 | James McCosh - Intuition - 1882 - 472 pages
...Caesar lived, or that Jesus Christ died and rose again, or those by which we come to be assured that the square of the hypotenuse of a right-angled triangle is equal to the square of the other two sides. But in all such regressions we must at last come back to something... | |
 | Richard Wormell - Geometry, Plane - 1883 - 210 pages
...(AD = CD) = diff. of sqrs. on AD and D C. 112. Three times the sum of the squares on the .sides of a triangle is equal to four times the sum -of the squares of the lines joining the middle point of .each side with the opposite angle, (See fig. of Example 14.) The... | |
 | Euclides - 1884 - 434 pages
...angle of a triangle is greater than the squares on the other two sides. 15. Five times the square on the hypotenuse of a right.angled triangle is equal to four times the sum of the squares on the medians drawn to the other two sides. 16. Three times the square on a side of an equilateral... | |
 | John Casey - Geometry - 1886 - 262 pages
...4AE2 + 4EF2 +4FB2 = AC2 +BD2 + 4EF2. Prop. 5. — Three times the sum of the squares of the fides of a triangle is equal to four times the sum of the squares of the lines bisecting the sides of the triangle. Dem. — Let D, E, F be the middle points of the sides.... | |
 | Franklin Verzelius Newton Painter - Education - 1886 - 378 pages
...Pythagoras to this science was not fruitless. To him we owe the discovery of the geometrical truth that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. Religion formed the basis of moral action. Pythagoras,... | |
 | John Casey - Geometry - 1888 - 279 pages
...4AE2 + 4EP +4FB2 = AC2 +BD2 + 4EE2. Prop. 5. — Three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the lines bisecting the sides of the triangle. Dem. — Let D, E, F be the middle points of the sides.... | |
 | Horatio Nelson Robinson - 1888 - 372 pages
...may be solved 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... | |
 | George William Usill - Surveying - 1889 - 306 pages
...given we can 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... | |
 | Lewis Carroll - Mathematics - 1890 - 126 pages
...nor thirty 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... | |
 | Seth Thayer Stewart - Geometry - 1891 - 428 pages
...the diagonals of a quadrilateral is bisected by the lines joining the diameters of the quadrilateral. 4. Prove that five times the square of the hypotenuse...of the squares of the medians from its extremities. PROPOSITION XXIII. 416. Theorem : Of three similar figures constructed on the hypotenuse and the sides... | |
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The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. 
