| 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...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 : the... | |
| Euclides - 1840
...the sum of the 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 - 351 páginas
...rectangle AB, BC, 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,...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; the rectangle... | |
| Euclides - 1842
...rectangle AB, BC, is equal to the square of A B. If therefore a straight line, &c. QED PROP. III. THEOR. **IF a straight line be divided into any two parts,...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 rectangle... | |
| John Playfair - 1842 - 317 páginas
...multiplying both members of this equality by a, we shall have a~=ab+ad FE J o $ DEC K JL B 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 contained by the two parts, together with... | |
| 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,...contained 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... | |
| 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,...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. Then... | |
| Euclid, James Thomson - 1845 - 352 páginas
...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 páginas
...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.... | |
| John Playfair - 1846 - 317 páginas
...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,...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... | |
| |