at right angles and of the same
length, and through the extremities of those per-
pendiculars draw another straight line. This
will be parallel to the given line.

When several lines arc required to stand per-
pendicular upon another, and consequently pa-
rallel to one another, the shortest wray is to put
the triangular ruler against the common ruler,
and to keep it firm against it.XIX.	To draw through a given point opposite to a
given line another line parallel to this line, as, for
instance, the line h k parallel to the line lm through
the point h (fig. 16. pi. 2).

Seek, by means of prop. V., the distance of the
point h from the line I m ; place one end of the
compasses on this line / m very far from h, and
describe a small arc opposite to this point.
Afterwards put the common ruler against this
arc and the aforesaid point h, and draw the in-
tended line.

XX.	To take the distance of two parallel lines.

Proceed, either according to prop. V., selecting
at pleasure a point on one of the two lines, and
describe from this point an arc which closely
touches the other line. The opening of the com-
passes is, in that case, the required distance.

Or, put the ruler against one of the two lines,
and draw (which is most readily done with thetriangular ruler) a line at right angles upon it,
so as to intersect the other of the two given lines.
The length of this right angular line drawn be-
tween the two parallel lines is, in this case, the
required distance.

This process determines the length or breadth
of objects inclosed within parallel lines, as, fur
instance, of doors, windows, and such like. With
regard to diminutive objects, only the aforesaid
arc or the right angular line is to be attended to.

XXI.	To make three given lines meet at their ex-
tremities, or to form a figure with them ; as, for
instance, the lines n,p, q (fig. 17, plate 2).

Draw r s, a line as long as one of the three
given lines, for ex. n: then from both extremities
of the line r s describe, with the separate lengths
of the other two, arcs intersecting each other, as
at m; and draw two lines from the extremities r
and s, to the point of intersection. The figuremay also be begun with either of the other given
lines, instead of the line n.

A figure is a space completely bounded by
lines; an angle therefore, as for instance that at
fig. 11, is not a figure. But any figure inclosed
within three lines is called a triangle.

XXII. To describean equilateral Triangle, viz. one
whose sides are all equal, as, for instance, that
(fig. 18. plate 2-) with the given line tv.

Draw the line wx, as long as t v; and with an
opening of the compasses equal to/cormx, draw
small arcs intersecting each other in m, (see plate

2.	fig. 18). and from the point m where they inter-
sect each other, draw lines to the points w and x.

XXIII. To describe an Isosceles Triangle, viz. one
of which two sides only are equal; as, for instance,
the Triangle (fig. 19, plate 2,) with the given
lines p and q.

Draw the line s equal to the line q\ with thelength of the line p describe from both extremi-
ties of the line z two small arcs intersecting each
other in rrc, and draw lines from their common
intersection to the extremities of the line z.

XXIV. To describe a Scalene Triangle, viz. one of
which all the three sides are unequal; as, for in-
stance, the Triangle (fig. 17, plate 2,) with the
given lines, n p q.

The process is the same as in prop. XXI.

XXV. To describe a Right-angled Triangle, viz.

one which has one right angle.

By prop. XII. draw two lines to meet at right
angles; and when there are two given lines, make
them of equal length with the other two, front
the point where the former meet. Afterward*
draw the inclined line.XXVI. To describe arty proposed Triangle accu-

rately.

Consider the sides of the proposed Triangle as
given lines, and proceed,

When the triangle is equilateral, according
to prop. XXII.

When it is an Isosceles, according to prop.

XXIII.

When it is a Scalene, according to prop. XXIV.

And when it is a right-angled Triangle, ac-
cording to prop. XXV.

XXVII. To make four Lines meet at their Extre-
mities, as, for instance, those in fig. 23, pi. 2.

Let the four given lines be two of them each
equal to f\ and two each equal to g. Make two
of them meet in a point, making any angle at
pleasure, viz. make an angle and its two sides
equal to the two given lines, as here the line b
equal to the line g, and the line c equal to theline/. Afterwards with the length of the other
two lines describe, from the terminating points
of the lines b and c which do not meet, two arcs,
as here at d, and then draw two lines from the
point where the two arcs intersect each other to
meet the extremities of the lines b and c.

All quadrangular figures vary according as the
lines are varied, and according as the angles are
greater or less.

XXVIII.	To draw a Quadrilateral, viz. a Square
whose sides are all equal and ils angles all right ;
as, for instance, fig. 20, plate 2.

Let w, fig. 17, be the given line. Draw the line
f equal to the line n; and proceed as in prop.

XV.	or using the triangular ruler, draw a line at
right angles, and make this also equal in length
to the line n, from the point where it meets the
line/. Afterwards with the line/or n describe,
from the terminating points of the lines f and h,where they do not meet, two arcs intersecting
each other in tn; and then draw the other two
remaining lines.

XXIX. To draw a Rhombus, viz. a f gare whose
sides are all equal, but its angles not right; as^
for instance, fig. 21, plate 2.

Let the line k be the given line. Make two
lines meet at a given or any angle, and proceed
as with the preceding proposition.

XXX. To draw a Rectangle or Oblong, viz. a
Quadrilateral figure whose opposite sides are
equal, and angles right angles; as, for instance,
fig. 22, plate 2.

Let / and g be the given lines. Draw two
lines to meet at right angles, make them of equal
length with the two given ones from the point
where they meet, and proceed as in prop. XXVII.XXXI.	To draw a Rhomboid, viz. a Parallelogram
whose opposite sides are equal and the angles not
right; as, for instance, fig. 23, plate 2.

Let f and g, again, be the given lines; and ex-
cepting the right angle, instead of which another
angle must be formed, the process is the same as
with the rectangle in prop. XXX. or prop.

XXVII.

A quadrangle, a rhombus, a rectangle, and a
rhomboid, have also the common denomination
of Parallelograms; and the line which joins the
two opposite angles of a four-sided figure is called
a Diagonal.

XXXII.	To draw a Trapezium, viz. a Quadri-
lateral figure of unequal sides, two of which how-
ever are parallel; as, for instance, fig. 24,
plate 2.

Let/and g (fig. 22.) be the given lines. Place
the shorter line exactly on the middle of thelonger one, according to prop. VIII. Afterwards
draw on that point, as at h and k, lines at right
angles; make each from the greater line equal
to the distance at which the short line is to be,
and join the two points with a line. Then draw
the two inclined lines.

. Whenever ^the sides are all unequal, in any
four-sided figure, such a figure is usually called
a Trapezoid.

XXXIII.	To draw an irregular Polygon, viz. a
Figure of more than four unequal sides ; asKfor
instance, the irregular Pentagon, fig. 25,
plate 2.

Draw the lines and angles in proper succes-
sion : viz. first draw a line of any given length,
form at its extremity one of the given angles,
make its yet undetermined side equal to that of
another of the given lines, and form again at its
extremity one of the given angles, and so on.

To copy such a drawn polygon accurately, itmust be divided into Triangles, such as those
marked with dots (fig. 25), and these Triangles
must be copied in regular succession.

