| Euclides - 1862 - 140 sider
...line, &o. QED PROPOSITION 8. -THEOREM. If a straight line be divided into Any two parts, four times **the rectangle contained by the whole line and one of the parts,** together with the square on the other part, is equal to the square on the straight line which is made... | |
| Euclides - 1862 - 172 sider
...together with the square of BC. If, therefore, a straight line be divided, &c. QED PROP. IV. — THEOREM. **If a straight line be divided into any two parts; then the** square of the whole line is equal to the squares of the two parts, together with twice the rectangle... | |
| Euclides - 1864 - 448 sider
...other part. Let AB be the given straight line. It is required to divide AB into two parts, so that **the rectangle contained by the whole line and one of the parts,** shall be equal to the square on the other part. c KD Upon AB describe the square A CSB; (i. 46.) bisect... | |
| Euclides - 1865 - 402 sider
...of CB, is equal to the square of CD. Wherefore, if a straight line, &c. QE Du PROP. VII.— THEOREM. **If a straight line be divided into any two parts ; then the** squares of the whole line and of one of the parts, are equal to twice the rectangle contained by the... | |
| Euclid, Isaac Todhunter - 1867 - 426 sider
...line &c. QED B t> PROPOSITION 8. THEOREM. If a straight line be divided into any two parti, four times **the rectangle contained by the whole line and one of the parts,** together with the square en the other part, is equal to the square on the straight line which is made... | |
| Robert Potts - 1868 - 434 sider
...other part, Let AB be the given straight line. It is required to divide AB into two parts, so that **the rectangle contained by the whole line and one of the parts,** shall be equal to the square on the other part. FQ Upon AB describe the square A CDB ; (I. 46.) bisect... | |
| Schools inquiry commission - 1868 - 532 sider
...and having the angle В double of the angle C. Show that the side С В is double of the side A B. 3. **If a straight line be divided into any two parts : then the** squares of the whole line and one of the parts shall be equal to twice the rectangle contained by the... | |
| James Maurice Wilson - 1869 - 260 sider
...by addition that AB* + BC* = 2AD* + 2DB*. Ex. 3. To divide a straight line into two parts such that **the rectangle contained by the whole line and one of the parts is equal to the** square of the other part. Let AB be the given line. Construction. Draw a square ACDB '" " on AB; bisect... | |
| Euclides - 1871 - 136 sider
...that BGD is a straight line. /i as a If. a straight line be divided into any two parts, four times **the rectangle contained by the whole line and one of the parts,** together with the square on the other part, is equal to the square on the straight line which is made... | |
| Euclid, Charles Peter MASON - 1872 - 216 sider
...whole line BC and each of its parts. PBOPOSITION III. If a right line be divided into any two parts, **the rectangle contained by the whole line and one of the parts is equal to the** square on that part together with the rectangle contained by the two parts. The propositions required... | |
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