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 . eon AG, opposite to the angle B, shall be less than thes _^uares on GB, BA, by twice the rectangle GB, BD. First, let AD fall within thetriangle ABC. Then, because the straight lineCB is divided into two partsat the point D, the squares onCB, BD are equal to twice therectangle contained by GB, BDand the square on CD. [II. 7. To each of these equals add thesquare on DA. Therefore the squares on CB, BD, DA are equal to twicethe rec
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 . eon AG, opposite to the angle B, shall be less than thes _^uares on GB, BA, by twice the rectangle GB, BD. First, let AD fall within thetriangle ABC. Then, because the straight lineCB is divided into two partsat the point D, the squares onCB, BD are equal to twice therectangle contained by GB, BDand the square on CD. [II. 7. To each of these equals add thesquare on DA. Therefore the squares on CB, BD, DA are equal to twicethe rectangle CB, BD and the squares on CD, DA. \Ax. the square on xiB is equal to the squares on BD, DA,because the augle BDA is a right angle ; [I. 47. and the square on .J C is equal to the squares on CD,DA. [ the squares on CB, BA are equal to the squareon AC and twice the rectangle CB, BD ;that is, the square on ^C alone is less than the squares onCB, BA by twice the rectangle CB, BD. Secondly, let .4Z) fall withoutthe triangle because the angle at D isa right angle, {Construction. the angle AGB is greater thana right angle ; [I.
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Keywords: ., bookcentury1800, booksubjectgeometry, booksubjectmathematicsgree