XXXIV.	To draw a regular Polygon, viz. a
Figure of more than four sides, which, as well
as the angles, are all equal; as, for instance, the
Pentagon (fig. 2G, plate 2).

The easiest way, when no importance is at-
tached to the sides being of more or less consider-
able length, is to describe a circle, to divide this
circle into as many equal parts as there are sides
required, or as the Polygon is to have angles,
and afterwards to join these points of division by
straight lines.

A circular line, which is also called a periphery
or circumference, is such only when in whatever
part of this line we suppose a point, that point is
every "where at the same distance from a [joint in
its middle. This latter point is called the centre.The distance of the centre from the circumfer-
ence is called the Radius; the distance of any
point in the circumference to another point in
the same, in the direction through the centre, is
called a Diameter; but if the direction be not to
the centre, it is called a Subtense or Chord.

XXXV.	To draw a circular Arc through three
given Points which are not in a straight IJne:
as, for instance, through the Points I, m, n (fig.
27, plate 2).

Describe from / and m, with the same opening
of the compasses, small arcs intersecting each
other, as here at k and p, and likewise from the
points m and n similar arcs intersecting each
other, as at q and r. Afterwards draw through
these points of intersection k, p and q, r two lines,
and the point where these lines intersect each
other is the centre of the circular arc.

The same process takes place w hen in a cir-cular arc the point, from which the arc itself has
been described, is to be found, viz. by taking any
three points, in the circumference, at pleasure.

XXXVI.	To draw a regular Polygon upon a
given Line: as,for instance, the Pentagon
(fig. 26, plate 2).

Let s / be the given line. Draw upon it, os
at /, a line at right angles, making t v equal to
s t, and describe with its length the circular arc
s v. Then divide the length of this arc s v, into
as many equal parts as the figure is to have an-
gles, here therefore into 5 j take whatever poly-
gon it may be, the width, as here, from v to the
point where there are still four parts remaining,
and set them oft' from v to w, further upon the
arc. Then seek in s t and w for a point on which
to rest the end of the compasses, in order to de-
scribe the curve line which passes through the
points s, t, w, and set oft's l four times more uponit, after having actually drawn the curve line.
The rest is easy.

The width which is to be added to the divided
arc consists, consequently, of the parts made, in
the pentagon, of one, in the hexagon of two, in
the heptagon of three parts, and so on, so that
there be always four parts, left remaining.

XXXVII.	To draw an Elliptical Circumference,
such, for instance, as that (fig. 28, plate 2).

Draw a line, and placing the compasses on it,
describe two circles, each of which passes through
the centre of the other. Afterwards with the
length x z describe, upon and under that line,
two equilateral triangles, and lengthen, as may
plainly be seen here, the sides of these triangles;
this gives the limit of the arcs required to round
it, whose centres are in the angular points of the
triangles above and under fig. 26.XXXVIII.	To divide a Line into equal parts, so
that there shall be left a certain length; as, for
instance, the Line b (fig. 29, plate 2,) into two
equal parts, and two thirds of such a second part.

Draw any line at pleasure, somewhat longer
than that which is to be divided; open the com-
passes so wide that, as there are to be two equal
parts, this width may be set off' twice upon the
line, as is actually done here at b. Afterwards,
to get at the two thirds, divide one of the afore-
said two parts into 3 equal parts, and add two of
them to the former two parts. Then, with the
whole length, as has been done here, describe an
equilateral triangle, take with the compasses the
terminating points of the given line, and set off
the length of this line, as here from c to d and
from c to f Lastly, draw the line, as here d f,
and intersect it by placing the ruler against the
point c and against the dividing points of the
c 2line under b; thus this line, which is equal to
the given line, will be divided as required.

The same process may take place whenever a
line is to be divided into a certain number of
equal parts without any addition. But with re-
gard to this addition itself, it may he observed
that one of the greater parts is always divided
into as many equal parts as the number last men-
tioned in the addition; for instance, with three
filths into five ; and that as many parts are al-
ways to be added as mentioned by the number
which is first uttered, for instance with three
fifths, three.

XXXIX.	To make a Straight Line as long as a
Cuive Line.

Divide the curve line with dots into small parts,
and set off these parts upon the straight line in
the same order in which they follow each other.

The smaller the parts on the curve line, themore accurate will be the process : however, they
must not be made over small.

XL. To describe a Curve Line, of the same length
as another Curve Line.

The process is the same as in the preceding
proposition.38

CHAPTER III.



MODELLING WITH CUT PAPER FIGURES.

Preliminary Observations.

1. The proportions here given refer only to
the objects represented on the plates. They are
of indispensable necessity, and ought to be care-
fully attended to until a sufficient knowledge to
determine them, has been acquired by the young
artist.

2. Whenever height, length, and breadth, are
stated in general, these dimensions are to be un-
derstood of the main parts of the given object.
When the dimensions of the smaller parts are
meant, those parts are expressly mentioned.

3. Care must be had to have a distinct notionof the sides within which the object to be repre-
sented is inclosed. This is the main point. And
before you begin to draw, consider how much
paper is required, and how it can be best made
use of.

4. The dotted lines always direct the folding,
but they must not be dotted on your own draw-
ing. If you wish particularly to mark them, they
may be drawn finer than the others, or distin-
guished by little strokes.

5. Begin with making the given models with
white paper only, and as simple at first as pos-
sible, leaving out small and less necessary parts.
Adhere at first to the size here stated, and com-
pare your own flat paper figure with the one here
given.

6. Be not over hasty. Read only as much of
the directions at once as may be performed in a
little time, and endeavour to imitate directly
whatever you clearly comprehend.

7- But should you not succeed at once, be notdeterred ; try again with greater attention, seek
for the cause of your failure, and avoid the mis-
take into which you had been betrayed. Re-
peated attempts are sure to be crowned with
success.

A Cube or Die. Plate 3.

With the flat paper figure b c. Plate 12.

Proportions.

The Cube or Die is enclosed by six equal
squares, consequently it is as high as it is long or
broad.

Drawing.

1.	Draw the line b c; mark oft' from b to r
three times one of the sides of the Cube; draw on
the two middle points two lines at right angles
and produce them downwards.2. Draw from the points b and c two straight
lines at right angles ; make them from b and c as
long as one of the sides of the Cube ; and join
them by a line, so that you obtain, as here, three
quadrangles.

3. Afterwards draw, which now will be very
easy, the three remaining quadrangles, and leave
in the proper places the edges or margins requi-
site for joining.

Construction.

Cut out the flat paper figure. If the paper be
large, do it first by guess, but afterwards very
accurately. Both are easy. You need only ob-
serve the lines which here are drawn through and
not dotted on purpose. Care must be had not to
miss any of the principal surfaces nor any of tlie
edges left for joining. The latter may even be
left tolerably large. Afterwards proceed to the
folding. This too is not difficult. You areguided by the dotted lines by which it is clearly
pointed out. You then clip the edges for joining,
if needful, a little, and examine whether all the
parts will form a correct whole. The points
d, c, and/, for Instance, must meet exactly When
this is the case, the edges are done over with glue
or gum-water, and joined in such a manner as
not to be perceptible on the outside.

