iT^ Mo./o- 
 
 PRACTICAL 
 
 nANUAL= 
 
 TRAINING 
 
 AID. 
 
 HOW TO TEACH 
 
 PapBi-FoIilmg ^ Gutting 
 
 mm^ 
 
 MacLeod 
 
 MARCH BROTHERS, 
 
 Publishers, 
 
 LEBANON, OHIO. 
 
 LB 
 
 1542 
 
 .L5 
 
 Uq.. No. 10. 
 

 %0 
 
 LIBRAIF^OF CONGRESS. 
 
 UNITED STATES OF AMERICA. 
 
Manual-Training Series, No. 2 
 
 HOW TO TEAGH 
 
 PAPER-FOLDING AND 
 
 GUTTING 
 
 A PRACTICAL MANUAL-TRAINING AID 
 
 By^ MacLeod, \ 
 
 : Common , 
 tion 
 
 Author of" Lessons on Common Minerals," "Talks about Common 
 
 Things," " Practical Drill Problems," " Reproduction ^^A. 
 
 Stories," " Composition Outlines." 
 
 ^ '^^>:>X .:^^^ 
 
 <r.- f^ 
 
 1B92 
 
 uuif .^qj to92 / 
 
 3 % 2^9J ^ ' 
 
 LEBANON, OHIO 
 
 Mart)) %vot\)txSy l^ublisbcr? 
 
 1892 
 

 kii 
 
 U^ 
 
 COPYRIGHT 1892 BY MARCH BROTHERS. 
 
 Electrotyped, printed, and bound by 
 
 C. J. KREHBIEL & CO. 
 
 CINCINNATI. 
 
PREFACE, 
 
 T^HE author of this little book has endeavored 
 -■ to present in a brief and simple manner the 
 development of that portion of Manual Train- 
 ing which is usually designated as "Paper-Folding 
 and Cutting." Great care has been taken in the 
 arrangement of topics so that they may come in 
 natural succession, gradually increasing in difficulty 
 and awakening by their variety an ever new in- 
 terest in the minds of the pupils. The illustrations, 
 plentiful as they are, should not be considered as 
 all that are necessary or desirable. They are given 
 merely as samples of what may be done^ and, as is 
 stated more than once in the text of this volume, 
 pupils should be encouraged after a little instruc- 
 tion to form their own designs. 
 
 The benefits derived from this branch of Man- 
 ual Training are manifold. Neatness and accuracy 
 are developed in the mere manual operations, that 
 is, the cutting and pasting^ while the designing 
 
 3 
 
4 PREFACE. 
 
 calls into action a knowledge of drawing, love of 
 color and arrangement, and a cultivation of origi- 
 nality not to be surpassed by any other branch of 
 school work. The first step in this study — simple 
 grouping of plane figures — forms one of the class 
 of occupations for little fingers, so much in vogue 
 at the present time, known as "Busy Work." The 
 solid forms illustrated and explained in the latter 
 chapters will be found to form a useful basis both 
 for solid geometry and modeling in clay or wax. 
 Although originally intended as a guide for 
 teachers, the subject is treated in such a simple 
 manner, and there is such a total lack of technical 
 terms, that the book may be placed in the hands 
 of pupils of average intelligence, and its instruc- 
 tions be understood and applied by them without 
 
 difficulty. 
 
 MacLeod. 
 
Paper-Folding and Cutting 
 
 I 
 
 CHAPTER I. 
 
 NECESSARY IMPLEMENTS. 
 
 N order to have neat, accurate work, it is impera- 
 tive that each pupil be supplied with the neces- 
 sary helps, such as pencils, rulers, scissors, paper, 
 
 paste, etc. 
 
 The scissors should be about five inches long, 
 and the pencil medium hard, and sharpened to a fine 
 point. A ruler with a beveled edge is the most satis- 
 factory. Various kinds of glue and mucilage are 
 used for paper designs, but the writer, after numerous 
 experiments, decided that home-made paste of flour 
 and water answered the purpose better than anything 
 else. Bach pupil should be provided with a clean 
 rag with which to press the cut designs after pasting. 
 
 The art of folding and cutting paper can be taught 
 and learned just as well with the coarsest wrapping 
 
 5 
 
6 PAPER-FOLDING AND CUTTING. 
 
 paper as with paper of beautiful colors, but as the 
 taste of the pupils is to be cultivated quite as much 
 as skill in cutting, it is advisable to have the paper 
 as pretty as can be obtained. 
 
 THE SQUARE. 
 
 The square is taken as a basis for all the simplest 
 designs. Squares of paper are furnished to the 
 schools in many cities, and they can be bought at a 
 reasonable price at stationers. They are sold in 
 packages of one thousand, various colors represented 
 in each package. A four-inch square is a convenient 
 size for designs. 
 
 For the benefit of those who can not obtain these 
 squares, the following simple method of folding and 
 
THK SQUARE. 7 
 
 cutting a square is given. A piece of paper of any 
 shape may be used. Fold twice as represented in 
 the dotted lines A-B and C-D in figure No. i, and 
 the paper will assume the form shown in figure No. 2. 
 Fold again as indicated in this figure by the dotted 
 line E-F, and we have the paper in the shape repre- 
 
 % No. -2. 
 
 sented in figure No. 3. At the line H-K fold the 
 paper over evenly, making a right angle with the line 
 X-Y. This completes the folding, and if you cut 
 through the line H-K and open the paper, a square 
 will be the result. The size of the square is deter- 
 mined by the distance from K to Y. For instance, 
 if that measurement is two inches, you will have a 
 four-inch square. 
 
 FOLDING AND CUTTING. 
 
 It will be readily seen that the accuracy displayed 
 in the folding and cutting is a very important matter. 
 
8 
 
 PAPER-FOLDING AND CUTTING. 
 
 A few general hints may be found useful. Do not 
 fold the paper in the air, but lay it on a desk or table, 
 or any solid surface. Fold from the body and not 
 towards it. Press the folded paper evenly with the 
 thumb and forefinger. In cutting take long, deep 
 incisions, and not short, jerky ones. The latter 
 
 method produces an uneven edge, but if the scissors 
 are held firmly over the line to be cut, and as much 
 of the cutting performed with one closing of the 
 scissors as is possible, an even edge will be the result. 
 
 ARRANGEMENT OF DESIGNS. 
 
 The portion of this work requiring the most 
 delicate handling is the pasting of the design upon 
 the paper or cardboard used as a background. A 
 very little paste will go a long way, and as much as 
 would cover a silver quarter of a dollar will be suffi- 
 cient for the usual-sized design. The end of the 
 
ARRANGEMENT OF DESIGNS. 9 
 
 forefinger surpasses a brush as a means of applying 
 the paste. The design should be carefully placed in 
 position, and then one piece of it at a time taken up 
 and a thhi coating of the paste put on the under 
 surface of it. It must then be placed in position 
 again and pressed for a few seconds with the clean 
 
 Kg. No. ^ 
 
 rag ready for that purpose. Each section of the 
 design should be treated in the same manner 
 
 COLORS. 
 
