| Johann Georg Heck - Encyclopedias and dictionaries - 1851 - 714 pages
...particular case of this proposition is known as the Pythagorean : the square described upon the hypothenuse **is equivalent to the sum of the squares described on the other two sides.** As the unit of measure for the determination of the superficial relations of figures, we use a square... | |
| 1851
...a given angle, . •I. If the square described upon one of the sides _ 1C 3 of a triangle be equal **to the sum of the squares described on the other two sides,** the angle contained by those two sides is a right angle, . . 3. If a straight line be divided into... | |
| Daniel Leach, William Draper Swan - Arithmetic - 1851 - 280 pages
...the hypothenuse, and A Eas6' the other two sides the base and perpendicular. longest side , is equal **to the sum of the squares described on the other two sides.** Thus, suppose the longest side is 10 ft.., the base 6 ft., and the perpendicular 8 ft. 102:z=:100.... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...This proposition is equivalent to the algebraical formula, (a+b)x(ab)=o?-b*. PROPOSITION XI. THEOEEM. **The square described on the hypothenuse of a right-angled...equivalent to the sum of the squares described on the** two other sides. Let BCA be a right-angled triangle, right-angled at A : then will the square described... | |
| Charles Davies - Arithmetic - 1852 - 438 pages
...particular notice. 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 tria,ngle, right angled at C, then will the square D described on AB... | |
| Daniel Leach - Arithmetic - 1853 - 626 pages
...the base and perpendicular. 293. The square described on the hypothenuse, or longest side, is equal **to the sum of the squares described on the other two sides.** Thus, suppose the longest side is 10 ft., the base 6 ft., and the perpendicular 8 ft. 10a=100. 6a=36.... | |
| George Roberts Perkins - Geometry - 1856 - 460 pages
...COMPARISON OF SQUARES CONSTRUCTED ON CERTAIN LINES. THEOREM XXIX. The square constructed on the hypotenuse **of a right-angled triangle, is equivalent to the sum of the squares** constructed respectively on the other two sides. This Theorem is not a fundamental one, like Theorem... | |
| Benjamin Greenleaf - Arithmetic - 1857 - 452 pages
...Also, the line BC, being perpendicular to the base, is the altitude. 535. The square described upon **the hypothenuse of a rightangled triangle is equivalent to the sum of the squares described** upon the other two sides. Thus, if the hypothenuse AC be 5 feet, the base AB 4 feet, and the perpendicular... | |
| Adrien Marie Legendre - Geometry - 1857 - 444 pages
...right•angled triangle, right•angled at A : then will the square described on the hypothenuse BO be **equivalent to the sum of the squares described on the other two sides,** BA, AC. G Having described a square on each of the three sides. let fall from A, on the hy• pothenuse,... | |
| James Stewart Eaton - Arithmetic - 1857 - 376 pages
...circumferences. FIG. 12. 6. 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.** This will be seen by counting the small squares in the square of the hypothenuse and those in the squares... | |
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