 | 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...equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines. Let AB and BC be the two lines, AC... | |
 | 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...equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines. For a — c = b ; therefore, by involution,... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...property demonstrated in algebra, in obtaining the square of a binominal ; which is expressed thus : PROPOSITION IX, THEOREM. The square described on the...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, AC their difference ;... | |
 | 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 ; therefore, by involution,... | |
 | 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...equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines. For a — c=b ; therefore, by involution,... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...the square on the whole line would be equivalent to four times the square on half the line. PROP. V. THEOREM. The square described on the difference of two lines is equivalent to the sum of the squares of the two lines, diminished by twice the rectangle contained by the lines. Let AB, BC,be the two lines,... | |
 | 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.... | |
 | John Playfair - Euclid's Elements - 1844 - 338 pages
...=2ac+62. COR. From this proposition it is evident, that the square described on the difference oftwo 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=A ; therefore, by involution,... | |
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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. 