 At first it is wise to use but one color in the 
 design, with white as a background. Later, as the 
 pupils grow more expert in designing, two or more 
 colors may be used. Such combinations as purple 
 and red, blue and green, etc., should, of course, not be 
 allowed, and the children should be shown combi- 
 nations producing a pleasing effect. Pale tints on a 
 dark background, and vice versa, are very pretty. 
 
lO PAPER-FOLDING AND CUTTING. 
 
 CHAPTER 11. 
 
 SIMPLE DESIGNS. 
 
 IN figure No. 5 is shown a design which is obtained 
 by one cut of the scissors. The square, which is 
 used as a basis for all the designs in this article, is 
 folded twice diagonally and then once more, bringing 
 the longest folded sides together. Compare your 
 folded paper with figure No. 4. Now draw a line 
 parallel to the longest folded side, as represented by 
 the dotted line L-M. Cut through this line and you 
 will then have five pieces of paper, which may be 
 arranged to form the design illustrated in figure No. 
 5. A little variety in the arrangement of the four 
 small sections of the design will produce the designs 
 represented by figures Nos. 6, 7, and 8. 
 
 Another design may be produced by one cut of 
 the scissors by folding the square as directed for the 
 designs just illustrated, but instead of cutting parallel 
 to the folded side, cut obliquely, as shown by the 
 dotted line O-P in figure No. 9. Five pieces are 
 again the result, a cross and four triangles. Arrange 
 the latter around the cross as in diagram No. 10, and 
 a very effective design is formed. 
 
SIMPI^E DESIGNS. 
 
 II 
 
 Another design may be made by the arrangement 
 shown in illustration No. ii. These triangles may 
 also be placed in positions similar to those in the 
 
 
 designs represented by figures Nos. 8 and 9. Still 
 another design can be made by folding the paper as 
 described, but the cutting must be parallel to the 
 short folded side as indicated by the line R-S, in 
 figure No. 12. After cutting, there is a cross and four 
 small squares. These may be arranged as in dia- 
 gram No. 13; while by placing them as shown in 
 figure No. 14, a design of equal taste is formed. 
 
12 
 
 PAPER-FOLDING AND CUTTING. 
 
 In illustration No. 15, the square is represented as 
 folded three times as in the previous designs. The 
 line- for cutting reaches from the angle A to the mid- 
 
 dle of the short folded side. The four triangles which 
 we have after cutting may be arranged around the 
 central portion of the square in the styles shown in 
 figures Nos. 16 and 17. 
 
 It would require unlimited space to illustrate the 
 numerous designs that can be made from a square, 
 folded as mentioned and cut but once. One more 
 lesson, however, is advisable, in order to explain 
 
SIMPLE DESIGNS. 
 
 13 
 
 figure No. 18. An octagon is obtained by this cut- 
 ting, and as, in a little while, designs, having this 
 figure as a basis, will be illustrated, it is necessary to 
 
 Eg: MoJ. 
 
 explain how the octagon can be obtained in a very 
 simple manner. The line A-C is drawn from one 
 folded side to the other so that the distance from A 
 to B will be the same as from C to B. The octagon 
 can be cut just as easily from any shaped piece of 
 paper, no matter how irregular. Figure No. 19 shows 
 a pretty combination of the octagon and small pieces 
 resulting from cutting a square as directed. 
 
H 
 
 PAPER-FOLDING AND CUTTING. 
 
 LINES AND ANGLES. 
 
 It must be remembered that although paper-fold- 
 ing and cutting are so-called mamial training exer- 
 
 cises, that is, hand trainings the brain is not allowed 
 to be idle during these exercises. Short talks about 
 lines, angles, and plane figures, should form a part of 
 every lesson. This can be done from the very begin- 
 ning. The square can be explained, and the children 
 
I.INES AND ANGLES. 
 
 
 15 
 
 FTg.. M.. 9 
 
 taught that its four corners are called right angles. 
 After folding three times a three-sided figure is 
 
 Fig. No. Id 
 
iU PAPER-FOLDING AND CUTTING. 
 
 obtained. Here teach the term triangle^ and ex- 
 plain that as one of the angles is a right angle, the 
 
 Tig. tlo. /^ 
 
LINES AND ANGLES. 
 
 17 
 
 triangle receives the name right-angled triajtgle. 
 Various styles of triangles are seen in the different 
 
 % Ho. /3 
 
 designs, and the terms aaite and obtuse may be used 
 to designate the angles in them. In talking of draw- 
 ing the lines, use the terms oblique^ vertical^ and /<?;-- 
 pendicular until the children can distinguish them at 
 a glance. In figure No. 18 a chance occurs to teach 
 the term octagon, also the isosceles triangle, as seen 
 
i8 
 
 PAPER-FOLDING AND CUTTING. 
 
 in A-B-C. Show that such a triangle has two equa. 
 sides, and state that if all three sides were the same 
 
 length, the triangle would be equilateral. When you 
 have cut and opened the octagon, let the pupils count 
 the number of triangles forming it. 
 
LINES AND ANGLKS. 
 
 19 
 
 Tiq.K.17. 
 
20 PAPER-FOLDING AND CUTTING. 
 
 Fs'l^ci^. 
 
 Tig No. /f 
 
DESIGNS FORMED BY CUTTING TWICE. 21 
 
 CHAPTER HI. 
 
 DESIGNS FORMED BY CUTTING TWICE. 
 
 BY folding the paper as in the former designs, and 
 making two cuts with the scissors, a variety of 
 elaborite designs can be formed, a few of which will 
 be illustrated here. In figure No. 20, the line D-E 
 
 Fig. McM 
 
 represents the edge of the square. By cutting as 
 indicated by the dotted line, a design like that shown 
 in figure No. 21 may be formed. The eight small 
 triang.les may be arranged around the center piece m 
 at least half a dozen different ways, in each case form- 
 ing a pretty design. Illustration No. 22 shows 
 another manner of cutting twice. F-H is the edge 
 of the paper and G is midway between these two 
 points. Four squares, four triangles, and a star-shaped 
 centerpiece result from these cuts. 
 
22 
 
 PAPER-FOLDING AND CUTTING. 
 
 Two designs formed from these pieces are shown 
 in illustrations Nos. 23 and 24. Ingenious pupils 
 will find many different ways of arranging the squares 
 and triangles. The line I-K in figure No. 25 indi- 
 
 Fcg-. No. ^/ 
 
 cates the edge of the paper, and the dotted line shows 
 that an acute angle is to be cut out of the folded 
 paper. As a result we have a peculiar shaped center- 
 piece and eight small triangles. The latter may be 
 arranged in many ways, one arrangement being shown 
 in figure No. 26. 
 
