| John Radford Young - Euclid's Elements - 1827 - 228 pages
...The square of a line is equivalent to four times the square of half the line. , ' ^ . PROPOSITION VI. **THEOREM. The square described on the difference of two lines is equivalent to the** squares on the two lines diminished by twice their rectangle. The square upon AB, the difference of... | |
| Adrien Marie Legendre - Geometry - 1828 - 346 pages
...demonstrated in algebra, in obtaining the square of a binomial ; which is expressed thus : IF THEOREM. 1 82. **The square described on the difference of two lines, is equivalent to the sum of** thc squares described on the lines respectively, minus twice the rectangle contained by the lines.... | |
| Adrien Marie Legendre - Geometry - 1830 - 344 pages
...demonstrated in algebra, in obtaining the square of a binomial ; which is expressed thus : THEOREM. 182. **The square described on the difference of two lines is equivalent to the sum of the squares** described on the lines respectively, minus twice the rectangle contained by the lines. Let AB and BC... | |
| John Playfair - Euclid's Elements - 1835 - 336 pages
...adding <? to each member of this equality, we shall have, COR. From this proposition it is evident, that **the square described on the difference of two lines is equivalent to the sum of the squares** described on the lines respectively, minus twice the rectangle contained by the lines. For a — c... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...demonstrated in algebra, in obtaining the square of a binominal ; which is expressed thus : PROPOSITION IX, **THEOREM. The square described on the difference, of...two lines, is equivalent to the sum of the squares** described on the lines, minus twice the rectangle contained by the lines. Let AB and BC be two lines,... | |
| John Playfair - Euclid's Elements - 1837 - 332 pages
...equality, we shall have, COR. From this proposition it is evident, that the square described on Hie **difference of two lines is equivalent to the sum of the squares** described on the lines respectively, minus twice the rectangle contained by the lines. For a — c=4... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...member of this equality, we shall have, or <z2+c2=2ac+R Coa. From this proposition it is evident, that **the square described on the difference of two lines is equivalent to the sum of the squares** described on the lines respectively, minus twice the rectangle contained by the lines. For a — c=b... | |
| James Bates Thomson - Geometry - 1844 - 268 pages
...taking these two rectangles from each member of the equation we have AC2= AB2+BC'— 2(AB x BC). Hence, **The square described on the difference of two lines, is equivalent to the sum of the** sqt,ares described on each of the linesi minus twice the rectangle contained by those lines. BOOK IV.... | |
| Nathan Scholfield - 1845 - 894 pages
...into which a line may be divided. This is equivalent to the algebraical expression PROPOSITION XI. **THEOREM. The square described on the difference of...two lines is equivalent to the sum, of the squares** described on the lines, minus twice the rectangle contained by the lines. Let AB and BC be two lines,... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
....-.a2+c2=62+2c(6+c), « or a2+c2=2ac+62. COR. From this proposition it is evident, that the square described on tJte **difference of two lines is equivalent to the sum of the squares** described on the lines respectively, minus twice the rectangle contained by the lines. For a — c=b... | |
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