 | Euclides - 1821 - 294 pages
...6 -f- 6 X 2 is = to 8 X 8 — 8 X 2. PROP. 4T THEQR. If a right line be divided into any two parts, the square of the whole line is equal to the sum of the squares of the parts and twice the rectangle under the parts On the given line describe a D% draw a... | |
 | Rev. John Allen - Astronomy - 1822 - 516 pages
...DL, EH are equal to those under BD and A, DE and A, and EC and A. „ PROP. II. THE OR. If a right line (AB), be divided into any two parts (AC, CB) ; the square of the whole (AB), is equal to the recta ngles.(BAC, ABC), under the whole (AB), and each of the parts (AC, CB)... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...double rectangle under every distinct pair of them. Thus if it be divided into three parts x, y, z, the square of the whole line is equal to the sum of the squares of x, y, and z together with twice the sum of the rectangles x X y, y X «, and x X x. PROPOSITION... | |
 | John Playfair - Geometry - 1829 - 210 pages
...ABTLKE, there will remain AD, that is, AC" = AB3+ BC3 — 2AB .BC. Therefore, the square &c. QED COR. 1. If a straight line AB be divided into any two parts AC, CB, the squares of the whole line and of one of the parts are together equal to twice the rectangle contained... | |
 | Euclides - 1833 - 304 pages
...same base and of the same altitude. PROP. 2. THEOR. If a right line be divided into any two* parts, the square of the whole line is equal to the sum of the rectangles under the whole line and each of the parts. Describe on the given line an2 (prop. 46, 1.), and through... | |
 | Euclid - Euclid's Elements - 1833 - 216 pages
...under AC and CB. PROP. IV. THEOR. If a right line (AB) be divided into any two parts Fig. 6. (in 0), the square of the whole line is equal to the sum of the squares of the parts and twice the rectangle under the parts. On AB describe the square ACDB ; draw... | |
 | George Darley - Euclid's Elements - 1836 - 172 pages
...is, the rectangle under AC and CB. This, &c. ART. 92. If a right line be divided into any two parts, the square of the whole line is equal to the sum of the squares of the parts together with twice the rectangle under the parts. Let AB he a right line divided... | |
 | Euclides - 1840 - 192 pages
...contained by the whole line and that part, together with the square of the other part. M PROP. VIII. THEOR. If a straight line (AB) be divided into any two parts (AC, CB), the square of the sum of the whole line and one of its parts is equal to four times the rectangle contained by the whole... | |
 | Scottish school-book assoc - 1845 - 444 pages
...in the point C, the proposition becomes the following. If a straight line be divided into two parts, the square of the whole line is equal to the sum of the squares of the parts, together with twice the rectangle contained by the parts. Cor. 2. If AB and CB... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...restriction of the number of parts to tiao is unnecessary. : . ! PROPOSITION III.— ТНЕОЕБИ. . ., If a straight line (AB) be divided into any two parts (AC, CB), the rectangle contained ,by the whole and one of the parts is equal to the rectangle contained by the twoparts%... | |
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If a straight line be divided into any two, parts, the square on the whole line is equal to the sum of the rectangles contained by the whole and each of the parts*. 
