Cyclomathesis: Or, An Easy Introduction to the Several Branches of the Mathematics], Volume 4

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fold. plates (diagrs.), 1764
 

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Page 32 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Page 32 - To reduce an improper fraction to a whole or mixed number, — RULE : Divide the numerator by the denominator ; the quotient will be the whole or mixed number.
Page 315 - Recalling the fact that, from a purely mathematical point of view, a problem is adequately solved when the number of independent equations is equal to the number of unknown...
Page 6 - If the same quantity, or equal quantities, be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same quantity, or equal quantities, the products will be equal.
Page 25 - EXTRACT the root of the co-efficient, for the numeral part ; and divide the index of the letter or letters, by the index of the power, and it will give the root of the literal part ; then annex this to the former, for the whole root sought*. * Any even root of an affirmative quantity, may be either -for — : thus the square root of + a?
Page 23 - ... and the product be divided :by the number of terms to that place, it will give the coefficient of the term next following.
Page 54 - RULE. Multiply the index of the quantity by the index of the power to which it is to be raised, and the result will be the power required.
Page 107 - and there are three changes ^ from the firft to the fécond, from the third to the fourth, and from the fourth to the fifth term : therefore there are three affirmative roots.
Page 23 - Note. — The whole number of terms will be one more than the index of the given power ; and when both terms of the root are +, all the terms of the power will be + ; but if the second term be — , all the odd terms will be +, and the even terms — . Examples. 1. Let a + x be involved to the fifth power. The terms without the coefficients will be a', a4 x, a3 x*, a...
Page 43 - Also, when the two numerators, or the two denominators, can be divided by some common quantity, that quantity may be thrown out of each, and the quotients used instead of the fractions first proposed.

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