 | John Playfair - Geometry - 1829 - 210 pages
...Prop. 47. 1. In any right angled triangle the square described on the hypothenuse is equal to both the squares described on the other two sides. Let ABC be a right angled triangle, having the right angle ACB, and let the squares AE, FC, Cl be described on the... | |
 | Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...PROPOSITION XLVIII. THEOREM. — If the square described on one of the sides of a triangle, be equal to the sum of the squares described on the other two sides of it; the angle made by those two sides is a right angle. Let ABC be a triangle, which is such that... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...the two rectangles BDEF, CDEG, taken together, make up the square BCGF : therefore the square BCGF, described on the hypothenuse. is equivalent to the sum of the squares ABHL, ACIK, described on the Uvo other sides ; in ether wojrds, '. Cor. 1. Hence the square of one... | |
 | Adrien Marie Legendre - Geometry - 1838 - 382 pages
...GEOMETRY, PROPOSITION XI. THEOREM. The square described on the hypothenuse of a right angled triangle is equivalent to the sum of the squares described on the other two sides. Let the triangle ABC be right angled at A. Having described squares on the three sides, let fall from A,... | |
 | Charles Davies - Geometrical drawing - 1840 - 262 pages
...4=90 degrees. 10. In every right angled triangle, the square described on the hypothenuse, is equal to the sum of the squares described on the other two sides. Thus, if ABC be a right angled triangle, right angled at C, then will the square D described on AB... | |
 | Scotland free church, gen. assembly - 1847 - 554 pages
...makes the alternate angles equal. 2. If the square described on one of the sides of a triangle be equal to the sum of the squares described on the other two sides, these sides contain a right angle. 3. Divide a given line into two parts, so that the rectangle contained... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...Problem IV.) PROP. VII. THEOREM. The square described on the hypotenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides. Let the triangle be KDI, right angled at I. Describe squares onKD, KI, DI ; then we have to prove that... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...the two rectangles BDFE, CDEG, taken together, make up the square BCGF : therefore the square BCGF, described on the hypothenuse, is equivalent to the sum of the squares ABHL, ACIK, described on the other two sides; in other words, BC^AB'-f-AC". Therefore, The square described... | |
 | Nathan Scholfield - 1845 - 894 pages
...the two rectangles BDEF, CDEG, taken together, make up the square BCGF: therefore the square BCGF, described on the hypothenuse, is equivalent to the sum of the squares ABHL, AC1K, described on the two other sides ; in other words, BC"=AB'-fAC2. Cor. 1. Hence the square... | |
 | James Bates Thomson - Arithmetic - 1846 - 354 pages
...principle in geometry, that the square described on the hypothenuse of a right-angled triangle, is equal to the sum of the squares described on the other two sides. (Leg. IV. 11. Euc. I. 47.) Thus if the base of the triangle ABC is 4 feet, and the perpendicular 3... | |
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The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides. 
