. 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. the rectilinealfigures ABCDE, AF given in species aredescribed upon the same straight line AB,dat-the ratio of ABCDE to AF is given a:but the square AF is given in magnitude,therefore also the figure ABCDE isgiven in magnitude. PROB. To find the magnitude of a rectilineal ^figure given in species describe
. 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. the rectilinealfigures ABCDE, AF given in species aredescribed upon the same straight line AB,dat-the ratio of ABCDE to AF is given a:but the square AF is given in magnitude,therefore also the figure ABCDE isgiven in magnitude. PROB. To find the magnitude of a rectilineal ^figure given in species described upon astraight line given in magnitude. Take the straight line GH equal to thegiven straight line AB, and by the 53ddat. find the ratio which the square AFupon AB has to the figure ABCDE ; and make the ratio of GH to HK the same ; and upon GH de-scribe the square GL, and complete the parallelogram LHKM;the figure ABCDE is equal to LHKM : because AF is toABCDE, as the straight line GH to HK, that is, as the figureGL to HM ; arid AF is equal to GL ; therefore ABCDE isequal to HMc. PROP. LVH. IF two rectilineal figu-es are given in species, andif a side of one of tliem has a given ratio to a side ofthe other; the ratios of the remaining sides to tlie sides shall be gi^ DATA. 411 Let AC, DF be two rectilineal figures given in species, andlet the ratio of the side AB to the side DE be given, the ratiosof the remaining sides to the remaining sides are also given. a 3. def. Because the ratio of AB to DE is given, as also a the ratios of ^ jq ^^^^AB to BC, and of DE to EF, the ratio of BC to EF is the same manner, the Iatios of theother sides to the other sides aregiven. A^ The ratio Avhich BC has to EFmay be found thus: take a straightline G given in magnitude, and be-cause the ratio of BC to BA is given,make the ratio of G to H the same;and because the ratio of AB to DE isgiven, make the ratio of H to K thesame ; and make the ratio of K to Lthe same with
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
