 | Robert Chambers - Encyclopedias and dictionaries - 1890 - 866 pages
...concerned with measurement. An example of a metrical property is the theorem of the three squares : The square on the hypotenuse of a rightangled triangle is equal to the sum of the squares on the two sides. The geometry of Euclid s Elements is metrical. Descriptive geometry is... | |
 | James Frederick Ferrier - Philosophy - 1888 - 744 pages
...This, therefore, is not a truth valid at all times for all intelligence. Take another case. I say, The square on the hypotenuse of a right-angled triangle is equal to the squares on the other two sides ; or, to take a simpler case, I say that two straight lines cannot... | |
 | Horatio Nelson Robinson - 1888 - 372 pages
...by the use of the two following principles, which are demonstrated in geometry. 1st. The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. 2d. The areas of two circles are to each other as the squares of... | |
 | George William Usill - Surveying - 1889 - 306 pages
...define all the angles. Now the relations of trigonometrical ratios to one another (since the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the two sides) are as follows : — Since a1 + b' — c\ .. .... . , a2 62 c2 , dividing... | |
 | Isaac Hammond Morris - Geometry, Plane - 1890 - 440 pages
...double of the triangle. (Eue. i. 41.) ABСD = twiceABС. (Fig. 6.) E FG H = twice EF J. (Fig. 7.) 7. The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides. (Eue. i. 47.) The sq. CBDE = thesq. ABFG + the sq. AH JC. (Fig.... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...Euclide in Elementorum libro VI. allatam' (1668) : — Ex. 740. — The equilateral triangle described on the hypotenuse of a right-angled triangle is equal to the sum of the equilateral triangles described upon the other two sides. Let BLC, CM A, ANB be the equilateral... | |
 | Euclid - Geometry - 1890 - 442 pages
...sides parallel and equal to BH. (Pappus extension of\. 47.) 64. The area of the equilateral triangle on the hypotenuse of a right-angled triangle is equal to the sum of the areas of the equilateral triangles on its sides. A NOTE— Let APB, BQC, CRA be the As, BAG being... | |
 | Lewis Carroll - Mathematics - 1890 - 126 pages
...centuries, affect the clearness, or the charm, of Geometrical truths. Such a theorem as ' the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the sides ' is as dazzlingly beautiful now as it was in the day when Pythagoras first... | |
 | Sir George Newnes, Herbert Greenhough Smith - England - 1901 - 792 pages
...that if the equal sides be produced the angles on the other side of the base are equal also ; or that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the two other sides. By demonstrating our knowledge of these things we should demonstrate... | |
 | Seth Thayer Stewart - Geometry - 1891 - 428 pages
...line which is made up of the whole line and that part. PROPOSITION XXIV. 218. Theorem: The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the two other sides. Statement : Let ABC be any right-angled triangle. Let AL be a square... | |
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Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides. 