A Chair. Plate 3.

With the flat paper figure over g h. Plate 12.

Proportions.

Without the back, the height, breadth, and
width, must be equal. The back itself as broad
as high. But the seat is somewhat narrower
than its length. On considering the flat paper
figure attentively, you find over g h three qua-
drangles for the feet, a rectangle over the mid-
dle one for the seat, and over this seat another
quadrangle for the back.If the seat is to be a little narrower behind, the
back must consequently be so, and the former
in that case is not a quadrangle but a trapezium.

The thickness of the feet in the upper parts is
about one sixth of their height; but in the lower
parts only half of a sixth of their height. The
thickness of the seat is about the fifth of its length.
Several parts of the back, in front and on the
side below, are as thick as the upper parts of the
feet; and the back on the side above is as thick
as the lower parte of the feet. The upper cross
piece of the back is as high as the 6eat is thick in
front.

Drawing.

1.	Draw the line g h: erect upon it three suc-
cessive times the front line of the seat, and place
on the points right angular lines, the two exterior
ones about as long as the breadth of the seat;
but the two middle ones a little more than three
times as long as that breadth.2. Take the height of the seat from g to k, and
from h to /, and drawing the line I k, determine
the three adjoining quadrangles. Afterwards
draw, which will now be very easy, the middle
rectangle and the upper quadrangle. The for-
mer is lower than the quadrangle by the thick-
ness of the lower side of the back.

3. Draw under the line Ik a line parallel to it
at a distance equal to the thickness of the seat,
and extend upon it the thickness of the upper
parts of the feet to the right and left of the lines
right angularly drawn upon g h. Then in the
same manner mark off upon the line g h the
lower thickness of the feet, and draw the in-
clined lines by which the feet are distinguished.

4. Having attended to the given proportions
and first drawn parallel lines, delineate the open
work of the back,and, as here, its lateral breadth.
Lastly, mind the margins for joining.Construction.

After-the flat paper figure has been cut out in
the rough, fold it so that the sides not marked
coine to lie one upon the other, excepting how-
ever the back, the marked side of which comes
to lie upon the marked side of the seat.

The figure then is cut out more accurately, so
that the feet stand free; the open work of the
back appears, and margins of proper breadth are
left for joining.

If the parts now meet exactly, as for instance
the point I the point m, proceed to glueing so
that the margins be not visible on the outside.
The back must be a little inclined.

Observations.

Should coloured paper be preferred, brown,
spotted, or streaked like wood, will be most suit-
able.If the upper cross piece of the back is to pro-
ject a little sideways as on the chair in the third
Plate, or as it is to the right of d, draw and cut
out separately a narrow rectangle like that at t,
and fix it properly. It may be clipped after it
has been joined.

A Table. Plate 3.

With the flat paper figure over n p. Plate 12.

Proportions.

Two-thirds as broad as long; that is to say, if
you allow two parts to the breadth, the length
must have three. The height is a little more than
the breadth. If this height is to be proportioned
to the chair, half of the height of the latter may be
added. The upper cross ledge of the plinth has
nearly a fourth of the height of the plinth itself.
The lower ledge is half as much raised from the
bottom.

/The breadth of the upper parts of the feet is
about an eighth of their height up to the upper
cross ledge; lower down they are less thick.
The drawer has half the height of the cross-ledge,
and its length is double its breadth. The table
board projects on all the four sides half the height
of the upper cross ledge.

Drawing.

1. Draw the line n p ; set off upon it from n,
first the length of the pedestal, then its breadth,
then again the length, and once more the breadth,
and erect at these points perpendicular lines as
long, or even a little longer, as the pedestal is to
be high.

2. Make the line n q and p r of the height of
the pedestal; draw the line q r, and under it,
parallel to it at the proper distance, another for
the upper cross-ledge. Afterwards draw the
feet, as before for those of the chair.3. Determine by taking correctly n and p the
lower cross-ledge, and observe the margins for
joining.

4. Draw the rectangle for the table board
with small margins at the four sides, either for
joining or to represent the thickness of the table
board.

5. Draw as at s and t, (see plate XII), the
pieces requisite for the drawer. The part t is
fixed to it in front.

Construction.

After having made a cube or a chair, it is easy to
cut and fold the fiat paper figures of a table. The
feet may be cut out after the folding.

If the edges correspond exactly, join first the
parts of the pedestal. The point q must here
correspond with the point r. Afterwards fasten
the pedestal to the board, so that the latter may
project.And, in order that the drawer may not sink be-
hind on being put into the table, fasten at the
upper part of the plinth, a small slip of paper on
which the drawer may rest. A very small pea,
or a grain of pimento, put in front, in the middle,
will serve as a knob for pulling.

Obsei vaiions.

If coloured paper be employed, brown of the
colour of wood is the most suitable. The table
board may be of a different colour; you may, for
instance, give it the appearance of being covered
with oil cloth. Should the making of a separate
drawer give too much trouble, a slip of paper,
like that at t, upon the upper cross ledge, may
supply its place.

A Chest ok Drawers. Plate 3.

With a flat paper figure like that of the Table,only that the feet are very short, and that there
are several drawers.

Proportions.

Two-thirds as broad as long, and nearly as high
as broad. The top projects but little. The height
ot the drawers is according as there are two,
three, or four, of them. The height of the feet is
about a seventh of the height of the chest of
drawers.

Drawing.

After having drawn the four rectangles, as if
it were to be a table, and taken one of them for
the sliding in of the drawers, proceed as on the
left, below plate 13, over v.

1.	The distance of the drawers, or rather of the
openings for their sliding in, is determined ac-
cording to the directions in Prop. IX. of the In-
troductory exercises.2.	Draw, according to the directions given re-
specting a table, the feet, the top, and the draw-
ers ; and attend to the margins for joining.

Construction.

Like that of a table. Instead of real drawers,
narrow rectangles may be fixed.

A Sentrv-hox. Plate 4.

With the flat paper figures over and under
te x. Plate 13.

Proportions.

As long as broad; blit laterally, or from the
front to the baek, a little more than one-third of
the height. The door is half as broad as the
breadth, and about five times and a half as high as
it is broad.Drawing.

1. Set off upon the previously drawn line w x
four successive times the length or breadth, and
draw lines from these points, at right angles, to
the line w x. If the height be determined from
w and x, and a line drawn parallel to w x, you
obtain four similar rectangles.

2. Draw over two of these rectangles equila-
teral triangles, and rub out the lower lines. Af-
terwards determine, as here, the door and the
small windows as well as the margins for joining.

3. Appropriate, as under x, the equally divided
rectangle to the roof. This rectangle ought to
be somewhat longer than twice a side of the tri-
angles, and a little broader than the sentry-box
itself.

Construction.

When the flat ^paper figure is cut out in the
rough, fold it properly, and afterwards cut itout more correctly, as well as the door and win-
dows.

On joining-, the edge, over x, must come exactly
upon that over w, and the sentry-box must be
fixed upon the ground. Then the roof is placed
upon it; and the whole is joined in such a man-
ner that none of the margins be visible on the
outside.

