 | Joseph Ray - Algebra - 1848 - 250 pages
...both terms Vb by i/6, the denominator will become rational. Thus, Since the sum of two quantities, multiplied by their difference, is equal to the difference of their squares ; if the fraction is of the form -_, and we multiply both terms by 6— i/c, the denomin6+i/c ator... | |
 | Joseph Ray - Algebra - 1852 - 408 pages
...factor as will render the exponent of the given radical equal to unity. Since the sum of two quantities, multiplied by their difference, is equal to the difference of their squares (Art. 80) ; if the fraction is of the form , and we multiply both terms by i — Jc, the denominator... | |
 | Ezra S. Winslow - Business mathematics - 1853 - 264 pages
...and BDC, DC a leg common to both. Or, A/(AC-f AD X AC— AD) = DC ; for the sum of any two quantities multiplied by their difference is equal to the difference of their squares. -£2 + i BC = B g, and V(ABS - B?) = A g, perpendicular to BC produced. ^ - * °2 + y = A h, and V(AB2... | |
 | John Radford Young - 1855 - 218 pages
...2ax— 2, and then multiplied by — 4a'6x3. In like manner, the second factor in (7) is 7a'*-4. 3. The sum of two numbers multiplied by their difference...is equal to the difference of their squares. Thus, take the two numbers 7 and 3 ; their sum is 10, and 102=72 + 32 + 21 x 2 = 100. The difference of the... | |
 | George Roberts Perkins - Algebra - 1856 - 276 pages
...difference of two numbers, is equa 4 , to the sum of their squares diminished by twice their product. III. The sum of two numbers multiplied by their difference, is equal to the difference of their squares. Under Chapter VII. we have derived many interesting propositions, by translating algebraic formula... | |
 | Charles W. Hackley - Engineering - 1856 - 530 pages
...m ; Ave have therefore DG tangent = 800 ft., n — 16 6 and m — 12°. * The sum of two quantities multiplied by their difference is equal to the difference of their squares. ___ __ „_ ___ ^^ 398 Iff800 __ '800 __ .. £ m ~~ tan. 8°'+ tan. 6C'~ •HoEI+^l'oslO ~ 32oG'' 3256-7... | |
 | Horace Mann, Pliny Earle Chase - Arithmetic - 1857 - 398 pages
...2021 ; 42 X 48 = 2016 ; 44 X 46 = 2024 ; 7 X 8 = 56, and 72 X 78 = 5616 ; 71 X 79 = 5609, &c. (12.) The sum of two numbers multiplied by their difference, is equal to the difference of their squares. Hence we may readily find the product of two numbers, one of which is as much above as the other is... | |
 | Horace Mann, Pliny Earle Chase - Arithmetic - 1857 - 388 pages
...47 = 2021;' 42 X 48 = 2016; 44x46 = 2024 ; 7X8 = 56, and 72 X 78 = 5616 ; 71 X 79 = 5609, &c. (12.) The sum of two numbers multiplied by their difference, is equal to the difference of their squares. Hence we may readily find the product of two numbers, one of which is as much above as the other is... | |
 | Charles Davies, William Guy Peck - Mathematics - 1857 - 608 pages
...a1 - i1, is a formula, being the algebraic expression of the fact, that the turn of two quantities multiplied by their difference, is equal to the difference of their squares. This is true, whatever may be the nature of the quantities ; that is, the form of the expression does... | |
 | Richard Dawes - Teaching - 1857 - 272 pages
...instance, that (1.) (a -f 6) (a — 6) = a2 — S2: that this means that the sum of .two quantities multiplied by their difference is equal to the difference of their squares. (2.) That (a + 6)2 = aa+2aJ+62, or that the square of the sum of two numbers is equal to the sum of... | |
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The sum of two numbers multiplied by their difference, is equal to the difference of their squares. 
