. 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. at the pointsG, B, in the straightline GB, make^ theangle BGH equal tothe angle DFE, andthe angle GBH e-qual to FDE; there-fore the remaining angle FED is equal to the remaining angleGHB, and the triangle FDE equiangular to the triangle GBH :then, because the angle AGB is equal to the angle CFD, andBGH to
. 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. at the pointsG, B, in the straightline GB, make^ theangle BGH equal tothe angle DFE, andthe angle GBH e-qual to FDE; there-fore the remaining angle FED is equal to the remaining angleGHB, and the triangle FDE equiangular to the triangle GBH :then, because the angle AGB is equal to the angle CFD, andBGH to DFE, the whole angle AGH is equal to the wholeCFE: for the same reason, the angle ABH is equal to the angleCDE ; also the angle at A i-s equal to the angle at C, and theangle GHB to FED: therefore the rectilineal figure ABHG isequiangular to CDEF : but likewise these figures have their sidesabout the equal angles proportionals: because the triangles GAB,FCD being equiangular, BA is^ to AG, as DC to CF; andbecause AG is to GB, as CF to FD; and as GB to GH, so,by reason of the equiangular triangles BGH, DFE, is FD toFE; therefore, ex xrjuali^, AG is to Gil, as CF to FE: inthe same manner it may be proved that AB is to BH, as CD toDE: and GH is to liB, as FE to ED c. Wherefore, becausy. OF EUCLID. ^^5 the rectilineal figures ABHG, CDEF are equiangular, and have ^^ sides about the equal angles proportionals, they are similar ^^to one another e. ^ Next, Let it be required to describe upon a given straight lineAB, a rectilineal figure similar, and similarly situated to the rec-*tilineal figure CDKEF. Join DE, and upon the given straight line AB describe therectilineal figure ABHG similar, and similarly situated to thequadrilateral figure CDEF, by the former case; and at thepoints B, H, in the straight line BH, make the angle HBL equalto the angle EDK, and the angle BHL equal to the angleDEK; therefore the remaining angle at K is equal to the re-maining angle at L
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