 A pretty and effective arrangement is shown in 
 figure No. 28. By turning the triangles around 
 another effect is produced. 
 
DESIGNS FORMED BY CUTTING TWICE. 
 
 23 
 
 No. 28 also shows two cuts, starting from the edge 
 of the paper L-M and forming an acute angle. The 
 triangles resulting from this cutting, eight in number, 
 are so irregular that to have a satisfactory design 
 they must be used in pairs. 
 
 Hg. No.^J. 
 
24 
 
 PAPER-FOLDING AND CUTTING. 
 
 MEASUREMENT. 
 
 Many pupils are extremely awkward in using the 
 ruler. They do not place it correctly on their draw- 
 
 % Mo .2^. 
 
 ings and fail to make a straight line. In cutting the 
 folded paper it is absolutely necessary, in order to 
 
 E^^oZS 
 
MEASUREMENT. 
 
 25 
 
 have a neat and perfect figure, that the lines should 
 be accurately drawn. Small, fractional measurements 
 
 also puzzle young pupils. They should be shown 
 how to draw lines whose lengths are estimated m 
 quarters or eighths of an inch. 
 
26 
 
 PAPER-FOIvDING AND CUTTING. 
 
 Ivittle more need be said about folding and cut- 
 ting designs in which straight cuts are made. A 
 couple of designs are here shown in which three cuts 
 have been made. Figure No. 29 shows the folded 
 
 n-^ Mo.^s'. 
 
 paper, the dotted lines indicating the lines for cut- 
 ting. In figure No. 30 we have the paper opened and 
 arranged in a pleasing design. Several different ways 
 of placing the small pieces of paper are allowable, 
 and it is a good idea to let the pupils exercise their 
 own taste in the matter. The vacant space in the 
 center of the design may be left as it is, so that the 
 background will show through, or the small piece of 
 paper which has been cut from it may be cut into 
 some fanciful shape and placed in the center of the 
 
MEASUREMENT. 
 
 27 
 
 space. In figure No. 31 three cuts are made as shown 
 by the dotted lines. Figure No. 32 illustrates a 
 simple arrangement of the pieces resulting from this 
 style of cutting. 
 
 iTjr. Ko. SO. 
 
28 
 
 PAPKR-FOIvDING AND CUTTING. 
 
 CURVED I^INKS. 
 
 " Curved is the line of beauty," some one has 
 written, and the truth of the statement is demonstra- 
 ted in paper-cutting designs. A true eye and a steady 
 
 ri-^.No.32. 
 
CURVED I.INES. 
 
 29 
 
 hand are necessary to draw and cut such lines. The 
 compass may be used to advantage in many designs 
 presenting curved lines. Figure No. 33 represents 
 
 FgMjs 
 
 the paper square folded as for previous designs. 
 Carefully draw lines such as are indicated by the 
 dotted lines in this figure, and then cut slowly through 
 the lines. A long, sharp cut, such as was advised in 
 
 fc^ No J^ 
 
30 
 
 PAPER-FOIvDING AND CUTTING. 
 
 designs with straight Hnes, can not now be used. The 
 scissors should not be removed from the paper until 
 the entire curve is cut. Turn the paper slowly until 
 
 Fig. No. 3^ 
 
 each portion of the line to be cut comes under the 
 edge of the scissors. Considerable practice will be 
 
 Rg No J6 
 
CURVED I.INES. 
 
 31 
 
 necessary before curved lines can be accurately cut 
 by the pupils. 
 
 Ilo.Hoj/ 
 
 Figure No. 34 represents a design made by cut- 
 ting as shown in figure No. 33. Here the center space 
 is left vacant, but the paper cut from this space may 
 
 leg. N'o.J^ 
 
 be cut into a circle and inserted in the center with 
 pretty effect. A simple combination of curved lines 
 is shown in figure No. 35. A design representing one 
 
32 PAPER-FOLDING AND CUTTING. 
 
 arrangement of the papers from this cutting may be 
 seen in figure No. 36. The small pieces may be 
 turned so that the curved sides face the centerpiece, 
 and quite a different effect will be produced. 
 
 A more complicated style of drawing and cutting 
 is illustrated in figure No. 37, being difiicult cutting, 
 but the pasting more simple, as the small pieces may 
 be discarded. Through the open spaces in this de- 
 sign the background shows plainly. In figure No. 38 
 the design is pasted first onto a four-inch square of a 
 color that will combine well with the cut paper, and 
 then the whole figure is pasted onto a larger sheet of 
 white drawing-paper. Quite an elaborate effect is 
 thus obtained in a simple manner. 
 
COLOR COMBINATIONS. 33 
 
 CHAPTER IV. 
 
 COLOR COMBINATIONS. 
 
 UNTIL this stage of designing is reached, it is ad- 
 visable to use but one color for the cut designs, 
 with white as a background. Now, to vary the ex- 
 ercise, the following method might be adopted: retain 
 
 Eg. No. J f 
 
 the white as a background, but allow the pupils to 
 exchange the small pieces of the designs with one 
 another. Be sure, however, that they exchange all 
 pieces of similar size and shape for others all of the 
 same color. If there are four small triangles and a 
 centerpiece, the centerpiece should be one color and 
 the four small pieces should all be of the same color, 
 and of a color that will combine well with the center- 
 piece. For instance, in figure No. 34, the background 
 might be white, the large portion of the design a pale 
 
34 
 
 PAPER-FOLDING AND CUTTING. 
 
 green color, and the eight little triangular pieces of 
 a pale pink or some color that will harmonize prettily 
 with the green. 
 
 n^,I\/o.¥0 
 
 New interest will be added to the lessons by this 
 little change of programme, and at the same time the 
 tastes of the pupils will be cultivated. A little talk 
 about primary and secondary colors will be instruct- 
 ive and in order, while these color combinations are 
 being made. 
 
COLOR COMBINATIONS. 
 
 35 
 
 In figure No. 39 we have a drawing, which, when 
 cut and opened, can be so placed as to make very 
 
 elaborate designs. Figure No. 40 illustrates one 
 arrangement. The placing of the small pieces of 
 
 n<^hfo.^^ 
 
 paper may be reversed and another pretty design will 
 be the result. If desired, some of the small pieces 
 
36 PAPER-FOLDING AND CUTTING. 
 
 may be discarded. The plan of exchanging papers, 
 advised in the last lesson, will be found very satis- 
 
 n^. ^0. ¥S. 
 
 factory in this design. Three colors may be used, 
 the centerpiece being of one color, four small pieces 
 
 %. No. ¥'ji 
 
COLOR COMBINATIONS. 
 
