| Euclides - 1837 - 88 sider
...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 contained by the...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 = AC x CB + CB*.... | |
| John Playfair - 1837 - 318 sider
...by a, we shall have azs=ab+ad FE, 6 • F K J. H A PROP. III. THEOR. If a straight line be divided **into any two parts, the rectangle contained by the...'by the two parts, together with the square of the** aforesaid part. Let the straight line AB be divided into two parts, in the point C ; the B E rectangle... | |
| Euclid, James Thomson - 1837 - 390 sider
...manner similar to this, several of the following propositions nay be 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** square of that part, together with the rectangle contained by the two parts. Let the straight line... | |
| Euclides - 1838
...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...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 : the rectangle... | |
| Euclides - 1841 - 351 sider
...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...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; the rectangle... | |
| Euclides - 1842
...square of A B. 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...by the two parts, together with the square of the** aforesaid part. Let the straight line AB be divided into two parts in the point c : the rectangle AB,... | |
| John Playfair - 1842 - 317 sider
...PROP. III. THEOR. If a straight line be divided into any two parts, the rectangle contained by tke **whole and one of the parts, is equal to the rectangle...by the two parts, together with the square of the** aforesaid part. Let the straight line AB be divided into two parts, in the point C ; the rectangle... | |
| 1844
...two sides of it, the angle contained by these two is a right angle. 6. If a straight line be divided **into any two parts, the rectangle contained by the...by the two parts, together with the square of the** aforesaid part. 7. Describe a square equal to a given rectilineal figure. 8. Find the centre of a circle.... | |
| Euclides - 1845
...of AB. If therefore a straight line, &c. QED PROPOSITION III. THEOREM. If a straight line be divided **into any two parts, the rectangle contained by the...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. Then the rectangle... | |
| Euclid, James Thomson - 1845 - 352 sider
...established by continual appeals to original principles. PROP. III. THEOR. — 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** square of that part, together with the rectangle contained by the two parts. Let the straight line... | |
| |