. The Elements of Euclid : viz. the first six books, together with the eleventh and twelfth : the errors, by which Theon, or others, have long ago vitiated these books, are corrected, and some of Euclid's demonstrations are restored : also, the book of Euclid's Data, in like manner corrected. the BookXf,solid AB to the solid CV, so is the solid CD to the solid CV; v—y—^that is, each of the solids AB, CD has the same ratio to the solid c ; and therefore the solid AB is equal to the solid CD. Second general case. Let the insisting straight lines FE,BL, GA, KH; XN, DO, MC, RP not be at ri
. The Elements of Euclid : viz. the first six books, together with the eleventh and twelfth : the errors, by which Theon, or others, have long ago vitiated these books, are corrected, and some of Euclid's demonstrations are restored : also, the book of Euclid's Data, in like manner corrected. the BookXf,solid AB to the solid CV, so is the solid CD to the solid CV; v—y—^that is, each of the solids AB, CD has the same ratio to the solid c ; and therefore the solid AB is equal to the solid CD. Second general case. Let the insisting straight lines FE,BL, GA, KH; XN, DO, MC, RP not be at right angles tothe bases of the solids; and from the points F, B, K, G; X,D, R, M draw perpendiculars to the planes in which are thebases EH, NP meeting those planes in the points S, Y, V, T ;Q, I, U, Z; and complete the solids FV, XU, which are pa-rallelepipeds, as was proved in the last part of prop. 31, ofthis book. In this case, likewise, if the solids AB, CD beequal, their bases are reciprocally proportional to their altitudes,viz. the base EH to the base NP, as the altitude of the solidCD to the altitude of the solid AB. Because the solid AB isequal to the solid CD, and that the solid BT is equal s to the g 29. qrsolid BA, for they are upon the same base FK, and of the
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
