 | Euclid - 1835 - 540 pages
...QED PROP. VIII. THEOR. JJ F E a 34. 1. 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 t/ie other part, is equal to the square of the straight line which is made... | |
 | 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... | |
 | John Hind - Algebra - 1837 - 584 pages
...answer the symbolical condition. • Ex. 3. Divide 20 into two parts, so that the product of the whole and one of the parts, may be equal to the square of the other part. Let a? = one part : .-. 20 - as = the other : whence, 20a? = (20 - off = 400 - 40a? + of : .-. a? -... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...their product ; that is, 49 = .J.)+ .1~pJl '. into two parts, so that the rectangle under the whole and one of the parts, may be equal to the square of the other. Upon AB describe (I. 46.) the square AD ; bisect (I. 10.) AC in E, and join E with B, the remote extremity... | |
 | 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... | |
 | 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... | |
 | 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 - 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 - 82 pages
...line made up of the 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...parts may be equal to the square of the other part. rtl PROP. XII. THEOR. In an obtuse-angled triangle, the square of the side subtending the obtuse angle... | |
 | 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... | |
| |
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... 
