| John Playfair - Geometry - 1837 - 332 pages
...also derived from the above algebraical equality, by transposition. PROP. VIII. THEOR. If a straight **line be divided into any two parts, four times the...square of the other part, is 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... | |
| Euclid - Geometry - 1837 - 410 pages
...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
...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 times the...square of the other part, is 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... | |
| 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...square of the other part, is 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... | |
| Euclides - 1840 - 82 pages
...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 - 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 ;... | |
| Euclides - 1841 - 378 pages
...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 times the...square of the other part, is 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... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...also derived from the above algebraical equality, by transposition. PROP. VIII. THEOR. If a straight **line be divided into any two parts, four times the...square of the other part, is 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... | |
| Euclides - 1842 - 320 pages
...together with the square of AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOR. IF a straight **line be divided into any two parts : four times the...parts, together with the square of the other part, is** equivalent to the square of the straight line, which is made up of the whole and that part. ELEMENTS... | |
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