| Joseph Raphson, Jacques Ozanam - Mathematics - 1702 - 84 pages
...is that which extends Univerfally to any Quantity, without Diftinftion. Such is this :. The Product **of the Sum and Difference of any two Numbers is equal to the** Different «f their- Square t, A A Theorem may be either Vniverfal, Partial lar, Simple, Compounded,... | |
| Sir John Leslie - Arithmetic - 1820 - 258 pages
...simple and ready method of multiplying large numbers may be derived from the property, that the product **of the sum and difference of any two numbers is equal to the difference of** their squares. This elegant theorem is easily demonstrated by the operation of palpable arithmetic.... | |
| Ira Wanzer - Arithmetic - 1831 - 396 pages
...mean required. Ex. Find an arithmetical mean between the two numbers 4 and 10. . Ans. 7. * The product **of the sum and difference of any two numbers is equal to the difference of the squares of** the numbers ; whence the reason of the rules [or Problems 6ih and 7th is obvious. B. IX. — To find... | |
| Euclides - 1840
...the squares of half their sum and half their difference, may be also thus enunciated : the product **of any two numbers is equal to the difference of the squares of** half their sum and half their difference. Therefore four times the product of two numbers is equal... | |
| Great Britain. Poor Law Commissioners - Political Science - 1841 - 421 pages
...= 32; .-. if + 3x - 4 ; 9 g 9,5 3 j. 5 2 8 ... x =__ + _ = —or 1; or - _ = t4. (2d.) The product **of the sum and difference of any two numbers is equal to the difference of** their squares. Hence dividing botli numerator and denominator by 4 + x the equation will become 4 +... | |
| John M'Nevin - Arithmetic - 1841 - 280 pages
...greater number. From half the sum, take half the difference for the lesser number. THEOREM 2. The product **of the sum and difference of any two numbers is equal to the difference of** their squares. THEOREM 3. If the difference of the squares of two numbers be divided by their difference,... | |
| Algebra - 1870
...their squares, the quotient is equal to the difference of the two numbers. 33. Shew that the product **of the sum and difference of any two numbers is equal to the difference of** their squares. 34. Shew that the square of the sum of any two consecutive integers is always greater... | |
| Robert Potts - Algebra - 1879
...equal to twice the greater number: and (efi)x(e — i) = a* — i5, also denotes, that the product **of the sum and difference of any two numbers is equal to the difference of** their squares.* 8. The names of the elementary processes of Arithmetic and Algebra are the same ; Addition... | |
| Robert Potts - Algebra - 1879
...equal to twice the greater number : and (e+i) x (a — J) = a1 — V, also denotes, that the product **of the sum and difference of any two numbers is equal to the difference of** their squares.* 8. The names of the elementary processes of Arithmetic and Algebra are the same ; Addition... | |
| James Hamblin Smith - 1883
...their squares, the quotient is equal to the difference of the two numbers. 33. Shew that the product **of the sum and difference of any two numbers is equal to the difference of** their squares. 34. Shew that the square of the sum of any two consecu tive integers is always greater... | |
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