 | 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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Iff 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 of the other part, is equal to the square of the straight line which is made up of the whole and that... 