 37 
 
 of similar shape of another color and the four remain- 
 ing pieces of a third color. Figure No. 41 shows a 
 
 /7^. No. VJT 
 
 combination of curved cuts. If the small pieces are 
 discarded and the elaborately cut centerpiece is 
 
 /7^ No, y'<^, 
 
 arranged over a contrasting color, a pleasing effect 
 will be produced. x\rranged simply on a white back- 
 
38 
 
 PAPER-FOIvDING AND CUTTING. 
 
 ground, it has the appearance indicated by illustration 
 No. 42. Straight cuts and curves both appear in 
 figure No. 43. It is advisable to use the small tri- 
 
 Ilg.Mo-'/^t 
 
 angles resulting from these cuts, as a much more 
 elaborate design can thus be formed. An easy ar- 
 Tangement of these triangles is shown is figure No. 
 
 44. The triangles can be arranged in many ways. 
 A small star or circle placed in the center of the 
 design, where the background shows, will add greatly 
 
COLOR COMBINATIONS. 39 
 
 to the effect. Another combination of straight and 
 curved lines is shown in figure No. 45. Opened and 
 arranged as in iUustration No. 46, with a four-inch 
 square of another color placed under it, and then the 
 whole design pasted on white paper, a very beautiful 
 figure is produced. Call the attention of the pupils 
 to the small octagon in the center of the figure. 
 
 Rather complicated cutting is represented in 
 figure No. 47. By easy degrees the pupil has been 
 led to that point where he can without hesitation 
 make a multiplicity of cuts. It is suggested that this 
 design also be placed over a square of a contrasting 
 color as represented in figure No. 48. 
 
40 
 
 PAPER-FOLDING AND CUTTING. 
 
 CHAPTER V. 
 
 ORIGINAL DESIGNS. 
 
 BY this time pupils possessing an atom of origi- 
 nality will be anxious to try a design "all their 
 own," as they say, and I should counsel the teacher to 
 indulge this desire. All children do not possess the 
 
 Kg. No. ^9 
 
 Ti^. No. 50. 
 
 same artistic taste and skill, therefore when their 
 originality has full play the results obtained from 
 different pupils will vary greatly. Some scholars can 
 produce designs of great beauty with apparent ease, 
 while others, after steady work and patient plodding, 
 have nothing to offer but commonplace lines and 
 angles that recall the first lessons on this subject. 
 
SHOW-WORK. 
 
 41 
 
 SHOW-WORK. 
 
 As an incentive to the pupils and an encourage- 
 ment in their artistic labors, it is an excellent plan to 
 
 FtgNo SI 
 
 select a few designs at the end of each lesson and 
 keep them as samples of the work done. They may 
 
 be used to decorate the walls of the class-room, or 
 arranged in a scrap-book 
 
 I would suggest that the 
 
42 
 
 PAPER-FOLDING AND CUTTING. 
 
 naturally dull pupil should be occasionally encourage- 
 ed by having his conscientious efforts (even if plain 
 and unattractive in effect) selected and placed among 
 the designs reserved for special inspection. 
 
 LEAF DESIGNS. 
 
 The teacher can now make use to some extent 
 of the lessons in free-hand drawing. Conventionalized 
 
 leaves and flowers have probably formed a portion of 
 the free-hand instruction, and these same leaves and 
 flowers may be cut from folded paper and formed 
 into pretty designs. Illustration No. 49 represents a 
 lilac leaf, true to nature, and the same leaf conven- 
 tionalized is shown in figure No. 50. Explain right 
 here the difference between a natural leaf and a con- 
 ventional one. As both sides of a conventional leaf 
 are exactly the same, the folded paper is so arranged 
 that a drawing of but one half of the leaf is made. 
 See figure No. 51 in which the same lilac leaf is used, 
 half of it being outlined. The paper is folded as in 
 
LEAF DESIGNS. 
 
 43 
 
 all preceding lessons, and the midrib of the leaf is 
 placed on the longest side of the folded triangle. The 
 stems all point toward the center of the paper. Care 
 must be exercised not to cut through the stems by 
 
 mistake. Opened and arranged upon a square of 
 paper of a harmonizing color, the design appears as 
 represented in figure No. 52. If the stems are weak 
 in the center where the paper has been folded so 
 many times, a small circle, such as is shown in this 
 figure, or a star or square may be placed in the center 
 of the design. It will serve the twofold purpose of 
 hiding the creases in the stems and adding to the 
 
44 
 
 PAPER-FOLDING AND CUTTING. 
 
 beauty of the design. Another simple leaf is shown 
 in figure No. 53 which, when drawn on folded paper 
 for cutting, appears as indicated in illustration No. 54. 
 
 Opened and placed over a square of a contrasting 
 color, it forms the design seen in figure No. 55. The 
 square of paper placed under the leaves may, if pre- 
 ferred, be arranged in a similar position to that in the 
 former design, with the corners beneath the tips of 
 the leaves. The elaborate design pictured in figure 
 No. 56 is obtained in a very simple manner. It con- 
 sists of two squares of paper of different colors, folded 
 and cut as shown in figure No. 54, and then one 
 
I.EAF DESIGNS. 45 
 
 paper placed above the other in such a manner that all 
 eight leaves can be seen. In delicate tints that form 
 a pleasing combination, and with white as a back- 
 ground, the result is very effective. The veining of 
 the leaves is a matter that depends upon the individ- 
 ual taste of each teacher. In the designs pictured 
 here the principal vein is drawn, but it may be 
 omitted, or all the veins may be drawn. 
 
46 
 
 PAPER-FOLDIJ^G AND CUTTING. 
 
 CHAPTER VI. 
 
 LEAF DESIGNS. 
 
 IN figure No. 57 we have a more difficult leaf. 
 Arranged on the folded paper as explained in the 
 previous lesson, it is represented in figure No. 58. A 
 
 No 57. 
 
 pretty design formed of these leaves is shown in the 
 next drawing. A square of paper of a contrasting 
 color is placed under the leaves as a background. In 
 all leaf designs great care must be ^exercised in cut- 
 ting and pasting the stems, which are so slender and 
 have so many creases that they are easily torn. The 
 ivy leaf represented in the next figure. No. 60, will be 
 found both simple and graceful for designing pur- 
 poses. Draw as illustrated in figure No. 61, having 
 
LEAF DESIGNS. 
 
 47 
 
 the points of the leaves touch the edges of the folded 
 paper. In cut No. 62 we have one arrangement of 
 
 Ti^,Ss^ 
 
 ivy leaves. Here, again, a square of another color is 
 used as background. The square may be placed in 
 
 Ug.Mo.^y 
 
 the same position as in the previous design if so de- 
 sired. A conventionalized maple leaf next claims 
 
48 
 
 PAPER-FOLDING AND CUTTING. 
 
 our attention. See figure No. 63. It is so pretty in 
 itself and is made up of such graceful curves that a 
 design formed of such leaves can not help but be 
 pleasing. Draw as indicated in figure No. 64. Illus- 
 
 N06O 
 
 tration No. 65 shows the leaves unfolded and spread 
 in position. No additional decoration is needed. 
 Figure No. 66 represents a leaf of the oxalis, which 
 from its peculiar shape is very effective as a basis for 
 
 rig- MM 
 
 ornamental designs. The long stems may be short- 
 ened by drawing at their base as shown in figure No. 
 67 and when opened a pretty centerpiece will appear 
 which will add greatly to the beauty of the design. 
 
