| William Emerson - Algebra - 1780 - 531 pages
...ss 4- iid + dd 4 ss — <isd + dd and Lb ~ 4 and AA— EE = ±^ = sd. 4 Cor. "The produff of the fum **and difference of two quantities^ is equal to the difference of their** fquares. PROBLEM LXVIII. *Two quantities being given to find the fquare of the fum. Let a be the greater... | |
| Edward Riddle - 1824
....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 — cot2A 1... | |
| Jeremiah Day - Algebra - 1827 - 332 pages
...y~3Xy*=y° = l. 235. If 0+6 be multiplied into 0 — 6, the product will be n3-6* : (Art. 110,) that is TlIE **PRODUCT OF THE SUM AND DIFFERENCE OF TWO QUANTITIES, IS EQUAL TO THE DIFFERENCE OF THEIR SQUARES.** T'lis is another instance of the facility with which general truths are demonstrated in algebra. See... | |
| Industrial arts - 1830
...the right angle ; let AC= 100000000000 1, AB:=999999999999. Now, since the rectangle under the sure **and difference of two quantities is equal to the difference of their squares** .'. (AC+AB) • (AC-AB) = AC2 - AB2 = BC2 = 2000000000000 x 2 = 4(100000000000 .'. BC = */ 4000000000000... | |
| Olinthus Gregory - 1833 - 427 pages
...quantities is equal to the sum of the squares of the two quantities together with twice their product 2. **That the product of the sum and difference of two...quantities is equal to the difference of their squares.** 3. That the cube of the binomial a + b, is a* + 3 a* b + 3 a b3 + b3. SECTION IV. — Division. 1.... | |
| William Smyth - Algebra - 1833 - 280 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 - 427 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 + v/2 'v/5— v/2... | |
| Ireland commissioners of nat. educ - 1834
...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 ; or (5 + 4) X (5... | |
| Mathematics - 1836 - 472 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 ; or by placing... | |
| Robert Mudie - Mathematics - 1836 - 496 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. Therefore, four... | |
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