...from the proof of this prop" that the opposite aides of a square are parallels. PEOP. XL VII. THEOE. In any right-angled triangle the square, which is described on the side opposite to the right angle, shall be equal to the squares, which are described on the sides including...

...angles. PROP. XLVII. — 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 which contain the right angle. Let ABC be a right-angled triangle having the right angle...

...equal to a given rectilineal angle. 9. 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 which contain the right angle. 10. Find a point within a given triangle, from which...

...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...

...can be thus inscribed. PROP. XLVII. THEOREM. In any right-angled triangle, the square described upon the side subtending the right angle, is equal to the squares described upon the two sides, containing the right angle. Let ABС be a right-angled triangle, having the right...

...the square which is to be the sum of the four given squares, and so on, for any number. REASON : " In any right-angled triangle, the square which is...the right angle, is equal to the squares described upon tlie sides which contain the right angle." (Euclid, Book I. Prop. 47.) Note. — Any similar figures...

...are equal to two right angles. 3. 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 which contain the right angle. ignominy, and his memory will be covered with reproach....

...greater than two right angles. 5. 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 which contain the right angle. 6. If a straight line be divided into any two parts,...

...of the interior opposite angles. 2. 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 which contain the right angle. VOLUNTARY PORTION. 1. Describe a circle about a given...

...Master's degree, is thus enunciated. "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 which contain the right angle." This interesting problem, on account of its great utility...