The elements of Euclid for the use of schools and colleges : comprising the first two books and portions of the eleventh and twelfth books; with notes and exercises . nstruction, the square on EG is equal to the square on GF; therefore the squares on EG, GF are double of the square on GF. But the square on EF is equal to the squares on EG, GFj because the augle EGF is a right angle j [L 47. therefore the square on EF is double of the square on GF. And GF is equal to CD; [I. 34. therefore the square on ^i^is double of the square on CD. But it has been shewn that the square on AE is also double
The elements of Euclid for the use of schools and colleges : comprising the first two books and portions of the eleventh and twelfth books; with notes and exercises . nstruction, the square on EG is equal to the square on GF; therefore the squares on EG, GF are double of the square on GF. But the square on EF is equal to the squares on EG, GFj because the augle EGF is a right angle j [L 47. therefore the square on EF is double of the square on GF. And GF is equal to CD; [I. 34. therefore the square on ^i^is double of the square on CD. But it has been shewn that the square on AE is also double of the sc^uare on AC. Therefore the squares on AE, EF are double of the squares on AC, CD. But the square on ^i^ is equal to the squares on AE,EF, because the angle AEF is a right angle. [I. 47. Therefore the square on ^i^ is double of the squares onAC, CD. But the squares on AD, DF are equal to the square onAF, because the augle ADFis a right angle. [I. 47. Therefore the squares on AD, DF are double of thesquares on AC, CD. And DF is equal to DB ; therefore the squares on AD, DB are double of thesquares on A C, CD. Wherefore, if a straight line &c q.£. 64 EUCLIDS ELEMENTS, PROPOSITION 10. THEOREM. If a straight line he bisected^ and prodiiced to anypointy the sqtiare on tlie ichole line thus produced^ andthe square on tlie part of it produced^ are together doubleof the square on half tJte line bisected and of the squareon the line made up of the halj and the part produced. Let the straight hne AB he bisected at C, and pro-duced to Z>: the squares on AD, DB shall be togetherdouble of the squares on A C, CD. From the point Cdraw CEdX right angles to AB, [I. make it equal io ACor CB; [ andjoin^^, EB; throughE draw EF parallel toAB, and through D draw2>i^ parallel to CE. [ because the straightline ^/^meets the parallelsEC, FD, the angles CEF, EFD are together equal to tworight angles ; [I. 29. and therefore the angles BEF, EFD are together lessthan tw
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Keywords: ., bookcentury1800, booksubjectgeometry, booksubjectmathematicsgree
