| 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 - 472 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 - 240 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 - 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 - 194 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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