...angles of a triangle are equal to two right angles. 3. In any right angled triangle, the square which is described, upon the side subtending the right angle,...described upon the sides which contain the right angle. Pythagoras used to deliver a most admirable lecture on the emblem of an angle of ninety degrees or...

...the first book, and is as follows : — THEOREM. " In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides containing the right angle." THE DEMONSTRATION. In {geometrical solutions and demonstrations of quantities,...

...angles of a triangle are equal to two right angles. 3. In any right-angled triangle, the square which is described upon the side subtending the right angle,...described upon the sides which contain the right angle. ignominy, and his memory will be covered with reproach. Some think that he earned the comparison beyond...

...angles are together greater than two right angles. 5. In any right-angled triangle, the square which is described upon the side subtending the right angle,...described upon the sides which contain the right angle. 6. If a straight line be divided into any two parts, the rectangles contained by the whole and each...

...47. In any right angled triangle the square which is described on the hypothenuse, or side opposite the right angle, is equal to the squares described upon the sides which contain the right angle. Let ABC (Fig. 36) be a right angled triangle having the right angle BAC ; the square described on the...

...greater than either of the interior opposite angles. 2. In any right angled triangle the square which is described upon the side subtending the right angle...described upon the sides which contain the right angle. VOLUNTARY PORTION. 1. Describe a circle about a given triangle. 2. If four straight lines be proportionals,...

...any right-angled triangle, the square which is described upon the side subtending, or opposite to, the right angle, is equal to the squares described upon the sides containmg the right angle. CONSTRUCTION. — P. 46. To describe a square on a given straight line....

...emblem in the Master's degree, is thus enunciated. "In any right angled triangle, the square which is described upon the side subtending the right angle,...described upon the sides which contain the right angle." This interesting problem, on account of its great utility in making calculations, and drawing plans...

...its denominator ; determine the fraction. Euclid. 1. In any right angled triangle the square which is described upon the side subtending the right angle...described upon the sides which contain the right angle. 2. In obtuse angled triangles if a perpendicular be drawn from either of the acute angles to the opposite...

...point parallel to a /• given straight line. 7. In any right-angled triangle, the square which is described upon the side subtending the right angle...described upon the sides which contain the right angle. 8. What is meant by the term corollary ? Give an example ** from Euclid, Book I. ; and its proof. 9....