| 1844
...squares described upon the other 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,...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
...AB, BC is equal to the square of AB. If therefore a straight line, &c. QED PROPOSITION III. THEOREM. **If a straight line be divided into any two parts,...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
...them, instead of being established by continual appeals to original principles. PROP. III. THEOR. — **If a straight line be divided into any two parts,...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... | |
| Euclid - 1845 - 199 sider
...straight line, &c. QED CB FE BOOK II. PROP. m. IV. • 46. 1. t 31. 1. PROPOSITION III. THEOK. — **If a straight line be divided into any two parts,...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
...rectangle AB, BC, is equal to the square of AB. Wherefore, If a straight line Sjc. QED PROP. III. THEOR. **If a straight line be divided into any two parts,...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
...multiplying both members of 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,...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
...two sides of it, the angle contained by these two sides is a right angle. Section 3. 1. Prove that **if a straight line be divided into any two parts,...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
...whole and each of the parts, are together equal to the square of the whole line. PROP. III. THEOREM. **If a straight line be divided into any two parts,...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
...contained by two straight lines AB, AC is sometimes simply called the rectangle AB, AC. PROP. III. THEOR. **If a straight line be divided into any two parts,...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... | |
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