| Andrew Bell - 1837 - 240 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 - 88 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 - 390 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 - 215 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.... | |
| Euclid, Robert Simson - 1838 - 416 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
...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
...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 - 1840
...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 - 1841 - 351 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 - 317 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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