| Charles Reiner - Geometry - 1837 - 215 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
...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
...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
...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
...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 - 317 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... | |
| Euclid, James Thomson - Geometry - 1845 - 352 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
...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
...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
...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... | |
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