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 (1834)
Euclid, Euclid, Simson, Robert, 1687-1768 · Philadelphia : Desilver & Thomas · leaf 171
the same plane and do not meet, though produced either way,are parallel: therefore EF is parallel to GH. Wherefore, if twoparallel planes. Sec. Q. E. D. PROP. XVH. THEOR. If two straight lines be cut by parallel planes, theyshall be cut in the same ratio. Let the straight lines AB, CD be cut by the… … * See Note. BOOK XI. THE ELEMENTS OF EUCLID. KL, MN are cut by the planeEX, BD, are parallel (16. 11.).the two parallel planes GH, KLare cut by the plane AXFC, thecommon sections AC, XF, areparallel: and because EX is pa-rallel to BD, a side of the triangleABD, as AE to EB, so is (2. 6.)AXtoXD.…
Mathematics, Greek · Geometry · Trigonometry
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