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 . en thepetyendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having theobtuse angle ACB, and from the point A let AD ho drawnperpendicular to reproduced : the square on AB shall begreater than the squares on AC, CB, by twice the rectangleBC, CD. Because the straight lineBD is divided into two partsat the point C, the sipiare onBD is equal to the squares onBC, CD, and twice the rectangleBC, CD. [II. 4. To each o
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 . en thepetyendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having theobtuse angle ACB, and from the point A let AD ho drawnperpendicular to reproduced : the square on AB shall begreater than the squares on AC, CB, by twice the rectangleBC, CD. Because the straight lineBD is divided into two partsat the point C, the sipiare onBD is equal to the squares onBC, CD, and twice the rectangleBC, CD. [II. 4. To each of these equals add thesquare on DA. Therefore the squares on BD, DA are equal to the squares onBC, CD, DA, and twice the rectangle BC, CD. [Axiom the square on BA is equal to the squares on BD, DA,because the angle at /> is a right angle ; [I. 47. and the square on (7^ is equal to the squares on CD,DA.[l. the square on BA is equal to the squares onBC, CA, and twice the rectangle BC, CJ-f ;that is, the square on BA is greater than the squares onBC, CA by twice the rectangle BC, CD. Wherefore, in obtuse-angled triangles &o. , 5—2. 68 EUCLIDS ELEMENTS. PROFOSITION 13. THEOREM. In every triangle, the square on the side subtendinga I acute angle, is less than the squares on the sides con-taining that angle, by ticice the rectangle contained hyeither of these sides, and the straight line interceptedhetween the perpendicular let fall on it from the oppositeangle, and tfce acute angle. Let ABC be any triangle, and the angle at B an acuteaiigle; and on BC one of the sides containing it, let fallthe perpendicular AD from the opposite angle : the s([uareon 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 o
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