The Elements of Algebra Preliminary to the Differential Calculus: And Fit for the Higher Classes of Schools in which the Principles of Arithmetic are TaughtTaylor and Walton, 1837 - 248 pàgines |
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The Elements of Algebra Preliminary to the Differential Calculus, and Fit ... Augustus De Morgan Visualització completa - 1835 |
The Elements of Algebra Preliminary to the Differential Calculus: And Fit ... Augustus De Morgan Visualització completa - 1837 |
The Elements of Algebra Preliminary to the Differential Calculus, and Fit ... Augustus De Morgan Visualització completa - 1835 |
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1+x+x²+x³ algebraical quantities altered Anomaly answer applied aq-bp arithmetical arithmetical meaning ax² called common Consequently contains convergent correct cube root cubic feet cubic foot denote differential calculus diminishes without limit divided division divisor equal numbers example exponent functions given gives greater Hence impossible subtraction inches increase without limit infinite number instance Lemma less letters loga logarithm mantissa meaning method miles multiplied nearly equal negative quantity number of terms number or fraction numerator and denominator polynomial preceding equation problem proceed proved question rational rational polynomials remainder result rules shew shewn shillings a yard solution specific gravity square root suppose supposition symbols taken tion true twelfth root unknown quantities whence whole number word
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Pàgina xxviii - ... 2. From looking at the preceding instances, it appears that the rule of multiplication is as follows : Consider the first terms as having the sign + ; multiply every term of the multiplicand by every term of the multiplier, and put + before the products of terms which have the same sign, and — before the products of terms which have different signs. The preceding example is here written in the usual way, with the proper signs written to every term by the preceding rule. a + b — 2c d — a...
Pàgina 64 - Then, f=|&, becomes, 5 : 7 : : 20 : 28, the numerator of one is, to its denominator, as the numerator of the other, to its denominator. It follows that any four numbers are proportionals, when the first divided by the second is equal to the third divided by the fourth. They are not proportionals when this is not the case ; therefore, by this test, we can determine if any four numbers are proportionals.
Pàgina v - The operation of division is also indicated by writing the divisor under the dividend with a line between them ; thus 14 by 2 is also frequently denoted thus y.
Pàgina 228 - If the curiosity of any gentleman that has leisure, would prompt him to undertake to do the logarithms of all prime numbers under 100,000 to 25 or 30 figures, I dare assure him that the facility of this method will invite him thereto ; nor can anything more easy be desired. And to encourage him, I here give the logarithms of the first prime numbers under 20 to 60 places.
Pàgina xxxix - ... arithmetic knows nothing, and therefore as we may suppose, uses language, finds methods, and adopts interpretations, of which arithmetic furnishes no examples. If the student have read* a little of geometry (a science which he * In England, the geometry studied is that of Euclid, and I hope it never will be any ether ; were it only for this reason, that so much has been written on Euclid, and all the difficulties of geometry have so uniformly been considered with reference to the form in which...
Pàgina xl - If equal numbers be added to equal numbers, the sums are equal numbers. That is, if a = b and c = d, then a + c = b + d, If a = b — c and x = p — g, then a + x = (b — c) + (p — q) = b +p — c — q.
Pàgina 31 - ... will be in equilibrium when the sum of the moments of the weights on one side of the pivot is the same as that of the weights on the other side.