...feet, and the space travelled over two, then, by the forty-seventh proposition first hook of Euclid, the square of the hypothenuse of a right-angled triangle is equal to the squares of both the other sides : Hence 1O x 10 = lOo, and and 2 x 2 = 4+ 100=^/104=10 feet -J&;...

...gave himself up to the study of geometry with wonderful ardour and success. It was he who discovered that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. To express his joy and gratitude for this great discovery, we are...

...kind from those by a series of which, did he know the previous propositions, he might be convinced that the square of the hypothenuse of a right-angled triangle, is equal to the sum of the squares of the sides. CHAPTER XV. On Axioms. GEOMETRY, then, is the application of strict logic...

...chains. <AI Ans. \ i° *™ f 6d 45 ) ( xjC 21o t , - j To find the other two sides. * Demonstration. The square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the sides (theo. 14) ; hence the log. of (4CMi32) — the log. of 5C2, and by the nature...

...acoustics the ancients were very learned ; yet we are told that Tliales, when he solved the proposition " that the square of the hypothenuse of a right-angled triangle is equal to the squares of the other two sides," (upon which many others depend,) sacrificed to the gods from thankfulness...

...physical science. That " a whole ia greater than any of its parts," — that " the square described on the hypothenuse of a right-angled triangle is equal to the sum of the squares described on its remaining sides," are facts, the one deduced from observation or simple...

...kind from those by a series of which, did he know the previous propositions, he might be convinced that the square of the hypothenuse of a right-angled triangle, is equal to the sum of the squares of the sides. CHAPTER XV. On Axioms. GEOMETRY, then, is the application of strict logic...

...kind from those by a series of which, did he know the previous propositions, he might be convinced that the square of the hypothenuse of a right-angled triangle, is equal to the sura of the squares of the sides. CHAPTER XV. On Axioms. But the rigour of this science is carried...

...physical science. That " a whole is greater than any of its parts," — that u the square described on the hypothenuse of a right-angled triangle is equal to the sum of the squares described on its remaining sides," are facts, the one deduced from observation or simple...

...constant ratio of equality between the square of the hypotenuse of a right-angled triangle, and the sum of the squares of the two sides containing the right angle ; we are enabled to substitute either quantities generally as expressed by algebraical notation, or...