 | Robert Simson - 1827 - 546 pàgines
...together with the square of BC. If therefore a straight line, &c. QED PROP. IV. THEOK. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. Let the straight... | |
 | Jeremiah Day - 1827 - 352 pàgines
...than in ordinary language. The proposition, (Euc. 4- 2.) that when a straight line is divided into two parts, the Square of the whole line is equal to the squares of the two parts, together with twice the product of the parts, is demonstrated, by involving... | |
 | Euclid, Dionysius Lardner - 1828 - 542 pàgines
...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 - 1829 - 210 pàgines
...the rectangle contained by the two parts together with the square of the foresaid part. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts together with twice the rectangle contained by the two parts. Or, in other... | |
 | William Grier - 1832 - 366 pàgines
...25.) and AE, and AD and FB : thus expressed, AD . AB = AD . AE + AD . EF + AD . FB.»— (Fig. 26.) If a right line be divided into any two parts, the square on the whole line, is equal to both the rectangles of the whole line and each of the parts. 30. Let... | |
 | 1833 - 412 pàgines
...rectangle contained by the two parts together with the square of the aforesaid part. 5. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts together, with twice the rectangle contained by the parts. a. Find the value... | |
 | Euclid - 1833 - 216 pàgines
...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... | |
 | Euclid - 1835 - 540 pàgines
...together with the square of BC. " If, therefore, a straight line," &c. QED PROP. IV. THEOR. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. Let the straight... | |
 | George Darley - 1836 - 172 pàgines
...together with the rectangle under DE and CB, that 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... | |
 | William Grier - 1836 - 380 pàgines
...AD and AE, and 9 BC Al) and EF, and AD and FB: thus expressed, AD. AB = AD . AE+ AD . EF + AD . FB.* If a right line be divided into any two parts, the square of the whole line, is equal to both the rectangles of the whole line and each of the parts. 30. Let the line AB be the sum of any... | |
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If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. 
