. 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. traight lines ; and let BC be divided *—V—^ into any parts in the points D, E ; the rectangle contained bythe straight lines A, BC is equalto the rectangle contained by A,BD, together with that containedby A, DE, and that contained byA, EC. a From the point B draw ^ BF at right angles to BC, and mak
. 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. traight lines ; and let BC be divided *—V—^ into any parts in the points D, E ; the rectangle contained bythe straight lines A, BC is equalto the rectangle contained by A,BD, together with that containedby A, DE, and that contained byA, EC. a From the point B draw ^ BF at right angles to BC, and make G b BG equal to A; and through G drawc GH parallel to BC; and through D, E, C draw ^ DK, F EL, CH parallel to BG ; then the rectangle BH is equal to the iectangles BK, DL, EH ; and BH is contained by A, BC, for it is contained by GB, BC, and GB is equal to A ; and BK is contained by A, BD, for it is contained by GB. BD, of which GB is equal to A ; and DL is d contained by A, DE, because DK, that is i, BG, is equal to A ;and in like manner the rectangle EH is contained by A, EC :therefore the rectangle contained by A, BC is equal to the se-veral rectangles contained by A, BD, and by A, DE; and alsoby A, EC. Wherefore, if there be two straight lines, E. PROP. n. THEOR. IF a straight line be divided into any two parts,the rectangles contained by the whole and each ofthe parts are together equal to the square of thewhole line. •i. 46. Let the straight line AB be divided intoany two pans in the point C ; the rect-angle contained by AB, BC, together withthe rectangle * AB, AC, shall be equal tothe square of AB. Upon AB describe » the square ADEB,and through C draw ^ CF, parallel to ADor BE ; then AE is equal to the rectanglesAF, CE ; and AK is the square of AB ;and AF is the rectangle contained by BA,
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
