| Jeremiah Day - 1827 - 332 páginas
...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 páginas
...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 - 186 páginas
...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... | |
| 1833
...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 - 183 páginas
...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 páginas
...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... | |
| 1836 - 472 páginas
...rectangle contained by the two parts, together with the square of the foresaid part. IV. 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. Сок. From the... | |
| John Playfair - 1836 - 114 páginas
...parallelogram, are equal so one another. Which was te be proved. PROP. XX. 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... | |
| William Grier - 1836 - 344 páginas
...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... | |
| William Grier - 1836 - 344 páginas
...and AD 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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