 | Robert Simson - 1835 - 544 sider
...equal to the square of AB. " If, therefore, a straight line," &c. QED PROP. III. THEOR. . If a straight line be divided into any two parts, the rectangle contained by the whole and one of tJie parts, is equal to the rectangle contained by the two parts, together with the square of the foresaid... | |
 | 1835 - 684 sider
...parts, shall be together equal to the square of the whole une. PROP. 31. (Eue. ii. 3.) If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts, shall be equal to the rectangle contained by the two parts, together with... | |
 | 1836 - 488 sider
...whole and each of the parts, are together equal to the square of the whole line. III. If a straight line be divided into any two parts, the rectangle...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... | |
 | Euclides - 1837 - 112 sider
...= figures AF + CE ; and that these are = AB x AC + AB x BC. PROPOSITION III. Theorem. If a straight line be divided into any two parts, the rectangle...rectangle contained by the two parts, together with the square of the aforesaid part. Proved by showing that AB x BC = figures AD + CE, and that these are... | |
 | Andrew Bell - 1837 - 290 sider
...together with the rectangle AB-BC, is equal to the square of AB. PROPOSITION III. THEOREM. If a straight line be divided into any two parts, the rectangle...rectangle contained by the two parts, together with the square of the foresaid part. Let the straight line AB be divided into two parts in the point C ; the... | |
 | Euclid, James Thomson - 1837 - 410 sider
...square of A B. In a manner similar to this, several of the following propositions nay be IF a straight line be divided into any two parts, the rectangle...by the whole and one of the parts, is equal to the square of that part, together with the rectangle contained by the two parts. Let the straight line... | |
 | Euclides - 1838 - 264 sider
...restriction of the number of parts to two is unnecessary. PROP. III. THEOR. If a straight line be dieided into any two parts, the rectangle contained by the...rectangle contained by the two parts, together with the square of the aforesaid part. Let the straight line AB be divided into any two parts in the point C... | |
 | Robert Simson - 1838 - 434 sider
...square of AB. If therefore a straight line, &c. Q^ ED PROP. III. THEOR. IF a straight line be diyided into any two parts, the rectangle contained by the...rectangle contained by the two parts, together with the square of the foresaid part. Let the straight line AB be divided into two parts in the point C ; the... | |
 | Euclides - 1840 - 82 sider
...rectangles contained by the whole line and each of its parts. ED f B PROP. III. THEOR. If a straight line be divided into any two parts, the rectangle contained by the whole line and either of its parts, is equal to the square of that part, together with the rectangle under... | |
 | Euclides - 1841 - 378 sider
...is equal to the square of AB. If therefore a straight line, &c. QED PROP. III. THEOR. If a straight line be divided into any two parts, the rectangle...rectangle contained by the two parts, together with the square of the aforesaid part. Let the straight line AB be divided into any two parts in the point C;... | |
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If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part. 