The roof may be painted red, blue, black, or
brown, or covered with paper of any of these
colours: but it must be done before it is placed
upon the box.

Observations.

The size of this sentry-box corresponds with
that of children’s pewter or leaden soldiers. It
may be less. The bottom is in the shape of a
quadrangle or rectangle, and may be contrived
with very strong paper or thin pasteboard.

The roof may be represented as made of boards,
by means of fine wood shavings cut into smallpieces of the breadth of a common goose quill,
glued crossways on each side, and projecting a
little one over the other. When sufficiently dry,
they may be clipped even with scissars; which is
far more expeditious than to cut them separately
of equal length.

A Thatched House.

With a flat paper figure similar to that of the
sentry-box. Plate 13.

Proportions.

The sides double the length but only half the
height of the breadth of the thatched house. The
remainder is evident from the

Drawing,

which is exactly like that of the flat paper figure
of the sentry-box, only altering the length,
breadth, and height, making the door somewhathigher, and leaving out the side-windows. The
roof and the bottom must, of course, be longer,
and project a little.

Construction.

It is nearly the same as that of the sentry-box.
The roof may be painted, or actually covered with
thatch, in the following manner: Cut good straw
of a fine yellow colour into small pieces some-
what longer than the length of the roof down-
wards, split them, do the hollows over with paste
or glue, and fix them one close to the other on
the roof, beginning by the gable end, so as to be
all even at the top. When sufficiently dry, clip
them equal with a pair of scissars, and make
them project a little. Lay also some straw
cross ways at the top. See plate 4, above to the
left.A Pigeon-house. Plate 4.

With the flat paper figures Plate 14, and under
k, Plate 15.

/

Proportions.

The bottom and side-walls are five equal qua-
drangles. The roof consists of four equilateral
triangles. The door is about half as high or as
broad as one side of the quadrangles. Each of
the four perches is about as long as the door is
high, and a fourth as broad.

The pole, which goes below through the bottom
of the pigeon-house, is altogether four times as
long as the house is broad; its lower end is a
little thicker than the fourth (if this breadth, but
the upper end not so thick.

The ground of the base is a quadrangle which
has double the length or breadth of the pigeon-
house ; but the sliding ledges are full as long asthe building is high without the roof, and about a
fourth as broad.

Drawing.

1. The flat paper figure of the building. First
draw the line b c, and set off on it the breadth of
the house four successive times; then draw, as
here, five adjoining quadrangles, the undermost
of which forms the bottom. After this, determine
the door and perches as well as the round hole in
the bottom for the passage of the pole ; the spot
for this hole is found by drawing from one angle
to the other in the direction of the centre two
lines that shall intersect each other. Attend
likewise to the margins for joining.

2. The flat paper figure for the base. Having
given to the line df its proper length, draw
against and with it a quadrangle, and determine
its centre by means of two diagonals Then set
off on the middle of each side of the quadrangle
the breadth of the sliding ledges, and placing theruler on the two opposite points, draw lines, and
at the same distance two more for the sides of the
sliding ledges. Then make these of the requisite
length, and observe here and there, as at g, the
inclined segments and the margin for fixing the
sliding ledge on the pole.

3. The flat paper figure for the pole. This
consists merely of a slip of paper about as long
as the pole is to be high, and about a fourth of the
breadth of the pigeon-house in its broadest part.
It is represented on a small scale at h, plate XIV.

4. The flat paper figure for the roof. See
under k, Plate 15. Only draw, as ty?re, four
adjoining equilateral triangles. But each side of
these triangles must be somewhat larger than
the breadth of the pigeon-house, else the roof
would not project sufficiently; and the margin for
joining must not be omitted.

Construction.

Begin with the flat paper figure of the pigeon-house; after having cut and folded it in the
rough, fit the edges b and c upon each other, and
then fix the four walls of the building on its
bottom. The margins are all folded inwards:
but the upper ones are only a little bent and kept
rather erect, to facilitate the roofing.

The roof may be painted, or covered crossways,
with wood shavings, like the sentry-box.

Afterwards proceed to the pole and the pedes-
tal. To make the former, roll the afore-men-
tioned slip of paper to its proper thickness,
beginning at the sharp-pointed end, as here h to
the left, opposite, and fix it; if you wish to paint
it, the most suitable colour is brown.

When the base or pedestal is ready, fix the
thicker part of the pole on the middle of the bot-
tom, and on the pole itself the sliding ledges;
and afterwards insert the pole through the round
hole at the bottom into the pigeon-house.Observations.

The roof is best painted; the ground itself on
which the pigeon-house stands may be painted
grey, and covered here and there with moss, par-
ticularly where the sliding ledges may happen not
to fit exactly.

Instead of making the pole of paper, you may
take a young straight twig properly dried and co-
vered with bark. A small pearl of wax or a ju-
niper-berry may serve as a knob on the roof.

An Ink-stand. Plate 5.

Chiefly with the flat paper figures of the cube.
Two dice, like the one on the third Plate, give

one the ink glass, the other the sand-box. De-
scribe therefore on the flat paper figure of each,
in the centre of the surface which is to be upper-
' most, a circle, and thi« cut out will be the holeof the ink-glass ; pricked through with a tine pin,
it will give the holes for the sand to pass through
the sand-box. But to find the middle points tor
the circular line, draw two diagonals on each of
the two quadrangles.

A chest, like the table drawer, will serve for
the stand itself; only the front ledge must be ex-
actly like the back one. The ink-stand must not
be too small, that there may be sufficient room for
the ink-glass and sand-box; the latter may be
rendered moveable by means of an uncovered cube,
into which it might be placed ; but this is rather
difficult and tedious to contrive.

Observations.

The ink-stand may be pair, d, o~ m.-rle with
coloured paper. A grain of eed, or a *e» y small
wax pearl, may be fixed with a little >r gum
against the sand-box, to serve as a knA German Stove. Plate 5.

With the flat paper figures over I m and close
to q. Plate 15.

Proportions.

The stove, independent of the two supporters,
consists of two parts. The lower part is as high
as it is long, but only two-thirds as broad. The
upper is as high as the lower part, but about a
tenth or twelfth shorter and narrower. The
height as well as the breadth of these two parts
consequently are determined by the given length.

The height of the two supporters is a fourth of
this length. But the hearth-plate on which the
lower part of the stove rests, projects but little,
say as much as the upper is narrower than the
lower part. The door-shaped space in the upper
part is a rectangle, which on both sides and at
the top recedes about a third of the front breadth
of the upper part.Drawing.

1. Take twice upon the previously drawn line
I mf as here, the lower length and breadth; erect
on these points perpendicular lines, and by de-
termining the height from I and m, and drawing
a line, finish the four lower rectangles.

2. Draw a line parallel to the common or ge-
neral upper line of these rectangles at a distance
equal to what the upper part wants of the length
and breadth of the lower one; take, as here at
it p, the breadth of the upper part exactly in the
middle of the lower one, and then draw the rect-
angles for the. upper part in the same way as for
the lower one.

