...deserving of attention. We have here the celebrated proposition, that the square on the hypotenuse of a rightangled triangle is equal to the squares on...other propositions which form part of the system of modem geometry. There is one proposition remarkable, namely, that which discovers the area of a triangle...

...treatises on geometry are pronounced to be inferior in excellence to those on algebra ; but they contain the celebrated proposition, that the square on the...squares on the sides containing the right angle ; and others which form part of the system of modern geometry. Among these, that which discovers the area...

...mensuration. The celebrated proposition, that the square on the side opposite to the right angle of a right-angled triangle, is equal to the squares on the sides containing that angle, was familiar to them ten centuries before it was known to the Greeks. Yet this important...

...geometry, written as early as the year 1150 AD, contains the celebrated proposition that the square of the hypothenuse of a right-angled triangle is equal to the squares on the sides containing the triangle. As a striking example üf tl-. absurd superstitious which may possess a strictly mathematical...

...figurative. The geometrical part of this work contains the celebrated proposition that the square of the hypothenuse of a right-angled triangle is equal to the squares on the sides containing the triangle. And among other propositions the one which discovers the area of a triangle when the three...

...to the square. On a given straight line to describe a square (I. 46). The square on the hypothenuse is equal to the squares on the sides containing the right angle, in any right-angled triangle, and conversely (I. 47, I. 4S). EUCLID'S ELEMENTS. BOOK I. PROPOSITION...

...this Proposition. 3. In any right-angled triangle, the square on the side subtending the right angle is equal to the squares on the sides containing the right angle. 4. If a straight line be divided into any two parts, the squares on the whole line and on one of the...

...deserving of attention. We have here the celebrated proposition that the square on the hypotenuse of a right-angled triangle is equal to the squares on...part of the system of modern geometry. There is one remarkable proposition, namely, that which discovers the area of a triangle when its three sides are...

...BFto £G. PROPOSITION 47. In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle. Let ABC be a right-angled triangle having the angle sJSAC right; I say that the square on BC is equal...

...This method depends on the Euclid proposition that " the square on the sides subtending a right angle is equal to the squares on the sides containing the right angle." The measurements of 3, 4 and 5, and their multiples fulfil these conditions. 3x3 = 9. 4 x 4 = 16. 9...