 | George Darley - Euclid's Elements - 1836 - 172 pages
...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 - Mechanical engineering - 1836 - 384 pages
..., 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 - Mechanical engineering - 1836 - 380 pages
...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... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...equal to the square of BC, together with the rectangle AC.CB. * If, therefore, &c. PROP. IV. THEOR. IF a straight line be divided into any two parts,...the squares of the two parts, together with twice their rectangle, t Let the straight line AB be divided into any two parts in C ; the square of AB is... | |
 | Jeremiah Day - Algebra - 1839 - 354 pages
...than in ordinary language. The proposition, (Enc. 4. 2.) thai when a straight line is divided into two parts, the square of the whole line is equal to the squares of the iwo parts, together with twice the product of the parts, is demonstrated, by involving a binomial.... | |
 | Dionysius Lardner - Curves, Plane - 1840 - 386 pages
...several rectangles under the line and each of its parts. (242.) If a line be divided into two or more parts, the square of the whole line is equal to the squares of the several parts together with twice the rectangles under every pair of parts. Let theline AB (fig.l 1... | |
 | Euclides - 1840 - 82 pages
...contained by the whole line and that part, together with the square of the other part. PROP. VIII. THEOR. If a straight line be divided into any two parts, 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... | |
 | Euclides - 1840 - 192 pages
...by the parts. F T» PROP. IV. THEOR. If a straight line (AB) be divided into any two parts (AF, FB), the square of the whole line is equal to the squares of the parts, together with twice the rectangle contained by the parts. Upon AB describe the square ACDB ;... | |
 | Jeremiah Day - Algebra - 1841 - 362 pages
...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 tv/ice the product of the parts, is demonstrated, by involving a binomial. Let the side of a square... | |
 | William Grier - Mechanical engineering - 1842 - 320 pages
...and AE, 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 on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the parts. 
