. 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. t, let it be equal: then becauseAB is equal to LX, and that AB is also equal to BC, and LX toXM, AB and BC are equal to LX and XM, each to each ; andthe base AC is, bv construction, equal to the base LM: where-fore the angle ABC is equal to the angle LXM^. For the same d 8 , the angle DEF is equal
. 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. t, let it be equal: then becauseAB is equal to LX, and that AB is also equal to BC, and LX toXM, AB and BC are equal to LX and XM, each to each ; andthe base AC is, bv construction, equal to the base LM: where-fore the angle ABC is equal to the angle LXM^. For the same d 8 , the angle DEF is equal to the angle MXN, and the an-gle GHK to the angle NXL;therefore the three angles ABC,DEF, GHK are equal to the threeangles LXM, MXN, NXL: but thethree angles LXM, MXJ^, NXLare equal to four right angles <=:therefore also the three anglesABC, DEF, GHK are equal to fourright angles : but, by the hypothe-sis, they are less than four right an-gles ; which is absurd; thereforeAB is not equal to LX: but nei-ther can AB be less than LX:for, if possible, let it be less, andupon the straight line LM, onthe side of it on which is the cen-tre X, describe the triangle LOM, the sides LO, OM of which are equal to AB, BC; and becausethe base LM is equal to the base AC, the angle LOM is equal 2 E. e 2. 218 THE ELEMENTS
Size: 1430px × 1747px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
