| Jeremiah Day - Algebra - 1814 - 304 pages
...• ' 6. j 235. If a+b be multiplied into a— b, the product will be «*— 6a: (Art. 110.) that is, **The product of the sum and difference of two quantities, is equal to the difference of** their squares. This is another instance of the facility with which general truth are demonstrated in... | |
| Edward Riddle - Nautical astronomy - 1824 - 572 pages
....sin A— B=;gin A . cosB + cos A . sinB. sin A . cos В — cos A . sin B. And as the rectangle, or **the product, of the sum and difference of two quantities, is equal to the difference of** their squares } sin A . cos В + cos A . sin В . sin A . cos В «- ços A • ein В, is equal мл... | |
| Jeremiah Day - Algebra - 1827 - 352 pages
...multiplied into a binomial surd containing only the squre root, may be found by applying the principle, fhat **the product of the sum and difference of two quantities, is equal to, the difference of** their squares. (Art. 235.) The binomial itself, after the sign which connects the terms is changed... | |
| Jeremiah Day - Algebra - 1831 - 358 pages
...multiplied into a binomial surd containing only the square root, may be found by applying the principle, **that the product of the sum and difference of two quantities, is equal to the difference of** their squares. (Art. 235.) The binomial itself, after the sign which connects the terms is changed... | |
| Jeremiah Day - Algebra - 1832 - 354 pages
...!/" ' ya y"!/"" 3. -a-3xo~3=-a~6. 4. fl-3xrf=rf~'2=<P. 5. a -nx o'"=a"'~"• 6. «-8 THE PRODUCT OP **THE SUM AND DIFFERENCE OF TWO QUANTITIES, IS EQUAL TO THE DIFFERENCE OF** THEIR SQUARES. This is another instance of the facility with which general truths are demonstrated... | |
| William Smyth - Algebra - 1833 - 288 pages
...quantity, minus the double product of the first by the second, plus the second power of the second. 6. **The product of the sum and difference of two quantities is equal to the difference of** their second powers. SECTION V. — ALGEBRAIC FRACTIONS. 55. When the division of two algebraic quantities... | |
| Olinthus Gregory - Mathematics - 1834 - 472 pages
...changing its value ; while the expression becomes freed from the surds in the denominator, because **the product of the sum and difference of two quantities is equal to the difference of** their squares. Examples. 8 v/5+ y/3 _ 8 (у'б + y/3) — v/3 ' v/5 + v/3 ~ ~ 8~ _ __ v/5 + ^2 v/5... | |
| Ireland commissioners of nat. educ - 1834 - 370 pages
...truth of this rule is evident from 47. I. and from Cor. S. II., which says, that the rectangle under **the sum and difference of two quantities is equal to the difference of** their squares. 3. Given AB : 5, B С 4 ; required AC : 52 — 4* = 9 ; then V 9 = 3 the side A С ;... | |
| Mathematics - 1836 - 488 pages
...multiplication between them. Powers of the same root may be multiplied, by adding their expoDents. **The product of the sum and difference of two quantities is equal to the difference of** their squares. Powers may be divided, by rejecting from the dividend, a factor equal to the divisor... | |
| Robert Mudie - Mathematics - 1836 - 542 pages
...product, and + a 6 — a 6 is =0, and may be left out in adding. Hence we have this principle : — **the product of the sum and difference of two quantities is equal to the difference of** their squares. If we subtract the square of a — 6 from that of a +6, we have, 4ab — difference.... | |
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