 | William Nicholson - Natural history - 1821 - 356 pages
...universal, which extend to any quantity, without restriction, universally ; as this, that the rectangle of the sum and difference of any two quantities is equal to the difference of their squares; or particular, which extend only to a particular quantity ; as this, in an equilateral right-lined... | |
 | William Nicholson - Natural history - 1821 - 356 pages
...universal, which extend to any quantity, without restriction, universally ; as this, that the rectangle of the sum and difference of any two quantities is equal to the difference of their squares; or particular, which extend only to a particular quantity ; as this, in an equilateral right-lined... | |
 | 1854 - 1112 pages
...readily be imagined, by supposing m to equal a — n. Again, (m + ») (in — «) = m' — «* ; or, the product of the sum and difference of any two quantities is equal to the difference of their squares. In like manner, (»i! + if) (>»« — »s) = m4 - »', («3 + »') (m'-n:1) = »i1>-»6, &c. It is... | |
 | Peter Nicholson - Architecture - 1823 - 210 pages
...product of the sum and difference of the roots : hence x2— y"= (x+y) (x—y), and, reciprocally, that the product of the sum and difference of any two quantities is equal to the difference of their squares. Thus (a+z) (a- *)=a2- Xs. ALGEBRAIC DIVISION AND FRACTIONS. 107. DIVISION is the converse of Multiplication... | |
 | Thomas Kerigan - Nautical astronomy - 1828 - 776 pages
...16x16 = 256 ; — 10-6 = 4x4= 16.— Now, 256- 16 = 240 ; and lOx 6 x4 = 240. The sum of the squares of the sum and difference of any two quantities, is equal to twice the sum of their squares. — Thus, 10 + 6= 16x16 =2565 and 10-6=4x4=16; then 256 + 16 =272.... | |
 | Peter Nicholson - Algebra - 1831 - 326 pages
...— * * * — x5, or Note. It may be useful to observe that according to Euclid, Lib. II. Prop. V. the product of the sum and difference of any two quantities is ryuat to the difference of their squares ; thus, (>) (a+4)(a— 4) = a2-42. f For the operation, v.... | |
 | John Hind - Algebra - 1837 - 584 pages
...47. Using the same symbols as in article (44), we have (•» + y) x (a? - y) = a?2 - y'! ; that is, the product of the sum and difference of any two quantities is always equal to the difference of the squares of the same quantities ; and conversely. This theorem... | |
 | Thomas Kerigan - Nautical astronomy - 1838 - 804 pages
...10-4 = 6, and 14x6= 84.— Now, 10x10= 100; 4x4 = 16, and 100-16 = 84. The difference of the squares of the sum and difference of any two quantities, is equal to. four times the rectangle of thost quantities. — Thus, Let 10 and 6 be the two quantities ; then 10... | |
 | Ormsby MacKnight Mitchel - Algebra - 1845 - 308 pages
...b=JbX.fb, and that «/6c=W6X «/c; that 6 — c=«/6+*/6 — vcXvc; or, =(v6+vc)(v6 — vc); since the product of the sum and difference of any two quantities is equal to the difference of their squares. Substituting these values, we obtain, x= — - - — and a?= Observing, that aJb is a factor common... | |
 | Charles William Hackley - Algebra - 1846 - 542 pages
...produce a rational result : thus, V& =« V* 3 =* Again, since the product of the sum and difference of two quantities is equal to the difference of their squares, we have, evidently, =a —b y)=x — y 9 Hence it is obvious that, in these and similar equalities, if one of... | |
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... the product of the sum and difference of any two quantities, is equal to the difference of their squares. 