LEAF DESIGNS. 49 
 
 Figure No. 68 shows the design formed from this 
 drawing. In this design, as in all the others here 
 
 Eg. No. U 
 
 shown, a contrasting square of paper used as a back- 
 ground will add much to the general effect. A com- 
 bination of leaves is shown in the next design. 
 
 •^^.No6S 
 
 The necessity for careful drawing and cutting is 
 greatly increased but the appearance when completed 
 
50 
 
 PAPER-FOLDING AND CUTTING. 
 
 compensates for the extra trouble. But one style of 
 leaf is used in the design, one leaf being consider- 
 
 ably smaller than the other. See figure No. 69. 
 
 When opened and pasted as illustrated in figure No. 
 
LEAF DESIGNS. 5^ 
 
 70, this design is very elaborate and looks even more 
 
 difficult than it really is. If eight leaves of the same 
 
 size are desired, draw one on the folded paper as 
 
 ■ngN.bf. 
 
52 
 
 PAPER-FOIvDING AND CUTTING. 
 
 shown in figure No. 71. When opened the leaves 
 will form a circle as represented in the next design. 
 The long, delicate stems are shortened by drawing 
 the centerpiece as indicated in the illustration. 
 
 i7^ ^o./O: 
 
 If a circle of darker color be placed under the 
 leaves a very showy effect is produced, as shown in 
 figure No. 73. 
 
LEAF DESIGNS. 
 
 53 
 
 F,g f/o 7JZ.. 
 
 K^.^^o.yJ^ 
 
54 
 
 PAPER-FOLDING AND CUTTING. 
 
 CHAPTER VII. 
 
 POLYGONS. 
 
 IN all the previous designs illustrated in these lessons 
 on folding and cutting paper, the square has been 
 used as a basis. This was considered wise for several 
 reasons. vSquares are simple to cut and easily fold- 
 
 ed, and above all other considerations, was the one 
 that, in many cities where such work is desired in 
 the schools, colored paper, cut in squares of a con- 
 venient size, could be obtained. It is time now, how- 
 ever, to consider plane figures having more than four 
 sides. One, the octagon, has already been shown, and 
 an explanation given how the figure may be easily 
 cut. We will now take the pentagon, hexagon, andi 
 heptagon. Explain to the pupils the derivations and 
 meanings of these words so that they will thoroughly 
 understand what you are talking about. 
 
POLYGONS. 
 
 55 
 
 These figures can be cut from paper of any size or 
 shape, but for convenience we will first cut them from 
 the squares, such as we have been using all along. For 
 
 the hexagon, fold the paper once across, as shown m 
 figure No. 74. Then with the folded side down, from 
 the center A, fold the paper as illustrated by the dotted 
 lines in this drawing. Fold the paper carefully, and 
 
 do not press it down firmly until you have divided 
 the folded oblong into three exactly equal parts. 
 Much precision is necessary, and there should be no 
 
56 
 
 PAPER-FOLDING AND CUTTING. 
 
 undue haste. No. 75 represents the folded paper. 
 Now draw the line B-C, forming an isosceles triangle ; 
 that is, B-A is the same length as C-A. Cut through 
 
 this dotted line and open the paper^ Illustration No. 
 76 shows the result of our folding and cutting, a per- 
 fect six-sided figure, or hexagon. For the pentagon, 
 even greater care is necessary, for instead of folding 
 into equal parts, we fold so as to have two equal parts, 
 and a part equal to half of one of these sections. 
 
 Fold the squares as for the hexagon (see figure No. 77), 
 and then double the paper over until it presents the 
 appearance shown in figure No. 78. Form the isos- 
 celes triangle as in the previous polygon by drawing 
 
POLYGONS. 
 
 57 
 
 through B-C. Opening the folded paper, a pentagon 
 appears as represented in figure No. 79. Similar fold- 
 ing is required to cut the heptagon. Three equal 
 
 ^o.7f. 
 
 sections are folded and then a portion equal to half of 
 one of these parts. Figure No. 80 shows the direc- 
 tion of the folds, and figure No. 81 the appearance of 
 the paper when folded. Cut through the line B-C. 
 
 Uo U 
 
 Illustration No. 82 shows the result. In all probabil- 
 ity many trials will be needed before perfect poly- 
 gons will be cut. The eye must be trained. After 
 
58 
 
 PAPER-FOLDING AND CUTTING. 
 
 practicing with the squares, take irregular-shaped 
 pieces of paper and fold and cut them. 
 
 POLYGONS AS A BASIS FOR DESIGNS. 
 
 Very beautiful designs can be formed from these 
 polygons. It will be readily seen that anything 
 drawn on one of the folded triangles forming the 
 
 j^o. n. 
 
 polygon, will be repeated on the other triangles when 
 the design is cut. Figure No. 83 shows a simple 
 design based upon the pentagon. The same orna- 
 
POIvYGONS. 
 
 59 
 
 mental drawing appears five times. In figure 84 a 
 more elaborate design is shown, cut from the hexagon, 
 and in illustration No. 85 the heptagon was the basis. 
 
 Xo. fd. 
 
 These polygons afford a large field for the originality 
 of the pupils. Church and cathedral windows are 
 often designed from these shapes, and an intelligent 
 
 child may get pretty ideas from them. Figure No. 86 
 shows the folded hexagon with very simple drawing 
 upon it, composed entirely of straight lines. When 
 
6o 
 
 PAPER-FOLDING AND CUTTING. 
 
 cut and arranged as in figure No. 87, a very effective 
 design is formed. A circle, cut from paper of con- 
 trasting color and placed under any designs formed 
 from these polygons, adds much to the appearance. 
 
 J^o.^S 
 
 As far as possible the teacher should work with the 
 pupils. He should have a larger square of paper and 
 fold and cut it in plain view of the scholars. If the 
 blackboard be moistened by passing a damp sponge 
 over it, and the paper design pressed into the dampen- 
 
 jVo ^(0 
 
 ed surface, it will adhere for quite awhile. Occasion- 
 ally allow a pupil to arrange a design on the board 
 and it will stimulate the whole class to greater efforts. 
 Again, I repeat, do not have this lesson too entirely 
 
POLYGONS. 
 
