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" ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares. "
An Introduction to Algebra: Being the First Part of a Course of Mathematics ... - Σελίδα 124
των Jeremiah Day - 1831 - 332 σελίδες
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A treatise of algebra: in two books ...

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...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...

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....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...

An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1827 - 332 σελίδες
...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...

The Mechanics' Magazine, Museum, Register, Journal, and Gazette, Τόμος 13

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...

Elements of Algebra

William Smyth - 1833 - 280 σελίδες
...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...

Mathematics for Practical Men: Being a Common-place Book of Principles ...

Olinthus Gregory - 1834 - 427 σελίδες
...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...

A treatise on practical geometry, mensuration, conic sections, gauging, and ...

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...

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Silas Totten - 1836 - 304 σελίδες
...place of a and b, it follows, that this property is general. This property may be thus enunciated : — The product of the sum and difference of two quantities is equal to the difference of their squares. Having demonstrated this property, we can make use of il to shorten the operation of multiplication...

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...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...

Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - 1836 - 496 σελίδες
...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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