. 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. is a equal ^ to the angle GHF. Again,because the straight line GKcuts the parallel straight linesEF, CD, the an^le GHF is equalto the angle GKD ^ ; and it wasshown that tlie angle AGK isequal to the angle GHF ; there-fore also AGK is equal to GKD ;and they are alternate angles ; b therefore AB
. 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. is a equal ^ to the angle GHF. Again,because the straight line GKcuts the parallel straight linesEF, CD, the an^le GHF is equalto the angle GKD ^ ; and it wasshown that tlie angle AGK isequal to the angle GHF ; there-fore also AGK is equal to GKD ;and they are alternate angles ; b therefore AB is parallel ^ to CD. Wherefore, straight lines, & E. D. PROP. XXXL PROB. TO draw a straight line through a given point pa-rallel to a given straight line. Let A be the given point, and BC the given straight line ; itis required to draw a straight line through the point A, parallel to the E A F straight line BC. In BC take any point D, and joinAD ; and at the point A, in the A straight line AD, make * the angle DAE equal to the angle ADC ; and B D C produce the straight line EA to F. Because the straight line AD, which meets the two straight lines BC, EF, makes the alternate angles EAD, ADC equal to b one another, EF is parallel ^ to BC Therefore the straight line. OF EUCLID. 37 EAF is drawn through the given point A parallel to the given Book line BC. Which was to be done. V-i-Y^i^* PROP. XXXII. THEOR,
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