3. Draw over the rectangle close to n p an-
other rectangle equally broad, but as high as
the stove is long at the top, as well as the two
rectangles for the door-shaped openings. After-
wards determine also the mouth of the stove, the
round hole for the flue, and the margins for join-
ing.Determine, as at q, the flat paper figure for
the supporters, afterwards a small rectangle to
be rolled up for the flue, and an additional rect-
angle to be folded for the exterior circumference
of the mouth of the stove. Draw also the before-
mentioned liearth-plate, like the table-board.

Construction.

The flat paper figures are first cut out in the
rough, according to the undotted lines, and then
folded according to the dotted ones. In joining,
the point I must fall exactly upon the point rn,
and all the margins are put under and concealed.
When the stove is fixed on its plate, and provided
with the flue and the circumference of the mouth,
it is placed 011 the supporters, and along with
these, fastened upon a piece of stiff paper or thin
pasteboard, in the shape of a rectangle.

The stove may be painted black with fine
white cross lines, imitating Dutch tiles, and thig
is best done before joining.Observations.

The oblong rectangle of thin pasteboard on
which the stove is to be fixed, may be folded in
such a way that one part represents the floor, and
the other the wall of a room, at such a distance
from each other as to make a right angle. The
stove will then be placed as stoves usually are
in Germany.

A Watch-stand. Plate 5.

With a flat paper figure similar to that of the
stove.

Proportions.

Distinguish the upper, middle, and lower part.
The middle one, as the principal part, is as broad
as it is long, but its Height is about a fifth more
than its length. The lower part is only a fourth

Das high as the middle one, and recedes about a
third of its height. The upper part is rather
sloping, and as high as the lower one.

Drawing.

Excepting the hearth-plate and the two sup-
porters of the German stove, the drawing is the
same as that of the stove, with this difference
only, that what is the lower part of the stove
is here still lower, and in the middle one a circle
must be described for the dial.

The upper part of this watch-stand must be
drawn separately. Describe a circular or curve
line like that round the point r, Plate 16. Set
off upon it the breadth of the upper part four
successive times, and from these points draw
lines towards the centre.

Afterwards draw the lines, s t, &c. and others
parallel to them, at the proper distance. Lastly
draw, as here, the quadrangle, and mind the mar-
gins for joining.Construction.

Having drawn the dial and the hands on a se-
parate paper, fix it in the interior of the watch-
stand, which may be painted black, brown, grey,
or spotted, and may have additional ornaments
made with a pen or pencil.

A Pair of Steps. Plate 5.

With the fiat paper figures over and under
v zo, Plate 15 ; but the young artist had better
•make it on a larger scale than represented in the
plate.

Proportions.

The steps here are chiefly to be attended to.
They are generally at the same distance from
each other as their breadth, and four times as
long. The side pieces must he of such a breadth
that the steps do not project.

d 2Drawing.

1.	Draw the line r a) as long as each step,
erect perpendicular lines on the points v w; and
if you want four steps, set off from v and w, four
times the slope of a step. This slope is deter-
mined as at .t; viz. two lines are drawn right-
ungularly one upon the other ; then set off from
,i to x the height of the step, and from x to b its
breadth, and afterwards draw the line z b as its
slope.

2. Join the points just obtained upon the lines
over v and w with cross lines, also dotted here,^
and then draw by means of parallel lines the
breadth and thickness of the side pieces, whose
breadth is found by determining, according to
Prop. V. of the Introductory Exercises, how far
the point x is distant from the line .

3. Determine likewise the slope of the side-
pieces at their extremities, as at re. The point
d in the prolongation of the line over w is here
equidistant from c and w.4.	Draw three times more such a step like the
two upper narrow rectangles over v w, with
margins to represent the thickness. Afterward
the supporters or props, as at f.

Construction.

Cut the flat paper figure over v w, as marked
here by the undotted lines, give it the proper
folds for the side pieces and the upper step, after-
wards cut and fold the remainder; viz. the three
lower steps and the two supporters ; the former
must be carefully cut, and then folded according
to the dotted lines, so as to leave about the same
spaces, to represent the thickness both of the
back and front of each step ; afterwards join the
steps to the side pieces upon the sloping lines.

When all is properly joined, the steps viewed
sideways must look as they do on the third
Plate.

The steps might also be contrived thusDe-termine the distance and breadth of the steps
four successive times, as under d; then fold this
flat paper figure in a zigzag, and join it so as to
form a whole, with the figure over v w.

Observations.

On taking twice from x the breadth of a step
upon the line close to b, and describing an arc
as here, you obtain also the slope for two steps,
by drawing this sloping line itself. Suppose
therefore you had delineated a flight of steps as
under d, and wished to determine the height of
the rectangle over v w, the height of two steps
would be that of the sloping line, and that of four
steps double its height, and so on in proportion.

A Small House with Gable Roof. Plate 6.

With the flat paper figures over/ g and over
h. Plate 1G.

Proportions.

Only two-thirds as broad as long. The heightup to the roof half the length of the building.
The gable side of the roof is an equilateral tri-
angle.

The height of the door is double its breadth.
'Hie windows in their exterior circumference are
quadrangles, a little less in height than the door
is in breadth. The chimney is half the breadth
of the door, and the height and breadth of a win
dow. The roof and the bottom of the house
project a little above the building.

Drawing.

First Case: When the gables at the top are
not broken.

1.	Draw the line/g and set olf upon it suc-
cessively the length, the breadth, then again the
length and ^gain the breadth of the building;
erect on these points lines at right angles, and
determine its two long lateral flanks after having
first taken from / and g the height of the build-
ing up to the roof.2. Draw the two equilateral triangles; sup-
plying the lower line in your mind, and then the
door and windows, either as here or according
to any different plan of your own; and observe
the margins for joining.

3. Determine the two conjoint rectangles for
the roof, as between k and h, neglecting the
sloping lines. The length of these rectangles is
but little more than the length of the building,
and the height of each a little more than one of
the sloping lines of the gable.

Second Case : When the gables are broken at
the top.

1. Draw all as 1 and 2 in the former case, and
afterwards shorten every gable side as below I;
vn n is here drawn so that I m is equal to I n.

2. Determine the bottom and roof; the latter
as between h and k: it is delineated as at 3 in the
first case. Then take from p to q the shortening
of the top, from p to r and s the length I m or / «,
and draw the lines q r and q s. On describingwith q r from q, and with ni n from r, small arcs
intersecting each other at /, and joining these
points with lines, you obtain the equilateral
triangle q r t. The opposite side must be drawn
in the same manner, and proper attention must
be paid to the margins for joining.

3.	Draw, as under c, the flat paper figure for
the chimney, by first taking twice upon one line
the breadth and length, and erecting lines at
right angles, and afterwards raise the line under
v to its proper height. The segments are de-
termined by describing equilateral triangles, the
gable side of the roof being such a triangle.

,	Construction.

After having cut in the rough and folded the
flat paper figure of the building, so that the point
f coincides with the point g, fix the roof, then the
chimney upon it, and afterwards the bottom.
The roof may be painted to represent either tiles
or slates.Observations.

If it be a tiled roof, paint it> first red or brown,
and then the tiles as below to the right and left
on the fourth Plate.

