. 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. e same straight lines AT, GX: and because the 2 G 234 THE ELEMENTS Book XI. parallelogram AB is equal k to SB, for they are upon the same <-. y—^ base LB, and between the same parallels LB, AT ; and that the g base SB is equal tothe base CD ; there-fore the base AB isequal to the base CD,and the
. 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. e same straight lines AT, GX: and because the 2 G 234 THE ELEMENTS Book XI. parallelogram AB is equal k to SB, for they are upon the same <-. y—^ base LB, and between the same parallels LB, AT ; and that the g base SB is equal tothe base CD ; there-fore the base AB isequal to the base CD,and the angle ALBis equal to the angle OCLD: therefore, bythe first case, the so-lid AE is equal to thesolid CF ; but the so-lid AE is equal to thesolid SE, as was demonstrated; therefore the solid SE is equslto the solid CF. But if the insisting straight lines AG, HK, BE, LM; CN,RS, DF, op be not at right angles to the bases AB, CD; inthis case likewise, the solid AE is equal to the solid CF: fromthe points G, K, E, M; N, S, F, P draw the straight lines GQ, hll. 11. KT, EV, MX; NY, SZ, FI, PU, perpendicular^ to the planein which are the bases AB, CD; and let them meet it in thepoints Q, T, V, X; Y, Z, I, U, and join QT, TV, VX, XQ;YZ, ZI, lU, UY: then, because GQ, KT are at right angles to.
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
