 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.  Plane and Solid Geometry: Teacher's Edition - Page 237by George Albert Wentworth, George Wentworth - 1912 - 590 pagesFull view - About this book
 | Adrien Marie Legendre - Geometry - 1830 - 344 pages
...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
...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
...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
...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... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...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
...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
...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... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...is expressed algebraically thus: (a+b)'=a'+2ab+V. PROPOSITION IX. THEOREM. The square described on the difference of two lines, is equivalent to the sum of the squares of the lines, diminished by twice the rectangle contained by the lines. squares on AB and CB, diminished... | |
| |
