 | Mathematics - 1836 - 488 pages
...of the difference of the lines. VIII. 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, James Thomson - Geometry - 1837 - 410 pages
...particular case of this problem in which the given lines are equal. PROP. XXIII. PROB. 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)... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...+ AC*. CBD 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 line made up of the whole... | |
 | 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.... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 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 - 264 pages
...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 - 192 pages
...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 ;... | |
 | Euclides - 1840 - 82 pages
...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... | |
 | Euclides - Geometry - 1841 - 378 pages
...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 - 332 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... | |
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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... 