If it be a slated roof, paint it first blue, and then
the slates as above to the right and left on the
fourth Plate.

Instead of cutting the windows out, they may
be painted black, and the sash or casement white.

Instead of cutting the door out and represent-
ing it as open, it may be painted as if it were shut.
The shutters may be painted in the same way.
But both door and shutters may likewise be made
with fine wood shavings.

A Cottage.

With a flat paper figure like that of the gable-
roofed house, Plate 16.

The proportions and drawing are likewise the
same with those of the gable-roofed hous e.Construction.

The same as with the aforesaid house; only if
the roof is to be thatched, it must be done like
the top on the left, or on the right below, in the
sixth Plate. In the former case it is actually
covered with thatch, like the thatched house; in
the latter it is painted and covered in front of the
gahle with fine wood shavings.

A Barn and Stable.

With flat paper figures like those of the gable-
roofed house.

Proportions.

1. The Barn; about two-thirds as broad as
long. If a cottage be joined to it, the barn must
be longer, broader, and higher than the cottage:
the door is as high as broad, and very rge.

2. The Stable. Twice as long as broad, but
low, and not so high as the cottage, if this be joinedto it. The windows as high as broad, and rather
small.

Drawing and Construction.

The same as the cottage. The barn-door mar
be contrived like the door of the gable-roofed
house.

A Paling, or a Palisade.

Plate /.

The flat paper figure is the same as under ®r,
Piute 16; but at the top there is a separate slip
of paper crossways, as in the seventh Plate. Such
a paling or palisade may also be contrived as the
drawing to the left on this seventh Plate.

A Small House with a Sloping Roof.

Plate 6.

With the flat paper figures over x z, Plate 16;
and over b c, Plate 17-Proportions.

Two-thirds as broad as long. The height up
to the roof half the length of the building. The
slope of the roof on the narrow side is an equila-
teral triangle. The height of the door is double
its breadth; every window is two-thirds as broad
as high.

Drawing.

The flat paper figure x z is only half of the
lower part of the house; the other half must be
supplied in the mind. The drawing itself is not
difficult. First, take twice the length and breadth
upon the line x z, and its prolongation, and then
draw each of the four large rectangles.

To make the roof.	^

1.	Draw the line b c, Plate 17, a little longer
than the length of the building, that the lower
end of the roof may project a little; and mark offexactly in the middle, the length of the top of the
roof, according to Prop. VIII. of the Introductory
Exercises. Afterwards erect straight lines on the
last-mentioned points

2. Take with the compasses one sloping side
of the roof on the broad side of the building, anti
about as much in addition as the roof is to project
011 both sides ; and carry this length from the line
be to the right-angular lines on the same; draw
the line which is parallel to this and the two
sloping lines, one of which is c d.

3. Having first taken the two right-angular
lines upon b c, draw once more the trapezium
over b c, as here ; and mark at the same time two
margins for joining.

4. Opening the compasses as wide as the
breadth of the building, and as much in addition
as the roof projects on both sides, describe from c
a small arc, like that at f; then from d with the
length c d another small arc which intersects the
former, and draw the lines c / and d f.5.	Draw another such triangle as c df opposite
to it, and the two small flat paper figures for the
windows in the roof, according to the directions
for the gable elevation of the house 011 the seventh
Plate.

Construction.

The same upon the whole as that of the gable-
roofed house, only that the roof here must not be
covered with thatch.

A Monument.

Consisting below of a cube, and above of a
truncated pyramid.

Make the cube as that in the first Plate, and the
pyramid like the upper part of the watch-stand ;
only with this difference, that it must be very
high, at least three times higher than the cube,
which must project a little.

The monument may be painted like stone or
marble, and decked with other ornaments j andthe ground on which it stands may be covered
with a little moss.

A Town House.

Like the house with the gable or sloping roof,
only higher ; with two or three rows of windows
one over the other, and a window over the door.

A House with a Gable Elevation in front.

Plate 7-

A small part of the flat paper figure is between
g h, Plate 18.

Proportions.

Three times as long as broad ; only one-third
as high as broad. The gable elevation in front
is about half as long as the whole building, and as
high as a fourth of this half. The roof itself is as
high as the building up to the roof.Drawing.

Altering only the length, breadth, and height,
it is the same as that of the house with the sloping
roof. The length of the gable elevation must be
taken exactly in the middle, according to Prop.
VIII. of the Introductory Exercises ; but the roof
of this elevation is to be drawn like k /, Plate 20.
This line k / is less than twice as long as one of
the sloping lilies of the gable elevation j but the
right-angular line 011 its middle is obtained, by
supposing, after the roof is fixed, a perpendicular
line from the sharp point of the gable elevation
to the roof, and taking its length with the com-
passes.

Construction.

The same with that of the two houses with
gable and sloping roof. A few steps may be
added to the door in front, by removing it a little
higher up.A Court or Garden Gate. Plate J.

In the way it is represented here, it is that of a
palisade or paling. It is therefore drawn like a
palisade, and may be painted; or if cut out, a slip
of paper on which the folding door is painted
separately, may be fixed in the opening, or this
opening may be left as if the gate were open.

ABridge. Plate 7*

With the flat paper figure at the top, Plate 18.

Proportions.

Three times as long as broad. Each arch is
described with a radius equal to the length of the
bridge. The height of the balustrade is a third
of the stated breadth.

Drawing.

After the rectangle under tn n has been drawnof the length and breadth of the bridge, take with
the compasses the length m n, and describe from
m and u, two small arcs which intersect each
other, as here at p.

Place one point of the compasses on p, and de-
scribe with the other not only the arc m //, but
also the arcs parallel to this, which serve to
form the balustrade.

The same is done with the similar lower arcs,
and the two balustrades are then drawn more
complete. Describe also the two innermost arcs
with a radius as long as the straight line between
the terminating points of each of these arcs.

The upper arch consists of a rectangle, which
nmst be bent, and which is as broad as the bridge,
but as long as the arc m n. Afterwards deter-
mine, according to the last but one of the intro-
ductory exercises, the length of this rectangle,
and mark at each of its sides the margins for
joining.Construction.

When joined, each part, like that over m n,
will stand straight upon the rectangle under m n,
and the upper part must be fixed in such a man-
ner that no margin may be seen.

Such a bridge looks very neat white; but it may
be painted gray, and the balustrade brown. The
upper part of the bridge, or rather the road over
it, may be represented as paved or covered with
gravel. The paper altogether should be very
strong and stiff.

An Ancient Tower. Plate 8.

With the flat paper figures which are partly in
the middle and partly below on Plate 19.

Proportions.

The tower, (which, like its principal roof, i*round), is up to this roof twice and a half as
high as the diameter, and the roof itself is as high
as the tower is in diameter. The height of the
upper ledge close under the root is an eighth ot
the height of the tower up to it, and the little
turrets lower down are about a half higher.
Each roof of these little turrets is one and a half
as high as a turret without the roof.

The balcony is about a third as broad as long,
half as long as the tower is in diameter, and half
as high as the door behind it. The pillars are a
third of the height of the tower without the roof,
and a fourth as broad as they are high. Their
lower part is about as narrow as half of their
lower breadth.

