. 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. BC is equal * to the triangle ADC : and a 34< !?because EKHA is a parallelogram, the diameter of which isAK, the triangle AEK is equal to the triangle AHK: by thesame reason, the triangle KGC is equal to the triangle KFC:then, because the triangle AEK is equal to the triangle AHK,and the triangle KGC t
. 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. BC is equal * to the triangle ADC : and a 34< !?because EKHA is a parallelogram, the diameter of which isAK, the triangle AEK is equal to the triangle AHK: by thesame reason, the triangle KGC is equal to the triangle KFC:then, because the triangle AEK is equal to the triangle AHK,and the triangle KGC to KFC; the triangle AEK togetherwith the triangle KGC is equal to the triangle AHK togetherwith the triangle KFC : but the whole triangle ABC is equalto the whole ADC; therefore the remaining complement BKis equal to the remaining complement KD. Wherefore, thecomplements, &c. Q. E. D. PROP. XLIV. PROB. TO a given straight line to apply a parallelogram,which shall be equal to a given triangle, and haveone of its angles equal to a given rectilineal angle. Let AB be the given straight line, and C the given triangle,and D the given rectilineal angle. It is required to apply tothe straight line AB a parallelogram equal to the triangle C,and having an angle equal to D. 46 THE ELEMENTS. Book I. Make » the ^--^-^^ parallelogr«im a , BEFG equalto the triangleC, and havingthe angle EBGequal to theangje D, sothat BE bein thC samestraight line b with AB, and produce EG to H; and through A draw • AH pa-rallel to BG or EF, and join HB. Then, because the straightline HF falls upon the parallels AH, EF, the angles AHF, HFE c are together equal*= to two right angles; wherefore the anglesBHF, HFE are less than two right angles : but straight lineswhich with another straight line make the interior angles upon d 12. Ax. the same side less than two right angles do meet •*, if producedfar enough : therefore HB, FE shall meet, if produced ; let themmeet in K, and through K draw
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
