 | Isaac Dalby - 1806 - 526 pages
...3i<z — I4x 'Ja'x + 601* — 3axy3 -4-X-4-1 1 the square of *+ 1. ** — j/'orx* — ^«, viz. t lie product of the sum and difference of two numbers is equal to the difference of their stjuiies. *—y * or **— ;V* «> -J- 1 or p + 1 . x* — a* + A * -»- e -(-c.ia — ca.r .4- cb... | |
 | 1826 - 490 pages
...CHKVERTON. Kingsdown, Bristol. (To be continued.) SQUARING NUMBERS. Sm, — It has been long known that the product of the sum and difference of two...numbers is equal to the difference of their squares, and hence, when a square is required to contain au area which is expressed by a number not a square.we... | |
 | 1826 - 478 pages
...CIIKVJ-.KTON. Kingsdown, Bristol. (Ta be continued.) SQUARING NUMBERS. Sin, — It has been long known that the product of the sum and difference of two...numbers is equal to the difference of their squares, and hence, when a square is required to contain an area which is expressed by a number not a si|uare,\ve... | |
 | 1828 - 888 pages
...embraces no new principle, seems, as far as I know, to have been hitherto unnoticed by every writer ou the subject of arithmetic. The method here pointed...to which difference, if we add the, square of the lessee number, we obtain the square of the greater. The principal advantage of this method is, that... | |
 | 1840 - 706 pages
...the hypotheneuse is one of the sides given, and it is merely an application of the well known theorem that " the product of the sum and difference of two...numbers is equal to the difference of their squares." Thus, suppose c and b given to find a ; then — ... A/(e-r6)(e — b) a=*/c* — b1, or = — s —... | |
 | George Peacock - 1842 - 426 pages
...66. To form the product of a + b and ab. the sum and differ- a + ft ence of two , numbers. a — o Or the product of the sum and difference of two numbers is equal to the difference of their squares. 67- To form the cube of a + b. (Art. 39.) Cube of a +b a +b 6'= (a + 6)* (Art. 62.) a + 6 a3 + 3a'6... | |
 | Davis Wasgatt Clark - 1844 - 394 pages
...Subtracting the 2d from the 1st equation, 26=s — d; ) Dividing ...... 6=|~2J Second Theorem. % 198. The product of the sum and difference of two numbers is equal to the difference of their squares. Let a, b, s, and d sustain the same relations as in the preceding theorem : * Then ----- s=a-\-b, And... | |
 | 1847 - 602 pages
...events; practical necessity, to voluntary actions ; and logical necessity, primarily, to propositions. That the product of the sum and difference of two...numbers is equal to the difference of their squares, that magnitudes which are equal to the same are equal to one another, are said to be necessary truths.... | |
 | Davis Wasgatt Clark - 1846 - 374 pages
...----- a Subtracting the 2d from the 1st equation, Zb=s — d; Dividing .»»«»» Second Theorem. 198. The product of the sum and difference of two numbers is equal to the difference of their squares. Let a, />, s, and d sustain the same relations as in the preceding theorem : Then ..... s=a+b, And... | |
 | James W. Kavanagh - 1846 - 304 pages
...the sum of two, three or four second powers,* thus, 5 = 2» + l» 13 = 3» + 2' 41 = 5a + 4»&c. 97. The product of the sum and difference of two numbers is equal to the difference of their second powers, thus 9 and 5. 9+5x9^5=9"— 5' =56. These properties might have been extended to considerable... | |
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The product of the sum and difference of two numbers is equal to the difference of their squares. 
