. 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. DATA. 413 to EG, so is H to L : and the figures A, EG are similar, andM is a mean proportional between H and L ; therefore, as wslsshown in the preceding proposition, CD is to EF as H to M. PROP. LX. IF a rectilineal figure be given in species and mag-nitude, the sides of it sliall be given in magnit
. 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. DATA. 413 to EG, so is H to L : and the figures A, EG are similar, andM is a mean proportional between H and L ; therefore, as wslsshown in the preceding proposition, CD is to EF as H to M. PROP. LX. IF a rectilineal figure be given in species and mag-nitude, the sides of it sliall be given in magnitude. Let the rectilineal figure A be given in species and magnitude,its sides are given in magnitude. Take a straight line BC given in position and magnitude,and upon BC describe a the figure D similar, and similarly a IS. , to the figure A, andlet EF be the side of thefigure A homologous toBC the side of D ; there-fore the figure D is givenin species. And becauseupon the given straightline BC the figure D gi-ven in species is described, D is given b in magnitude, H | *lCf Z * b 36. dat. and the figure A is gi-ven in magnitude, therefore the ratio of A to D is given : and the figure A is similar toD; therefore the ratio of the side EF to the homologous side ^nBC is given c ; and BC is given, wherefore d EF is given:and the ratio of EF to EG is givene, therefore EG is given.^ 2- ^^*^-And, in the same manner, each of the other sides of the figure ^ 3* ^cfA can be shown to be give
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