The remaining proportions are easily tound.

Drawing.

There is here only part of the fiat paper figure
of this tower without its roof, close to the line
k /, which is equal to the requisite height. Theexact length of this paper figure should he twelve
times a fourth of the thickness of the tower.

The aforementioned ledge, which goes round
the top under the roof, and is separately joined to
it, is a little longer than its substratum itself, or
the circumference of the wall on which it is '
fixed. It is best determined by compressing the
rectangle requisite for the tower.

Other windows and doors besides those marked
here must be supplied, and the two doors given
here must be placed neither higher nor lower
than the balcony and the draw-bridge will allow.

Draw the roof for the tower as under iw, Plate

19.	l ake with the compasses the length of one
of the sloping lines of the roof up to where it pro-
jects over the lower part of the tower, and
describe a circular arc; afterwards take upon it
twelve times a fourth of the lower width of the
roof, and from the two extreme points draw lines
towards the centre, or here the point m. Mark
also the margin for joining.As for the small turrets, draw the flat paper
figure for the lower part as at w, Plate 19; and
for the roof like that of the pigeon-house, taking
care, however, to alter the height.

Draw the flat paper figure for the balcony as
at;), for the drawbridge as at q, and for each pil-
lar as at r, Plate 19.

The wall consists in its principal parts of a
rectangle of about a fifth of the height of the
tower without the roof, and of at least ten times
its length.

Construction.

After having joined all the parts, and fixed the
small turrets, the balcony, and the pillars in their
proper places, fasten below at the entrance a
narrow rectangular slip of paper, to represent
that part of the bridge which may be drawn up.

The wall is best made of thick pasteboard co-
vered with paper, which is neatly clipped and
trimmed when dry. The whole building may beplaced on pasteboard, and painted like an old
ruin; but the roofs as if they were slated, or still
better, green, as if they had been covered with
copper. Doors and windows may be painted
instead of being cut out; some moss may be laid
in different parts, and vanes fastened to the tops
of the turrets, or flags kept flying as here, to ren-
der the whole more conformable to reality.

A Boat.

With the flat paper figure close to st,
Plate 19

Proportions.

The flat bottom is a rectangle six times as long
as high or broad.

Drawing.

1 • Draw the rectangle over s t six times as
long as high or broad; prolong the narrow late-ral lines on both sides, and resting one point of
the compasses on each of these prolongations, de-
scribe, with half the length of the rectangle,
arcs which meet, as here at v.

2. Make the length s w equal to the length of
the arc s v, and do the same with the other three
similar lengths ; determine also, upon the afore-
said prolonged lines, from the point where they
are met by the long lateral lines of the rectangle
above s t, the height of the two sides of the boat,
here two-thirds of the breadth of the rectangle
over s t ; then draw the remainder as here.

3. Mark the margins for joining, as those of s ar,
and others.

Construction.

The two parts here above and under w must
first be joined; the point must coincide with
the point x, and the same is to be observed with
the opposite part of the flat paper'figure.When all is dry, the other parts must he folded
according to the curve lines marked here. The
bottom and the side pieces must have the proper
bend, as over z. For the two benches or seats,
which are at a tolerable distance from each
other, a small slip of paper is to be folded as
under z.

Such a boat requires particularly strong paper,
and may be painted a brown or grey wood colour.

A Sledge. Plate 9.

With the flat paper figure close to b d, Plate

Proportions.

These are given by the following

Drawing.

1. Draw the rectangle b c and a similar oneover b d, each only one-third as high or broad as
long. With the distance c d, describe from/ the
two parallel arcs, distant from each other about a
ninth part of c d.

Produce the perpendicular lines g and h up to
the line bd, and draw the two lines g to the left, and
h to the right, in the proportion of two-thirdsof c d.

3.	Determine all the rest as is clearly seen
here

Construction.

After having cut out in the rough, and lined
the paper if it be too thin or coloured, fold ac-
cording to the dotted line b d, and cut according
to the undotted lines, holding the two halves of
the paper figure one upon the other. Hence
there is no occasion for any further delineation of
the rectangle over b d. Then open the paper,
smooth it, and finish the folding; all parts here
must be bent towards the point f. The body of
the sledge is soon formed, and the remainder iseasily done. The seat in the sledge may be con-
trived with a narrow slip of paper.

Observations.

If the rectangle over b d be drawn on the op-
posite side like that under b d, the folding accord-
ing to this line b d may be dispensed with. The
outer seat may also be made separately, and fixed
on the sledge. Indeed with a correct eye such
a sledge may be cut out of a card without any
drawing.

A Slup. Plate 9.

The main body is constructed nearly on the same
principles as a boat, only the flat paper figure is
in one part like that at g, Plate ‘20. There is
also a piece like that under g requisite for the
cabin; and for the covering in of this cabin, a
rectangle which is a little longer than the cabin,
and as broad as the length of its arc on the top.How the rudder is to be made of wood and
fastened, may be seen at h, Plate 20. The main-
mast is almost as long as the ship; the second
mast a little shorter. Each sail consists of a
rectangle, whose breadth is two-thirds of its
length. It is fastened here and there on the
inast.

The main body of such a ship may also be made
at both ends like the boat, only the two arcs
, must iu one place be made somewhat longer by
opening the compasses a little wider, and the
cabin made separately must be placed where the
shorter arcs begin and do not intersect each
other.

In this latter case the rudder consists only of a
single crooked piece of wood, somewhat like A,
Plate 21.A Church. Plate 10.

With flat paper figures like those of the house
with a sloping roof, and of the upper part of the
pigeon-house.

Proportions.

The length almost double that of the breadth ;
up to the roof as high as broad or rather a little
higher. The roof of the church and that of the
tower are both of that height. VV ithout the roof
the tower has not quite that height.

The large windows are three times as high a?
broad, but the window over the door is only a
little higher than broad. The door is but half as
broad as high. The window in the tower is a
quadrangle.

Drawing.

Like the house with the sloping roof, only with
different proportions. Draw the lower part ofthe tower as above I m, Plate 20. The two
segments, to fasten it on the church roof, are
found by drawing the narrow side of the church
roof separately as at n, and placing the lower part
of the tower exactly in the middle, as may be seen
here close to n. Each of the aforesaid segments
is a triangle like that at n.

The roof of the tower, altering only the height,
may be drawn like that of the pigeon-house; the
triangles are all equilateral.

Construction.

The same as of the house with the sloping roof
and of the pigeon-house. If, besides the roofs of
the church and tower, the lower parts of tin*
church are likewise to be painted, it may be
done as marked below to the left or in the middle
tothe right of the tenth Plate.A Round Hut. Plate 10.

Diu wing.

The bottom or ground is a circle described
with an opening of the compasses equal to the
height of the posts or pillars up to the roof, of
which the flat paper figure is to be drawn like
that under m, Plate 19, but so that the arc here
be somewhat longer than the circular line, for
the bottom to secure the proper projection of
the roof.

The posts or supporters, six or eight in num-
ber, must be drawn as at p or y, Plate 18.