 6l 
 
 manual or ''^ of the hand^ " but make the brains do their 
 share of the work. Have all the terms used during 
 the lesson defined and thoroughly understood. Dis- 
 
 cuss lines and angles at length, and lead the pupils 
 to make comparisons between the different poly- 
 gons. When the latter are irregular and out of pro- 
 portion, do not indicate the incorrect places, but 
 make the pupils find them. The leaf designs used 
 for the squares in a former lesson will be particularly 
 graceful in designs based upon these polygons. For 
 instance, the ivy or maple leaf, repeated six times as 
 it would be in a hexagon, the stems meeting in the 
 center, would form an elaborate figure. 
 
62 
 
 PAPER-FOLDING AND CUTTING. 
 
 CHAPTER VIII. 
 
 BORDERS. 
 
 THE subject of paper-cutting, as far as squares 
 and polygons are concerned, is by no means 
 exhausted ; in fact, it may be said to be ijzexhaustible^ 
 but if the teacher has carefully read and applied the 
 
 
 ^•'' 
 
 
 
 
 
 
 
 y^ 
 
 ^^ 
 
 " ^ 
 
 
 ,^ 
 
 
 •■ 
 
 
 \ 
 
 
 ^ 
 
 
 ^ 
 
 
 »^ 
 
 
 
 
 "'"-v,^ 
 
 '^'- 
 
 
 ''-^.^ 
 
 E^.Mo. 
 
 .0^. 
 
 Eg. M. rr 
 
 preceding chapters he will be able to continue giving 
 lessons of the style without any special directions. 
 
 It is therefore unnecessary to take up any more 
 space on the same figures. We will now consider 
 borders^ and if my experience in teaching is repeat- 
 ed, the pupils will hail the change with delight. A 
 good size for decorative borders is six by two inches, 
 and before the fancy work is commenced the paper 
 should be cut into slips of said size. For most bor- 
 
BORDERS. 
 
 63 
 
 ders it is prettier to fold the paper into six divisions, 
 each an inch wide. First fold the slips of paper in 
 half, so that it measures three by two inches. Now 
 you must, by carefully measuring with the eyes and 
 fingers, fold this into three parts. Fold in accordion 
 
 style as shown in No. 88, for if you fold one division 
 in and the others around it, the inner division will 
 be slightly smaller than the others. By folding as 
 represented, pleating it in fact, all the divisions will 
 
 n^.ifo.f/. 
 
 be the same size. Figure No. 89 represents the fold- 
 ed paper, with a simple design drawn upon it. The 
 drawing is made up entirely of straight lines, and will 
 be found simple and useful to a beginner. In figure 
 
 With a background 
 
 No. 90 the open paper is shown. 
 
64 
 
 PAPER-FOLDING AND CUTTING. 
 
 of a contrasting color the appearance is much im- 
 proved. 
 
 A combination of straight and curved lines is 
 shown in illustration No. 91, and 92 shows the opened 
 
 paper. A strip of dark paper, six inches long and 
 two inches wide, is placed under the cut work, and in 
 this way a very showy effect is produced. Careful 
 drawing is required for the next design, but the result 
 is well worth the trouble. Curved lines alone are 
 used. See figure No. 93. The border resulting from 
 
 Jio.p 
 
 drawing and cutting as indicated is remarkabl}^ pretty 
 and will be found to be a favorite with most pupils. 
 In illustration No. 94 this border is shown. It would 
 be advisable to practice drawing and cutting borders 
 
BORDERS. 
 
 65 
 
 no more difficult than this for several lessons. The 
 pupils' originality should be allowed full play, and 
 many of the designs given for squares may be adapt- 
 ed to borders. A difficult desien is illustrated in 
 
 n^g-JTcfif- 
 
 figure No. 95, the result of cutting as shown by the 
 dotted lines being the elaborate border represented 
 by figure No. 96. 
 
 Hp N'o. /Jf 
 
 LEAVES FOR BORDERS. 
 
 We can now make use of leaves for decorative 
 borders and find them quite as attractive as in former 
 designs. A conventional leaf is used as the basis of 
 the next design, with a small ornamental figure as 
 connecting link between the leaves. See figure No. 
 
66 
 
 PAPER-FOLDING AND CUTTING. 
 
 97. Right here I must caution both teacher and 
 pupils not to forget the connecting links between the 
 
 ru-^'^-~-J7*^-._-J7 
 
 I ^-- ^ ^- ^ ^--.-^^ 
 
 principal figures of the design, or the amusing ex- 
 perience of a certain city pupil may be repeated. 
 
 
 The pupil carefully drew and cut an elaborate design, 
 He opened the paper with considerable pride, expect- 
 
 ing to be highly complimented for his skill, when to 
 
BORDERS. 
 
 his consternation he found that instead of a border 
 he had only a number of pretty figures. There must 
 
 '-- 
 
 
 
 \ 
 
 
 "^'1 
 
 > 
 
 
 < 
 
 L-^ 
 
 
 ' ' f ~^ 
 
 ■- — 
 
 
 
 y 
 
 always be some portion of the design which runs the 
 entire length of the border. It need be nothing but 
 
 Kff M>. /M 
 
 a straight band, or the severity may be broken as 
 in the figure under discussion. The effect may be 
 observed in figure No. 98. Unconventional leaves, or 
 
 /c> J\^o- m 
 
68 PAPER-FOLDING AND CUTTING. 
 
 leaves coming naturally, may be used for borders. 
 The ivy-leaf is a general favorite, and may be drawn 
 as shown in representation No. 99. In this case the 
 ^aper is folded in four equal parts, each space for the 
 leaf being two by one and a half inches. A curved 
 
 Tt'^'Mo. /a-z. 
 
 line runs from leaf to leaf. In figure No. 100 the 
 elaborate border formed of these leaves is shown. 
 Fold the paper in the same way and draw a leaf 
 crosswise as shown in figure No. loi, and an odd and 
 pretty effect will be produced. The border thus 
 formed is shown in figure No. 102. These leaf designs 
 wi'll be greatly beautified by placing dark slips of 
 paper under them so that the edges of the leaf will 
 stand out in bold relief. Taking these designs as 
 models, and using different leaves, a great variety of 
 borders may be cut. The leaves of the oxalis and 
 maple, illustrated in a former chapter, will be found 
 graceful in border designs. Variety may be produced 
 by folding the slips of paper in a more or less number 
 of parts. For class-room decoration an oblong of 
 
BORDERS. 69 
 
 paper of a deep tint, with cut Dorders placed one 
 under the other at equal distances, forms a pretty 
 wall ornamentation, and serves at the same time as a 
 sample of the pupils' taste and skill in paper-cutting. 
 
PAPER-FOLDING AND CUTTING. 
 
 CHAPTER IX. 
 
 SOI.IDS. 
 
 LEAVING the ornamental squares, polygons, and 
 borders, we now take quite an important step 
 forward in our paper-folding and cutting. We will 
 develop in paper numerous solid, geometrical forms. 
 The implements necessary are pencil, compass, ruler, 
 
 and stiff, white drawing-paper. Also the best paste 
 that can be obtained. In all lessons relating to the 
 cutting of paper so as to make solid forms the form 
 itself should be before the class as a model. These 
 
SOLIDS. 
 
