 | Charles Reiner - Geometry - 1837 - 254 pages
...a c. M.—Express this truth in words. P.—If a straight line be divided into any two parts, twice the rectangle contained by the whole line and one of the parts is equal to twice the square upon that part, together with twice the rectangle contained by the parts.... | |
 | Euclides - 1840 - 192 pages
...half and the produced part. PROP. XI. PROB. To divide a given straight line (AB) in such a manner that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. Upon AB construct the square ACDB ; bisect AC in E ;... | |
 | Euclides - 1840 - 82 pages
...and the produced part. .n. . PROP. XI. PROB. To divide a given straight line in such a manner that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. rtl PROP. XII. THEOR. In an obtuse-angled triangle, the... | |
 | Euclides - 1842 - 316 pages
...twice the rectangle AB, BC, together with the square of AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOR. IF a straight line be divided into...parts, together with the square of the other part, is equivalent to the square of the straight line, which is made up of the whole and that part. ELEMENTS... | |
 | Scotland free church, gen. assembly - 1847 - 554 pages
...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... | |
 | John Playfair - Euclid's Elements - 1844 - 338 pages
...2 —2ac+c 2 =6 2 . This may be also derived from the above algebraical equality, by transposition. PROP. VIII. THEOR. If a straight line be divided into...one of the parts, together with the square of the olher part, is equal to the square of the straight line which is made up of the whole and thefirst-mentioned... | |
 | Euclides, James Thomson - Geometry - 1845 - 382 pages
...of two lines, is equal to the square of their difference, together with four tunes their rectangle. PROP. VIII. THEOR. — If a straight line be divided...parts, four times the rectangle contained by the whole and one of the parts, together with the square of the other part, is equal to the square of the straight... | |
 | Euclides - 1845 - 546 pages
...BC, together with the square of AC. Wherefore, if a straight line, &c. QED PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts, four times the reel" angle contained by the whole line, and one of the parts, together with the square of the other... | |
 | Euclides - Geometry - 1853 - 334 pages
...other part. Let AB be the given straight line. It is required to divide it into two such parts, that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. On AB describe (i. 46) the square ACDB ; and supposing... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 476 pages
...question in its literal meaning. 2. To divide a line of 20 inches in length into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Let x = the greater part ; then 20 — x = the less... | |
| |
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 up of the whole and that... 
