. 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. ight line BC describe^ the parallelogram BE^- equal to the figure ABC ; also upon CE describe * the paral-lelogram CM equal to D, and having the angle FCE equal,,^29. Lio the angle CBL : therefore BC and CF are in a straightl^*- 1-line I, as also LE and EM : between BC and CF find <= a meanc 13. 6. pro
. 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. ight line BC describe^ the parallelogram BE^- equal to the figure ABC ; also upon CE describe * the paral-lelogram CM equal to D, and having the angle FCE equal,,^29. Lio the angle CBL : therefore BC and CF are in a straightl^*- 1-line I, as also LE and EM : between BC and CF find <= a meanc 13. 6. proportional GH, and upon CiH describel the rectilineal fi-d 18. 6. gure KGII similar and similarly situated to the figUVe ABC :e 2. Cor. and because BC is GH as GH to CF, and if three straight20. (i. lines be proportionals, as the first is to the third, so is « the OF EUCLID. 18; figure upon the first to the similar and similarly described figure Book Vtupon the second; therefore as BC to CF, so is the rectilineal ^—v—^figure ABC to KGH : but as BC to CF, so is f the parallelogram f i. to the parallelogram EF: therefore as the rectilineal figureABC is to KGH, so is the parallelogiam BE to the parallelogramEF g: and the rectilineal figure ABC is equal to the parallelo- g 11. gram BE; therefore the rectilineal figure KGH is equal ^ to the h 14 EF: but EF is equal to the figure D ; whereforealso KGH is equal to D ; and it is similar to ABC. Thereforethe rectilineal figure KGH has been described similar to thefigure ABC, and equal to D. Which was to be done. • PROP. XXVI. THEOR. IF two similar parallelograms have a common an-gle, and be similarly situated; they are about the samediameter. Let the parallelograms ABCD, AEFG be similar and simi-larly situated and have the angle DAB common. ABCD andAEFG are about the same diameter. For, if not, let, if possible, theparallelogram BD have its diame-ter AHC in a different straightline from AF, the diameter of
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
