...right angled triangle any similar rectilineal ^figures be similarly described, the Jigure described on the side subtending the right angle is equal to the sum of the Jtgures on the other two sides which contain the right angle. From the right *Z- draw a perpendicular...

...the 47th of the first book of Euclid's Elements, that in, every right-angled triangle the square of the side subtending the right angle is equal to the sum of the squares of the other two sides, has immortalized his name ; and whether we consider the inherent beauty...

...Second, Third and Fourth Classes. \. IN any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the sum of the squares described upon the sides containing the right angle. 2. The sides about the equal angles of...

...two angles of a triangle be equal, shew that the sides subtending them are also equal. 6. Prove that, in a right-angled triangle, the square on the side subtending the right angle, is equal to the square on the sides containing the right angle. 7. If a straight line be divided into two equal, and...

...demonstrated. PROPOSITION XLVIII. THEOREM. — If the square described on one of the sides of a triangle, be equal to the sum of the squares described on the other two sides of it; the angle made by those two sides is a right angle. Let ABC be a triangle, which is such that...

...which itself is a part, which is absurd. PROP. 47. THEOR. In a right angled triangle, the squares of the side subtending the right angle is equal to the sum of the squares of the sides which contain the right angle. Describe squares on the sides of the triangle ;...

...plane passing through them. 6. In any right-angled triangle, the square which is described 1830 upon the side subtending the right angle, is equal to the sum of the squares described upon the sides containing the right angle. 8. If two straight lines meeting one another...

...result. The principle is as follows : In any right-angled triangle, the square of the hypotenuse or side subtending the right angle, is equal to the sum of the squares on the sides which contain the right angle. We repeat the diagram, in order that the reader...

...result. The principle is as follows : In any right-angled triangle, the square of the hypotenuse or side subtending the right angle, is equal to the sum of the squares on the sides which contain the right angle. We repeat the diagram, in order that the reader...

...same parallels, the parallelogram is double the triangle. 9. In a right-angled triangle, the square of the side subtending the right angle is equal to the sum of the squares of the sides containing the right angle. 10. In obtuse-angled triangles, if a perpendicular...