 71 
 
 forms may be bought, made of wood, at reasonable 
 prices, or the pupils may make their own models of 
 
 _/ 
 
 Eg. No. 
 
 /^^ 
 
 clay, clay-modeling being a portion of manual training 
 that usually either precedes or accompanies paper- 
 Before any drawing is commenced the 
 
 cutting. 
 
72 
 
 PAPER-FOLDING AND CUTTING. 
 
 pupils should be led by skillful questioning to form 
 ideas of how the drawings should be arranged. For 
 instance, take a cube as model. (See figure No. 103.) 
 
 JT^J^.//. 
 
 Tl^. jfp. /fi^c 
 
 Questions — " How many faces has it? What is the 
 shape of each face? How many angles altogether? 
 What kind of angles?" 
 
 Then place the cube on one of its faces and turn it 
 until it has stood on four face-s in succession, that is, 
 turn it as you would a wheel. These four faces will 
 be seen to be in a straii^ht line. Let the pupils then 
 
SOLIDS. 
 
 73 
 
 draw four equal squares in a row, as shown in figure 
 No. 104. A two-inch square is a convenient size. 
 Now examine the model again and call the attention 
 of the pupils to the position of the remaining square 
 faces and then complete the plan, as seen in No. 104. 
 
 The little flape indicated by the dotted lines are to 
 hold the paste when the paper cube is cut and folded. 
 In folding, keep one square entirely free of paste and 
 fold all the others, keeping the thumb and finger 
 pressed against the edges to be pasted. The finish- 
 ing requires great delicacy of touch. Haste is to be 
 avoided. Do not squeeze the figure or it will collapse. 
 In fact, the writer might fill a column with "Don'ts," 
 but the intelligent teacher will in one lesson learn 
 what to do and what to avoid in this department of 
 paper-folding. Do not expect many perfect figures at 
 first. The development of these forms is by no 
 means easy, and practice and patience will be neces- 
 sary before success will be acquired. The wall-pocket 
 
74 
 
 PAPER-FOLDING AND CUTTING. 
 
 represented in figure No. 105, and the box shown in 
 figure No. 106, are modifications of the cube. In the 
 latter figure the front of the box is ornamented with 
 a cut design in colored paper. From the cube to tjie 
 box form shown in illustration No. 107 is an easy 
 step. By turning the model the pupils may be led to 
 see that the four narrow sides form a continuous line, 
 and the position of the squares forming the top and 
 bottom of the box will be readily understood. The 
 plan is shown in figure No. 108. In this case the top 
 and bottom were two-and one-half-inch squares and 
 the sides were an inch high. A plan for an oblong 
 box is shown in next figure, No. 109. 
 
 PRISMS. 
 
 
 
 
 ,-'" 
 
 \ 
 
 
 
 
 
 
 
 
 
 / 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 TigJf^/n 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X 
 
 
 
 i:jif.,»j 
 
 
 
 
PRISMS. 
 
 75 
 
 The square prism, being an elongated cube, would 
 naturally follow here. The four oblong faces (see 
 figure No. no) will be seen to be in a straight line. 
 
 T^^.No 
 
 z/^- 
 
 and must be drawn as shown in illustration No. in. 
 The squares are next drawn, and the plan is complete. 
 The same directions that were given for pasting the 
 cube will apply to the prism. The box shown in 
 figure No. 112 is made by leaving one of the oblong 
 faces of the prism open. See if the pupils can form 
 anything else from the prism. 
 
76 
 
 PAPER-FOLDING AND CUTTING. 
 
 r 
 
 I, 
 
 
 \ 
 
 
 
 
 
 ( 
 
 
 ^ 
 
 \ 
 
 
 '': Kgf/,.u 
 
 
 
 THE TRIANGULAR PRISM. 
 
 Place a triangular prism before the pupils (see fig- 
 ure No. 113), side by side with the square prism, and 
 let them tell the points of resemblance and difference, 
 viz: Its sides are oblongs. It is tall and slender. 
 The oblongs are in a row. It only has three faces. 
 The bases are triangles, not squares. 
 
 Draw the oblong sides, and from the opposite ends 
 of one of the sides draw the triangles forming the 
 bases. To draw the triangle accurately and quickly, 
 use the compass. 
 
 Take the corners of each end of one of the faces 
 as a center, in turn, and with the width of the oblong 
 as a radius describe arcs as shown in figure No. 114. 
 Complete the triangles by drawing straight lines from 
 
PRISMS. 
 
 11 
 
 the corners of the oblongs selected, to the intersection 
 of arcs. Draw flaps for pasting, as indicated by the 
 
 Tt.g. J^^'c. //^. 
 
78 
 
 PAPER-FOLDING AND CUTTING. 
 
 dotted lines. As all three sides of these triangular 
 bases are equal, the prism may be described as an 
 "equilateral triangular prism." All triangular prisms 
 
 
 F.''&.H' 
 
 ( 
 
 i 
 
 X 
 
 V 
 
 \> 
 
 
 
 ! 
 ! 
 
 1 
 
 ! 
 s 
 
 { 
 j 
 
 
 
 
 
 n_g.£.,/s- 
 
 
 are not necessarily equilateral. The triangles may 
 be right-angled, isosceles, or irregular. In each case 
 the three sides of the prism will be oblongs, but not 
 
 prisms of the same size. Each of the three sides of 
 the triangular bases must have an oblong that will 
 agree with it in width. Examine figure No. 115, and 
 
PRISMS. 
 
 79 
 
 no further explanation will be needed. The plan for 
 a right-angled triangular prism is here shown. Two 
 of the sides of the triangle are equal, the third side 
 
 being considerably longer. The faces of the prism 
 must correspond in width with the lengths of the 
 sides of the triangle. A modification of the triang- 
 ular prism is shown in the triangular box represented 
 in figure No. ii6. The sides are an inch high, and 
 the plan is shown in figure No. 117. 
 
8o PAPER-FOLDING AND CUTTING. 
 
 CHAPTER X. 
 
 SOLID FORMS. 
 
