 | Jeremiah Day - 1827 - 352 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 - 210 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 - 412 páginas
...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 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 - 488 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 - 148 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 - 380 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 - 384 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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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. 
