. 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. > M S E F G H PR of the figures MF, NH : then because as AB to CD, so is EFto PR, and that upon AB, CD are described the similar and si-milarly situated rectilineals KAB, LCD, and upon EF, PR, inlike manner, the similar rectilineals MF, SR; KAB is to LCD,as MF to SR; but, by the hypothesis, KAB is to L
. 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. > M S E F G H PR of the figures MF, NH : then because as AB to CD, so is EFto PR, and that upon AB, CD are described the similar and si-milarly situated rectilineals KAB, LCD, and upon EF, PR, inlike manner, the similar rectilineals MF, SR; KAB is to LCD,as MF to SR; but, by the hypothesis, KAB is to LCD, as MFto NH ; and therefore the rectilineal MF having the same ratioS^.S. to each of the two NH, SR, these are equals to one another:they are also similar, and similarly situated ; therefore GH isequal to PR: and because as AB to CD, so is EF to PR, andthat PR is equal to GH ; AB is to CD, as EF to GH. If, there-fore, four straight lines, Sec. Q. E. D. PROP. XXHL THEOR. Se,eN. EQUIANGULAR parallelograms have to oneanother the ratio which is compounded of the ratiosof their sides. Let AC CF be equiangular parallelograms, having the angleBCD equal to the angle ECG: the ratio of the parallelogramAC to the parallelogram CF is the same with the ratio which iscom])ounded of the ratios of
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
