 | Euclides - 1842 - 316 pages
...straight line, &c. QED PROP. VIII. THEOR. 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 of the other part, is equivalent to the square of the straight line, which... | |
 | Scotland free church, gen. assembly - 1847 - 554 pages
...on the other two sides, these sides contain a right angle. 3. Divide a given line into two parts, so that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. 4. The angle in a semicircle is a right angle. 5. Of... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...particular case of this problem m which the given lines are equal. PROP. XXIII. PROR. — To divide a given straight line into two parts, such that the rectangle contained by the whole and one of the parts may have a given ratio to the square of the other. Let AB (see the last figure)... | |
 | Euclid - Geometry - 1845 - 218 pages
...line, &c. QED PROPOSITION VIII. THEOR. — 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 of the other part, is equal to the square of the straight line, which is made... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...equality, by transposition. PROP. VIII. THEOR. 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 of the other part, is equal to the square of the straight line which is made... | |
 | Euclides - 1848 - 52 pages
...of the other part. PROP. VIII. 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 of the other part, is equal to the square of the straight line, which is made... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...straight line, &c. QED PROP. VIII. THEOR. 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 of the other part, is equal to the square of the straight line which is made... | |
 | University of Durham - Education, Higher - 1851 - 222 pages
...square of the parts together with twice the rectangle contained by the parts. 5. To divide a given straight line into two parts, such that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 6. If two circles cut one another... | |
 | 1867 - 336 pages
...be less than twice their rectangle. 3. 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 of the other part, is equal to the square of the straight liue which is made... | |
 | Euclides - 1852 - 152 pages
...kc added together.] PROP. VIII. THEOR. 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 of the other part, is equal to the square of the straight line, which is made... | |
| |
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... 
