. 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 2. 218 THE ELEMENTS. Book XI. to the angle ABC^^: and AB, that is, LO, by the hypothesis, is V—y^ less than LX ; wherefore LO, OM fall within the triangle LXM ; d for, if they fell upon its sides, or without it, they would be equalto, or greater than LX, XM^: therefore the angle LOM, that
. 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 2. 218 THE ELEMENTS. Book XI. to the angle ABC^^: and AB, that is, LO, by the hypothesis, is V—y^ less than LX ; wherefore LO, OM fall within the triangle LXM ; d for, if they fell upon its sides, or without it, they would be equalto, or greater than LX, XM^: therefore the angle LOM, thatis, the angle ABC, is greater than f the angle LXM f: in the same man-ner it may be proved that the angleDEF is greater than the angle MXN,and the angle GHK greater than theangle NXL. Therefore the threeangles ABC, DEF, GHK are great-er than the three angles LXM, MXN,NXL; that is, than four right an-gles : but the same angles ABC,DEF, GHK are less than four rightangles; which is absurd: thereforeAB is not less than LX, and it hasbeen proved that it is not equal toLX; wherefore AB is greater thanLX. Next, let the centre X of the circle fall in one of the sides ofthe triangle, viz. in MN, and joinXL: in this case also AB is great-er than LX. If not, AB is eitherequal to LX, or less than it: first,let it be equa
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
