| Charles Reiner - 1837
...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.... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...square of AC. PROPOSITION 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... | |
| Euclides - 1838
...line, &c. t>. i:. i,. * PROP. VIII. THEOR. If a straight line be dieided 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 - 1840
...half 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 square... | |
| Euclides - 1840
...the 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 ; join EB,... | |
| Euclides - 1841
...straight line, &c. QED PROP. VIII. THEOR. 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... | |
| John Playfair - Euclid's Elements - 1842 - 317 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 - 1842
...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
...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 unequal... | |
| George Peacock - Algebra - 1845
...both cases. The first case is equivalent to the following problem. Its firet case stated and solved. " **To divide a given line into two such parts that the rectangle contained by the whole** and one of the parts shall be equal to the square of the other." If we call x the greater of the two... | |
| |