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" ... the product of the sum and difference of any two quantities, is equal to the difference of their squares. "
British Encyclopedia: Or, Dictionary of Arts and Sciences, Comprising an ... - Σελίδα 11
των William Nicholson - 1821
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Τόμος 12

William Nicholson - 1821
...Essential character : corolla bell-shaped, with oblong erect spreading segments; fruit one-celled, very large, roundish, many-seeded. There are two species,...impossibility of any assertion ; as, that the sum of two biquadpte numbers cannot make a square number. A local theorem is that which relates to a surface;...

The Youth's instructer [sic] and guardian, Τόμοι 18-19

1854
...imagined, by supposing m to equal a — n. Again, (m + ») (in — «) = m' — «* ; or, the product of the sum and difference of any two quantities is equal to the difference of their squares. In like manner, (»i! + if) (>»« — »s) = m4 - »', («3 + »') (m'-n:1) = »i1>-»6, &c. It is...

The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - 1823 - 596 σελίδες
...sum and difference of the roots : hence x2— y"= (x+y) (x—y), and, reciprocally, that the product of the sum and difference of any two quantities is equal to the difference of their squares. Thus (a+z) (a- *)=a2- Xs. ALGEBRAIC DIVISION AND FRACTIONS. 107. DIVISION is the converse of Multiplication...

The Complete Mathematical and General Navigation Tables: Including ..., Τόμος 1

Thomas Kerigan - 1828 - 664 σελίδες
...16x16 = 256 ; — 10-6 = 4x4= 16.— Now, 256- 16 = 240 ; and lOx 6 x4 = 240. The sum of the squares of the sum and difference of any two quantities, is equal to twice the sum of their squares. — Thus, 10 + 6= 16x16 =2565 and 10-6=4x4=16; then 256 + 16 =272....

The Complete Mathematical and General Navigation Tables: Including Every ...

Thomas Kerigan - 1838
...10-4 = 6, and 14x6= 84.— Now, 10x10= 100; 4x4 = 16, and 100-16 = 84. The difference of the squares of the sum and difference of any two quantities, is equal to. four times the rectangle of thost quantities. — Thus, Let 10 and 6 be the two quantities ; then 10...

Mechanics for Practical Men

1845 - 238 σελίδες
...represent its whole weight, we obtain 2JOD (rf+D) «;— ~~JQ - ~~3 d2— D2 and because, the product of the sum and difference of any two quantities is equal to the difference of their squares, we have _2j»D(rf + D) . ' -(rf+D)(rf-D)' therefore, by reducing the fraction, we finally get 2WD w=j...

An Elementary Treatise on Algebra: Designed to Facilitate the Comprehension ...

Ormsby MacKnight Mitchel - 1845 - 294 σελίδες
...and that «/6c=W6X «/c; that 6 — c=«/6+*/6 — vcXvc; or, =(v6+vc)(v6 — vc); since the product of the sum and difference of any two quantities is equal to the difference of their squares. Substituting these values, we obtain, x= — - - — and a?= Observing, that aJb is a factor common...

Elementary Course of Geometry ...

Charles William Hackley - 1847 - 103 σελίδες
...difference of the same, and that product by -7854 ;* which is still the same thing, because the product of the sum and difference of any two quantities is equal to the difference of their squares. Ex. 1. The diameters of two concentric circles being 10 and 6, required the area of the ring contained...

A Practical Treatise on Algebra: Designed for the Use of Students in High ...

Benjamin Greenleaf - 1853 - 360 σελίδες
...roots, to find a factor that will make the quantity rational. In Art. 158 we have shown that the product of the sum and difference of any two quantities is equal to the difference of their squares; therefore, when one or both of the terms are even roots, we multiply the given binomial or residual...

A Treatise on Elementary Algebra

James Hamblin Smith - 1869
...their squares, the quotient is equal to the difference of the two quantities. 2. Shew that the product of the sum and difference of any two quantities is equal to the difference of their squares. 3. Shew that the square of the sum of any two consecutive integers is always greater by one than four...




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