...generalizations. In pursuance of this view we may say that, so Jong as the geometrical truth, that the square of the hypothenuse of a right-angled triangle is equal to the squares of the other two sides, is recognized as experimentally true, it constitutes a part of...

...connecting the two points ; measure the line. 35. Find the square root of the sum of 82 and 6*. 322. The square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the two other sides. 61n 323. The square of either the base or the perpendicular...

...Columbus discovered America in 1492 ; water is composed of two parts hydrogen to one part oxygen ; the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides." Then he tried to repeat to himself the process of the...

...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. EOMETRY, then, is the application of strict...

...distance from X to T, by adding the squares of XY and YT, and extracting the square root of their sum. (The square of the hypothenuse of a rightangled triangle is equal to the sum of the squares on the legs.) Then take two tapes, and placing the ring of one at X, and of...

...fact. But it is fact under selected aspects only. When I set myself to solve the problem of whether the square of the hypothenuse of a rightangled triangle is equal to the squares of the other two sides, I start with what I treat as an actual thing, the idealised pictorial...

...distance from X to T, by adding the squares of XY and YT, and extracting the square root of their sum. (The square of the hypothenuse of a rightangled triangle is equal to the sum of the squares on the legs.) Then take two tapes, and placing the ring of one at X, and of...

...later, while in the adjoining class-room I strove to have the minds of the boys grasp the reasons why the square of the hypothenuse of a rightangled triangle is equal to the sum of the squares of the other two sides, noise of a great uproar came through the door opening...

...third so as to make the alternate exterior angles equal, the lines 5 Two triangles are similar when 6 The square of the hypothenuse of a right-angled triangle is equal to 7 To reduce a polygon to an equivalent triangle. 8 Prove that the lines joining the middle points of...

...measures itself. Let us again illustrate by that pivotal theorem still named after Greek Pythagoras: the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. In this equation we see one geometric form or concept...