| Euclid - 1845 - 199 sider
...BOOK II. PROP. m. IV. • 46. 1. t 31. 1. PROPOSITION III. THEOK. — If a straight line be divided **into any two parts, the rectangle contained by the whole and one of the parts,** w equal to the rectangle contained by the two parts, together with the square of the aforesaid part.... | |
| Euclides - 1846
...square of AB. Wherefore, If a straight line Sjc. 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... | |
| John Playfair - 1846 - 317 sider
...this equality by a, we shall have as=ab+ad FE K JL H 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 rectangle... | |
| John Playfair - 1847 - 317 sider
...parts, is equal to the rectangle contained 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 rectangle AB.BC is equal to the rectangle AC.BC, together with BC2. Upon BC describe (Prop. 46. 1.)... | |
| J. Goodall, W. Hammond - 1848
...contained by these two sides is a right angle. Section 3. 1. Prove that 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. 2. Prove that if a straight line be divided into two equal and also two unequal parts,... | |
| Euclides - 1848
...are together equal to the square of the whole line. PROP. 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. PROP. IV. THEOREM. If a straight line be divided into any two parts, the square of... | |
| Euclides, Thomas Tate - 1849 - 108 sider
...AC is sometimes simply called the rectangle AB, AC. 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** with the rectangle contained by the two parts, together with the square of the aforesaid part. Let... | |
| 1852
...squares described upon the sides which contain the right angle. III. 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. following sentence, shewing the variou» clauses, &c. :— " Not to do your best when... | |
| Euclides - 1852
...multiplied together.] 90 BOOK II. • xlvi. 1. THE ELEMENTS 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,... | |
| Euclides - 1853 - 147 sider
...If QED df therefore a straight line, &c. PROPOSITION III. — THEOREM. If a slraigM line be divided **into any two parts, the rectangle contained by the...rectangle contained by the two parts, together with** tlie square of the aforesaid part. LET the straight line ab be divided into any two parts in the point... | |
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