. 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. qual to the right Book EAB, AB and HF are parallels, and AH and BF are ^-^?^^i^parallels ; wherefore AH is equal to BF, and the rectangleEA, AH equal to the rectangle EA, BF, that is, to therectangle C, D : and because EG, GF are equal to one another,and AE, LG, BF parallels : therefore AL and LB
. 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. qual to the right Book EAB, AB and HF are parallels, and AH and BF are ^-^?^^i^parallels ; wherefore AH is equal to BF, and the rectangleEA, AH equal to the rectangle EA, BF, that is, to therectangle C, D : and because EG, GF are equal to one another,and AE, LG, BF parallels : therefore AL and LB are equal;also EK is equal to KH a, and the rectangle C, D from the a 3. , is not greater than the square of AL the halfof AB ; wherefore the rectangle EA, AH is not gieater thanthe square of AL, that is of KG : add to each the squareof KE ; therefore the square b of AK is not greater than the b 6. of EK, KG, that is, ^ C than the squre of EG ; andconsequently the straight lineAK or GL is not greaterthan GE. Now, if GE beequal to GL, the circle EHFtouches AB in L, and the square of AL is cequal to tiie rectangle EA,AH, that is, to the given rect-angle C, D ; and that wiiichwas required is done : but ifEG, GL be unequal, EGmust be the greater: and. c 36. therefore the circle EHF cuts the straight line AB ; let it cut it in the points M, N, and upon NB describe the square NBOP, and complete the rectangle ANPQ : because ML is equal to dj. 3. 3. LN, and it has been proved that AL is equal to LB ; therefore AM is equal to NB, and the rectangle AN, NB equal to the rectangle N A, AM, that is, to the rectangle e E A, AH, or the g q^^ gg. rectangle C, D : but the rectangle AN, NB is the rectangle 3. AP, because PN is equal to NB : therefore the rectangle AP is equal to the rectangle C, D ; and the rectangle AP equal to the given rectangle C, D has been applied to the given straight line AB, deficient by the square BP. Wiiich Vv^as to be done. 4. To a
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
