PROP. XLVII. THEOR. In any rt. angled triangle, the square which is described upon the side subtending, or opposite to the rt. angle, is equal to the squares described upon the sides containing the rt. angle. CON. P. 46. 31. Pst. 1. DEM. Def. 30. P. 14. Ax. 1. 2. P. 4. 41. Ax. 6. COR. I. If the sides of a rt. angle triangle be given in numbers, its hypotenuse may be found. COR. II. If the hypotenuse and one side be given in numbers, the other side may be found. COR. III. If any number of squares be given, a square equal to their sum may be found; or if one square be given, any multiple of it may be ascertained; or if two squares be given, the difference between them; or a square may be made that shall be the half, fourth, &c., of a given square. COR. IV. If a perp. BD be drawn from the vertex of a triangle to the base, the difference of the squares of the sides AB and CB, is equal to the difference between the squares of the segments AD and DC. COR. V. If a perp. be drawn from the vertex B to the base AC, or AC produced, the sums of the squares of the sides and alternate segments are equal. |