 | Andrew Bell - 1837 - 290 sider
...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, four...equal to the square of the straight line which is made up of the whole and the first mentioned part. Let the straight line AB he divided into any two parts... | |
 | Euclides - 1837 - 112 sider
...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, four...square of the other part, is equal to the square of the line made up of the whole and that part. R In the construction of the figure it is necessary to show... | |
 | Euclid, James Thomson - 1837 - 410 sider
...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 - 1837 - 254 sider
...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 - 1838 - 434 sider
...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...equal to the square of the straight line which is made up of the whole and that part. Let the straight line AB be divided into any two parts in the point... | |
 | Euclides - 1838 - 264 sider
...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...to the square of the straight line, which is made up of the whole and that part. Let the straight line AB be divided into any two parts in the point... | |
 | Euclides - 1840 - 192 sider
...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 sider
...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 - 1841 - 378 sider
...AB, BC, together with the square of AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOR. Iff a straight line be divided into any two parts, four...equal to the square of the straight line which is made up of the whole and that part. Let the straight line AB be divided into any two parts in the point... | |
 | John Playfair - 1842 - 332 sider
...This may be also derived from the above algebraical equality, by transposition. PROP. VIII. THEOR. If a straight line be divided into any two parts, four...equal to the square of the straight line which is made up of the whole and the first-mentioned part. Let the straight line AB be divided into any two parts... | |
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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... 
