 | John Playfair - 1842 - 332 sider
...instance, let the segments of BC be denoted by b, c, and d ; then, A(6+e+d)=A6-(-Ac-(-A<2. PROP. II. THEOR. If a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts, are together equal to the square of the whole... | |
 | Euclides - 1842 - 316 sider
...the 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, the rectangle contained by the whole and one of the parts is equal to the rectangle contained by the two... | |
 | Scotland free church, gen. assembly - 1847 - 554 sider
...two right angles. 3. Parallelograms upon equal bases, and between the same parallels, are equal. 4. If a straight line be divided into any two parts,...square of the whole line is equal to the squares of each of the parts together with twice the rectangle contained by the parts. 5. Equal straight lines... | |
 | James Bates Thomson - 1844 - 266 sider
...than in ordinary language. The proposition, (Euc. 4. 2,) that when a straight line is divided into two parts, the square of the whole line is equal to the squares of the two parts, together with twice the product of the parts, is demonstrated, by involving a binomial. •..-••' Let the side... | |
 | Euclides - 1845 - 546 sider
...line is equal to four times the square of half the line. Also, if a line be divided into any three parts, the square of the whole line is equal to the squares of the three parts, and twice the rectangle contained by every two parts. Prop. iv. Algebraically, (fig. Prop,... | |
 | Euclid, James Thomson - 1845 - 382 sider
...preceding them, instead of being 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... | |
 | Scottish school-book assoc - 1845 - 444 sider
...two parts in the point C, the proposition becomes the following. If a straight line be divided into two parts, the square of the whole line is equal to the sum of the squares of the parts, together with twice the rectangle contained by the parts. Cor. 2.... | |
 | Euclid - 1845 - 218 sider
...square of CB, is equal to the square of CD. Wherefore, if a straight line, &c. QED PROPOSITION VII. THEOR. — If a straight line be divided into any two parts, the iquares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the... | |
 | Euclides - 1846 - 272 sider
...under AC and CF. PROPOSITION IV. THEOREM. If a right line (AB) be divided into any two parts, (in O) the square of the whole line is equal to the squares of the parts, together with twice the rectangle under the parts. On AB describe the square ACDB, and draw... | |
 | Euclides - 1846 - 292 sider
...the 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, the rectangle contained by the whole and one of the parts is equal to the rectangle contained by the two... | |
| |
If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. 
