. 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. ed upon the same AB, BC,CD, DA, and solid parallelepipedsbe erected upon the parallelograms; the prisms upon thetriangles AEB, BFC, CGD, DILV arc the halves of the solid b 2 Cor. parallelepipeds ^. And the segments of the cylinder Avhich are7-12. upon the segments of the circle cut off by AB, BC, CD, DA,a
. 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. ed upon the same AB, BC,CD, DA, and solid parallelepipedsbe erected upon the parallelograms; the prisms upon thetriangles AEB, BFC, CGD, DILV arc the halves of the solid b 2 Cor. parallelepipeds ^. And the segments of the cylinder Avhich are7-12. upon the segments of the circle cut off by AB, BC, CD, DA,are less than the solid parallek])ipeds which contain the prisms upon the triangles AEB, BFC, CGD,DHA, are greater than half of the segments of the cylinder inwhich they are; therefore, if each of the circumferences be di-vided into two equal parts, and straight lines be drawn fromthe points of division to the extremities of the circumferences,and upon the triangles thus made, prisms be erected of the same c Lem- altitude with the cylinder, and so on, there must at length re- main some segments of the cylinder which together are less <=? than the excess of the cylinder above the triple of the cone. Let ihem be those upon the segments of tlic circle AE, EB, ]J1,. OF EUCLID. 271 FC, CG, GD, DH, HA. Therefore the rest of the cylinder, that B. , the prism of which the base is the polys^on AEBFCGDH, and ^ —^.mJof which the altitude is the same with that of the cylinder, isgreater than the triple of the cone : but this prism is triple ^ of d 1. pyramid upon the same base, of which the vertex is the same 7- 12-with the vertex of the cone ; therefore the pyramid upon the baseAEBFCGDH, having the same vertex with the cone, is greaterthan the cone, of which the base is the circle ABCD: but it isalso less, for the pyramid is contained within the cone ; which isimpossible. Nor can the cylinder be less than the triple of thecone. Let it be less, if poss
Size: 1646px × 1518px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
