 | Mathematics - 1835 - 684 pages
...square of the whole une. PROP. 31. (Eue. ii. 3.) If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts, shall be equal to the rectangle contained by the two parts, together with the square of the aforesaid... | |
 | Mathematics - 1836 - 488 pages
...the rectangle contained by the lines together with the square of the difference of the lines. VIII. If a straight line be divided into any two parts,...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 the... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...contained by the " lines together with the square of the difference of the " lines." PROP. VIII. THEOR. If a straight line be divided into any two parts,...contained by the whole line, and one of the parts, togetiier with the square of the other part, is equal to the square of the straight line which is made... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...KF, and that these = 2 AH + KF ; ;and that these = 2 AB x BC + AC*. CBD PROPOSITION VIII. Theorem. If a straight line be divided into any two parts,...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 and that part. R In the... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...are equal to twice the rectangle AB-BC, together with the square of AC. PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts,...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 the... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...equal to the square of their difference, together with four times their rectangle. PROP. VIII. THEOR. IF a straight line be divided into any two 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... | |
 | 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.... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...rectangle AB, BC, together with the square AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOR. Ir a straight line be divided into any two parts, four...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... | |
 | Euclides - 1838 - 264 pages
...AC. Wherefore, if a straight line, &c. t>. i:. i,. * PROP. VIII. THEOR. If a straight line be dieided into any two parts, four times the rectangle contained...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... | |
 | 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 ;... | |
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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 up of the whole and that... 
