 | George Darley - 1836 - 172 σελίδες
...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... | |
 | William Grier - 1836 - 384 σελίδες
..., 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... | |
 | William Grier - 1836 - 380 σελίδες
...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... | |
 | John Playfair - 1836 - 148 σελίδες
...in H, so that the rectangle AB, BH is equal to the square of AH. Which was to be done. E PROP. XXV. THEOR. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts are equal to twice the rectangle contained by the... | |
 | Euclides - 1837 - 112 σελίδες
...showing that AB x BC = figures AD + CE, and that these are = AC x CB + CB*. PROPOSITION IV. Theorem. If a straight line be divided into any two parts,...equal to the squares of the two parts together with twice the rectangle contained by the parts. * By the rectangle AX BC (the lines A and BC being separate)... | |
 | Charles Reiner - 1837 - 246 σελίδες
...the rectangle contained by ac and c b. M.- — Express this truth as a general proposition. P. — If a straight line be divided into any two parts,...equal to the squares of the two parts, together with twice the rectangle contained by the parts. The master will, here, have a suitable opportunity of directing... | |
 | Andrew Bell - 1837 - 290 σελίδες
...• BC is equal to the rectangle AC • CB, together with the square of BC. PROPOSITION TV. THEOREM. If a straight line be divided into any two parts,...equal to the squares of the two parts, together with twice the rectangle contained by the parts. Let the straight line AB be divided into any two parts... | |
 | Charles Reiner - 1837 - 254 σελίδες
...twice the rectangle contained by ac and c b. M.—Express this truth as a general proposition. P.—If a straight line be divided into any two parts, the...equal to the squares of the two parts, together with twice the rectangle contained by the parts. The master will, here, have a suitable opportunity of directing... | |
 | Euclid, James Thomson - 1837 - 410 σελίδες
...A and BD, by A and DE, and by A and EC. * Wherefore, if there be two straight lines, &c. PROP. II. THEOR. IF a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts, are together equal to the square of the whole... | |
 | Robert Simson - 1838 - 434 σελίδες
...equal to the rectangle AC, CB, together with the square of BC. If therefore a straight line, &c. QED PROP. IV. THEOR. IF a straight line be divided into...equal to the squares of the two parts, together with twice the rectangle contained by the parts. Let the straight line AB be divided into any two parts... | |
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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. 
