 | William James Milne - 1877 - 402 σελίδες
...sides of a rightangled triangle is expressed thus: 529. PRINCIPLES.— 1. The square described upon the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides. 2. The square on either of tie When the number of square units... | |
 | 1883 - 248 σελίδες
...to use all intelligible abbreviations and algebraic symbols.) 1. Prove that the square described on the hypotenuse of a right-angled triangle is equal to the sum of the squares described on the other sides. 2. Prove by a geometrical construction that the square' on... | |
 | James McCosh - 1882 - 472 σελίδες
...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... | |
 | John Trowbridge - 1884 - 408 σελίδες
...the philosophical proofs. Thus we can by actual measurement ascertain the truth that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the base and altitude of the triangle, and, knowing this fact, we can make a great and... | |
 | 1884 - 708 σελίδες
...is 8,545 feet ; determine whether the parallelogram is a rectangle. By Euclid I. 47, the square on the hypotenuse of a rightangled triangle is equal to the sum of the squares on the sides. Here the diagonal corresponds with the hypotenuse. Now 75842 + 3937* = 73.°i7.°25,... | |
 | Euclides - 1884 - 182 σελίδες
...which shall be equal to a given straight line." 9. Give the proposition equivalent to : " The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares upon the other two sides." 10. In the construction to XLVIII., show that it would be unsatisfactory... | |
 | Joseph Ray - 1885 - 358 σελίδες
...heing the base, BC the perpendicular, BI and AC the hypotenuse. ART. 290. It is a known principle, that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. REVIEW. — 287. What is the rule for square root? NOTES. How proceed... | |
 | Franklin Verzelius Newton Painter - 1886 - 378 σελίδες
...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, by a profound... | |
 | Horatio Nelson Robinson - 1888 - 372 σελίδες
...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 squares of... | |
 | George William Usill - 1889 - 306 σελίδες
...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 c2 , dividing... | |
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Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides. 
