What people are saying - Write a review
We haven't found any reviews in the usual places.
Other editions - View all
added affirmative alſo angle becomes caſe circle coefficients common cube denominator difference diſtance divide diviſor draw equal equation extracted figure firſt fourth fraction Geom given gives greater greateſt Hence indices infinite involved known laſt leaſt leſs letter limit means multiplied muſt negative operation parallel perpendicular Prob PROBLEM proceed proportion propoſed queſtion quotient R U L radius reduced remaining root rule ſame ſecond ſeries ſeveral ſides ſigns ſimilar ſince ſome ſquare ſquare root ſubſtitute ſubtract ſuch ſum Suppoſe ſurd taken tang theſe third tion triangle unknown quantity uſe whence whoſe
Page 30 - 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 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 4 - 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 23 - 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 21 - ... and the product be divided :by the number of terms to that place, it will give the coefficient of the term next following.
Page 52 - 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 105 - 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 21 - 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...