 | 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... | |
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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. 
