Scu. USE. PROP. XI. XII. 107 PROP. XII. THEOR. In obtuse angled ▲s, if a perpendicular be drawn from either of the acute s to the opposite side produced, the square of the side subtending the obtuse angle is greater than the squares of the sides containing the ob'use angle by twice the rect. contained by the side upon which when produced the perp. falls, and the st. line intercepted without the▲ between the perp. and the obtuse angle. CON. 12. I, Pst. 2. DEM. 4. II, Ax. 2. 47. I. BOOK II. 109 PROP. XIII. THEOR. In every ▲, the square of the side subtending either of the acute s is less than the squares of the sides containing that acute by twice the rect. contained by either of these sides and the st. line intercepted between the perp. let full upon it from the opposite angle and the acute angle. CON. 12 I. Pst. 2. DEM. 7. II. Ax. 2. 47. I, 16. I, 12. II, 3. II. Ax. 6. CON. E Exp. & PROP. XIII. 111 CASE II. AD being out of the triangle the positions of C and D are changed. Alg. Arith. CASE III. The perp. A D and A C coincide, and the points D and C. Alg. Arith. Con. If in the figure to Case II. a perp. C G be drawn from C to A B, the rect. under the side A B, and the part G B intercepted between the perp. and B, is equal to B C D B. SCH. |