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Fold along interior lines to bring the six triangles together around the shaded hexagon.






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Fold along interior lines to bring the six trapezoid shapes and small hexagon together around the larger shaded hexagon.





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Fold along interior lines to bring the eight triangles together around the shaded octagon.






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Fold along interior lines to bring the eight trapezoid shapes and small octagon together around the larger shaded octagon.






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I. Raise up one half of the figure, and fold it so that the point E may fall upon A, and the point F upon B, and raise up the parallelogram at the end, thus you have one of the prisms.
II. Then bring over the other part of the scheme, so that the corner C may likewise fall upon A, and the corner D upon B; thus will there be formed the whole parllelopipedon, and its section made by the plane passing through its diagonal A B.






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I. Lift up the figure, and bring the point A to C, and the point B to D.
II. Fold back the rest of the figure upon the line A B, which is properly cut for that purpose; so that the two parallelograms which are separated by A B may lie close together.
III. Then bring over the remaining part of the scheme, so that the points E and F may coincide with C and D; then folding together the four triangles, the whole parallelopipedon will be formed, and also its section made according to a plane passing through the diagonal of its base or end.






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I. First form the triangular pyramid, A C B, by making the line B C coincide with A C.
II. Fold back upon the line B C the triangle numbered 4, so that it may lie close to that which is marked 3.
III. Then fold over the sides 5, 6, and 7, bringing the line D E so that D may fall upon A, and E upon C, which, with the quadrilateral base that is shaded, forms one of the prisms.
IV. Then fold back the other part of the figure, so that the side 8 may be close to that marked 7; thus will there remain a triangular vacuity at the base of the pyramid A C B, which must be filled by folding together the sides marked 9 and 10, making the part F fall upon A, and the point G upon V; thus will the other prism be formed.
V. This done, there remains only to form the other pyramid, G I H, which is effected by folding its parts back upon the line G K, and folding round the triangles marked 12, 13, 14; the partition lines whereof are all cut on the front side of the figure, which being folded accordingly, completes the whole pyramid, and exhibits a view of the several sections described in the above theorem.






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To fold the figure contained in this plate.

I. First form the pyramid A B C, by bringing the point C to A, so that the line BC may fall upon A B.
II. Then form the pyramid B A D, by bringing D to B, making A D coincide with A B, and raising up the triangle at B.
III. Then turn back the rest of the figure upon the line A D, so that the triangle marked 7 may closely adhere to that marked 6.
IV. Lastly, the vacuity that is now between the two pyramids so formed will be filled exactly, by folding together the pyramid contained under the triangles marked 8, 9, 10, in such sort that E be connected with A and F with B; thus is the whole prism completed, and the sections above described clearly seen.
N.B. when the last-mentioned pyramid is introduced into the space remaining between the other two, by pressing a little upon that part which is the upper edge or side of the prism, the formation of the prism will be rendered more perfect.





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I. Bend the arc A B evenly round the arc EF, thereby causing A to come to E, and B to F.
II. Turn about the triangle B C D upon the side B C, so as to make B D coincide with the diameter of the base E F, and A C to coincide with D C; thus will one half of the cone be formed.
III. In like manner form the other half, by bringing G to E, and H to F, the other line G K even upon E F, and the sides H I and K I even to each other; so will the whole cone, and the section through its axis, both appear.






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I. Fold the arc A D round the base, so that A may come to B, and the arc D C in like manner, making C to unite A at the point B.
II. Make the lines A F unite together, which will form the frustrum of a cone cut parallel to its base, and show the section to be a circle.