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 229
nother as their bases, (U. 12.) there-fore the base ABCD is equal (A. 5.) to the base EFGH; and asthe base ABCD is to the base EFGH, so is the altitude MN tothe altitude KL. But let thealtitudes KL, MN be unequal,and MN the greater of the two,and from MN take MP equalto KL, and, through the pointP,… … See Note, BOOK XII. THE liLEMENTS OF EUCLID. 227 cylinder, the base of which is the circle EFHG, and altitude MP:and because the cylinder AX is equal to the cylinder EO, as AXis to the cylinder ES, so (7. 5.) is the cylinder EO to the same ES.But as the cylinder AX to the cylinder ES, so (11. 12.)…
Mathematics, Greek · Geometry · Trigonometry
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