 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.  Elements of Plane Geometry - Page 177by Franklin Ibach - 1882 - 196 pagesFull view - About this book
 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...E JJ 57 PROPOSITION XI. THEOREM. The square described on the hypotenuse of a right-angled triangle is equivalent to the sum of the squares described on the two sides. Let the triangle ABC be rightangled at A. Having formed squares on the three sides, let fall... | |
 | John Radford Young - Euclid's Elements - 1827 - 246 pages
...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. Let AD be the square on AB, BF the square... | |
 | 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,... | |
 | 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...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,... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...algebra, in obtaining the square of a binominal ; which is expressed thus : PROPOSITION IX, THEOREM. The square described on the difference, of two lines,...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, 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... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...each 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...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... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...the whole line would be equivalent to four times the square on half the line, j^ PROP. V. THEOREM. The square described on the difference of two lines is equivalent to the sum of the squares of the two Zines, diminished by twice the rectangle contained by the lines. then we have to prove that... | |
 | 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.... | |
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