 FROM prisms to pyramids is a natural and simple 
 step. In figure No. ii8 we have a representation 
 of a square pyramid. Place your model of this form 
 side by side with the square prism, already discussed, 
 and let the pupils name the points common to each, 
 also the respects in which the models differ. They 
 will observe that each of the models has a square 
 base and four sides, but in the case of the prism these 
 four sides are oblongs, while in the pyramid they are 
 triangles, joined so as to form a common vertex. In 
 drawing the plan on paper it will, therefore, be under- 
 stood that there must be four triangles, equal in all 
 respects, and one square which serves as the base. 
 The preliminary steps for drawing the plan of any 
 pyramid are shown in figure No. 119. The straight 
 line A-B is first drawn, the length of the sides of the 
 pyramid. Then with a radius equal to the length of 
 the line describe an arc of considerable length, as 
 shown by C-D. Examine illustration No. 120 and 
 you will see what the next steps are. Decide how 
 wide the triangular sides of the pyramid are to be at 
 
SOLID FORMS. 8l 
 
 their bases and arrange your compass so as to have a 
 radius of the desired length. With this radius place 
 your compass on B and draw arcs cutting C-D. From 
 these points of intersection as centers, and with the 
 
 same radius, draw two more arcs and connect the 
 points so formed by straight lines with point A. 
 Draw straight lines from point to point for the bases 
 of the triangles, and you then have the plan for the 
 four sides of your pyramid. For the base of the 
 pyramid select the base of either triangle and erect 
 thereon a square. Draw the narrow edges for past- 
 ing, and cut and paste as in previous forms. Pyr- 
 
82 
 
 PAPER-FOLDING AND CUTTING. 
 
 amids may have any number of sides, but in all cases 
 the manner of proceeding is the same. In No. 121 
 is shown the diagram of a triangular prism. Three 
 triangles form the sides, and an equilateral triangle 
 the base. To draw the equilateral triangle, use the 
 
 compass as directed in the last lesson for the triangu- 
 lar prism. It is a good idea in studying the formation 
 of pyramids to always compare each pyramid with a 
 prism having a corresponding number of sides. The 
 hexagonal pyramid is shown in No. 122. Six equal 
 triangles form the sides, and the hexagon, a plane 
 figure having six equal sides, forms the base. As 
 this is the first time we have been required to draw 
 a hexagon it will be in order to give a short and 
 simple method for this drawing. Draw a straight 
 line as shown in the next illustration, and with half 
 
SOLID FORMS. 
 
 83 
 
 the length of this line as a radius draw a circle. With 
 the same radius, and each end of the line as a center 
 in turn, cut the circumference on each side as indi- 
 cated in figure No. 123. Connect the points of inter- 
 
 section by straight lines and a perfect hexagon will 
 be the result. In representation No. 124 the plan for 
 the hexagonal pyramid is to be seen. Six triangles 
 are drawn with a common vertex, and the base of one 
 of them forms one of the sides of the hexagon for the 
 base of the pyramid. The hexagon is drawn in the 
 manner just described. To find the point which is 
 to be used as the center of the circle, proceed as if 
 
84 
 
 PAPER-FOLDING AND CUTTING. 
 
 you were drawing an equilateral triangle. {See pre- 
 vious chapter}) Then take the intersection of arcs 
 as a central point, and the length of the bases of the 
 triangles as a radius. 
 
 When the triangles forming the sides and base of 
 a triangular pyramid are all equilateral, the pyramid 
 is called an equilateral triangular pyramid. See fig- 
 ure No. 125. The next figure shows the plan for 
 this solid. It is very simple, and requires no special 
 explanation. Draw the large triangle first, then 
 arrange your compass so as to have a radius equal to 
 half of one of the sides of this large triangle, and do 
 not change the radius until the figure is complete. 
 
SOLID FORMS. 
 
 85 
 
 n^ M yj. 
 
 %. Jfo. /^c^ 
 
86 
 
 PAPER-FOLDING AND CUTTING. 
 
 Bff.-tL./s¥. 
 
 K^g.Jfo./JS 
 
SOLID FORMS. 
 
 87 
 
 n^ M. /^/ 
 
88 
 
 PAPER-FOLDING AND CUTTING. 
 
 11^. M- /Jit 
 
 COMBINATIONS OF SOLID FORMS. 
 
 From the explanations given for prisms and pyra- 
 mids up to this time, the teacher will be able to ad- 
 vance, making these forms with any number of sides. 
 •By combining prisms, cubes, and pyramids, very pretty 
 forms can be obtained. In illustration No. 127 is 
 shown a cube and square pyramid combined, the re- 
 sult being very effective. The next figure represents 
 
SOLID FORMS. 
 
 89 
 
 the plan for such a form combination. If, in place of 
 the cube, you draw the plan for a square prism you 
 
 will have still another combination. Also you may 
 omit the odd square at the lower part of the plan for 
 
90 
 
 PAPIER FOLDING AND CUTTING. 
 
 the cube, and instead draw another plan for a square 
 pyramid. When folded you will have a handsome 
 figure, which looks more difficult than it is in reality 
 
 K<gNo /J/ 
 
 — a cube connecting two square pyramids. A solid 
 which has eight equal faces, each face an equilateral 
 triangle, is called an octahedron. Such a solid is 
 represented in figure No. 129, and the plan is shown 
 in the next figure. Eight equilateral triangles are 
 drawn, two of them being joined at their bases. Draw 
 
SOIvID FORMS. 
 
 91 
 
 the flaps for pasting as indicated by the dotted lines. 
 In No. 131 is the plan for a solid with eight triangu- 
 
 rf /V-^^- M. /cS>^ 
 
 lar faces, the triangles being isosceles, not equilateral. 
 By using plan No. 130, and prolonging the arcs in 
 which each set of four triangles is drawn, until the 
 
 Fog.M/dd. 
 
92 
 
 PAPER-FOLDING AND CUTTING. 
 
 circle is complete, also completing the hexagon in 
 each circle, yon will have altogether twelve equilat- 
 eral triangles. These triangles, cut and pasted, will 
 
 Fig.ITo,/^^ 
 
 form a solid, such as is shown in figure No. 132. This 
 solid is known as a dodecahedron. A twenty-sided 
 solid is illustrated in No. 133. Each of the sides is 
 an equilateral triangle, and the plan for drawing, 
 cutting, and folding is represented in the next figure. 
 
SOLID FORMS. 
 
 93 
 
 FRUSTUMS. 
 
 If the upper part of a pyramid is cut off, the por- 
 tion remaining is called a frustum. In figures Nos. 
 
 % jic. /jr 
 
 135 and 136 are represented respectively frustums of 
 a square prism and a hexagonal prism. The upper 
 
 R.-Nc/ef^- 
 
 face of a frustum is the same shape as the base of the 
 pyramid, but, as a matter of course, is smaller. The 
 
94 
 
 PAPER-FOLDING AND CUTTING. 
 
 nearer the top of the pyramid the cutting is made, 
 the smaller is the upper face. By examining the 
 diagram shown in figure No. 137 you will see how 
 frustums are drawn on paper for the purpose of fold- 
 
 /T^ K. /c// 
 
 ing and pasting. Proceed as if to draw a pyramid. 
 Draw an arc the distance from the vertex that you 
 desire the frustum to be cut. Draw straight lines as 
 shown, which form the upper edges of the new figure, 
 and draw the upper face projecting from one of these 
 edges. The diagram illustrated here will fold into a 
 frustum of a triangular pyramid. 
 
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