...equivalent and the pyramids above the frustums are equivalent. "K PROPOSITION XX.— THEOREM. i BSyA truncated triangular prism is equivalent to the sum...E-CDF. The first of these pyramids, E-ABC, has the base ABO and the vertex E. The second pyramid, E-ACD, is equivalent to the pyramid BA CD ; for they have...

...are equivalent, since the pyramids are equivalent and the pyramids above the frustums are equivalent. PROPOSITION XX.— THEOREM. 52. A truncated triangular...vertices are the three vertices of the inclined section. p Let ABC-DEF be a truncated triangular prism whose base is ABC and inclined section DEF. Pass the...

...lower base, the upper base, and a mean proportional between the bases of the frustum. PROPOSITION XX. A truncated triangular prism is equivalent to the...vertices are the three vertices of the inclined section. BOOK Till. THEOREMS. PROPOSITION I. Every section of a cylinder made by a plane passing through an...

...lower base, the upper base, and a mean proportional between the bases of the frustum. PROPOSITION XX. A truncated triangular prism is equivalent to the sum of three pyramids whoso common base is the base of the prism and whose vertices are the three vertices of the inclined...

...circle. 7. To compute the ratio of the circumference of a circle to its •diameter, approximately. 8. A truncated triangular prism is equivalent to the...vertices are the three vertices of the inclined section. 9. The lateral area of a cone of revolution is equal to one-half of the product of the circumference...

...circle. 7. To compute the ratio of the circumference of a circle to its diameter, approximately. 8. A truncated triangular prism is equivalent to the...vertices are the three vertices of the inclined section. 9. The lateral area of a cone ot revolution is equal to one-half of the product of the circumference...

...---FP~ SF_V_ _ SA X SB X SC - - - V ~ SD X SE X SF (033) (375) (307) QED Proposition 22. Theorem.* 638. A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the lower base of the prism, and whose vertices are the three vertices of the upper base. Hyp. Let ABC-DEF...

...truncated triangular prism is equivalent to the sum of three pyramids whose common base is the lower base of the prism, and whose vertices are the three vertices of the upper base. Hyp. Let ABC-DEF be a truncated triangular prism. To prove ABC-DEF equivalent to the sum...

...truncated triangular prism is equivalent to the gum of three pyramids whose common base is the lower ba*e of the prism, and whose vertices are the three vertices of the upper base. Hyp. Let ABC-DEF be a truncated triangular prism. To prove ABC-DEF equivalent to the sum...

...lower base, the upper base, and a mean proportional between the bases of the frustum. PROPOSITION XX. A truncated triangular prism is equivalent to the...the prism and whose vertices are the three vertices «f the inclined section. PROPOSITION XXI. Only five regular (convex) polyedrons are possible. BOOK...