Construction.

When the parts have all been cut and folded,
the posts are fixed at equal distances from each
other on the circular bottom, and the hut is roofed
in. The roof may either be painted or actually
covered with thatch, and a little moss may be
strewed here and there upon the roof and post*.The flat paper figures for the body of the mill
are the same with those of the house with the
gable roof. The breadth sideways is a little more
than that in front; but the height up to the roof is
twice the breadth. The trestle or base on which
the mill stands is half as long as the height of
the mill. The sails are so long that they almost
graze the ground.

On the side opposite to the sails is a door, with
steps leading to it, tvhicli steps may be made
with a flat paper figure like that over p, Plate 20.
The two side pieces and the balustrade may be
cut out separately. These steps are fixed to the
long beam by which the mill turns on the tres-
tle, as may be seen at q, Plate 20.

The skeleton of the sails is partly given
below to the left of the 9th Plate; but the
rods or bars may also go through the middle of

Ethe sail*, and a small part of the skeleton will
then appear as below to the right of the said
Plate.

The trestle is contrived with small pieces of
wood ; but it may likewise be made as the base
of the pigeon-house. The slope of the sails and
their axle-tree are also indicated on the 11th
Plate.

An Arm Chair.

The same flat paper figure as that of a chair ;
only the three quadrangles one over the other
must be made broader, and the two arms must be
contrived with the flat paper figure at r, Plate

20.	The back as well as the seat may be covered
with paper of a different colour, to give them the
appearance of being stuffed.

A small Basket.

%

It may be made with a flat paper figure likethat under s or over r on the 16th Plate. The
handle may be made separately with a slip of
very strong paper.

A Chiffonnibre. Plate XXII. Fig. 1.

The flat paper figure is nearly the same as that
of the Table over n p, Plate XII. which served
also for the Chest of Drawers, Plate III.
Observe only that on this 22d Plate, Fig. 1.
a is the front, in which there are to be two
doors with a key-hole.

b b represent the two sides.
d the top, under and against w'hich are fastened
the joinings of the back and sides, as well as the
projecting part of the top.

The Chiffonnibre itself, when ready, may be
painted a brownish colour, so as to imitate ma-
hogany. The legs may have four small yellow
metal beads fastened to them, in imitation of balls,*n which case the legs may be made rather shorter
than the drawing.

A Sofa. Plate XXII. Fig. 2.

The flat paper figure of a Chair over g h,
Plate XII. which served for the Arm-chair,
may also be consulted here, but observe on Plate
XXII. fig. 2, that

the seat k is about two and a half times longer
than it is broad.

The sides I are twice as long as broad, and
joined to the back m taking the curve of the back;
but at n they are rolled close.

The Plate XXII. represents only half the sofa;
the other half, which is accurately to correspond
with this, must be supplied by the young artist.

The seat itself, and the sides, may be painted
black, as if they were horse-hair; and the legs
and frame may be painted brown, to imitate ma-
hogany.A Wheelbarrow. Plate XXII. Fig 3.

This, after all the preceding objects have been
properly constructed, will offer no difficulties.

Observe only the proportions as marked in
this 22d Plate.

The bottom a is twice as long as broad.
b b are the two sides, rather narrower towards
the handles.

c (I the two extremities.
e e the handles.

//the projecting pieces to which the axle of
the wheel is joined : they are similar to the han-
dles, but rather wider and shorter.

g g the points for placing the legs, which are
of the same length with f f.

The -wheel may be cither with or without
spokes. It may be made of a piece of card with
a narrow slip of paper glued round it; and a
small piece of wood may serve for the axle.APPENDIX.

The flat paper figures of the five regular geo-
metrical bodies. Plate 21.

The flat paper figure I. consists of three ad-
joining equilateral Triangles, and makes a Tetrae-
dron.

The figure II. consists of eight adjoining equi-
lateral Triangles, and makes an Octaedron.

The figure III. consists of twenty adjoining
equilateral Triangles, and makes an lcosaedron.

The figure IV. consists of twelve regular Pen-
tagons, and makes a Dodecaedron.

The flat paper figure close to b on the 12th
Plate, consists of six adjoining equal quadrangles,
and makes a Hexaedron, Die or Cube.

THE END.Books published by BoogEY and Soni, Broad Street, Ex-
change ; and to be had at T. Boosey and Co/s Foreign
Music Warehouse, 28, Holies Street, Oxford Street.

FAUSTUS, from the German of Goethe. A New
Translation, beautifully printed in 8vo. on fine paper, and embel-
lished with a correct Portrait of the Author, 6s. in extra bds.

It is not pretended that the following pages contain a full trans-
lation of this celebrated drama. The slight analysis drawn up as an
accompaniment to Retsch's Outlines being out of print, the pub-
lishers felt desirous to supply its place with a more careful ab-
stract of Faustus ; with this view, the most striking passages and
scenes of the original have been translated in blank verse, and con-
nected by a detailed description in prose.

The same Work printed in 4to. together with Retsch’s Series of
27 exquisite Outlines, illustrative of the Tragedy, engraved by
Henry Moses, in extra boards, 11. 1*.

The outlines may be had separately, boards, 15s.

SPECIMENS of the German Lyric Poets, consisting
of Translations in Verse from the Works of Burger, Goethe, Ja-
cobi, Klopstock, Schiller, &c. &c. interspersed with Biographical
Notices, and ornamented with Wood Cuts by the first Artists, 8vo.
boards, 8*. Royal 8vo- India proofs, 11. 5s.

Wood Cuts to the Specimens of German Lyric Poets, &c. India
proofs, inlaid and ruled, 4to. boards, 21*.

Favourite Songs (Twelve) in the above Specimens, with the ori-
ginal Music, 4to. Berlin, 1800. 3*.

The NATURE and GENIUS of the GERMAN

LANGUAGE, by D. BOILEAU. 8vo. boards, 12*.

This valuable work is strongly recommended both to those who
are beginning to learn this most copious of modern languages, and
to those who being already acquainted with it are desirous of ob-
taining a comprehensive knowledge of its peculiar characters and
beauties.—Eel. Rev. June 1821.Preparing fur Publication, in 12mo.

THE

ART OF WORKING IN PASTEBOARD;

EPITOMIZED FROM THE GERMAN,

BY

D. BOILEAU.

This little book, which has already gone through four editions
in Germany, is from the pen of one of the professors in the cele-
brated Seminary of Schnepfenthal, where such useful and inge-
nious arts are judiciously combined with the usual branches of
education.

It will be found well calculated for those who are desirous of
learning an agreeable manual occupation, cither as a matter of
amusement or emolument. . Parents and heads of Schools, who
are often at a loss how to furnish rational employment for the
leisure hours of their young people, will find this a suitable book to
put in their hands, as the art of which it treats is founded upon the
knowledge of Geometry.

And lastly, manufacturers of articles in pasteboard, by combining
a degree of Science with their manual experience, will be enabled
to save time and materials, and to give a greater perfection to
their productions.

W. WILSON, PRINTER. *7, SKINNER-STRF.ET, LONDOK.