Mathematical Manual for the Use of Colleges and Academies, Volume 1J.W. Butler, and sold by J. Conrad, 1807 - Mathematics |
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Page 95
... letters of the alphabet , which , having no determined value , are thereby very proper to re- present all kinds of magnitude or quantities . We perform upon algebraical quantities , the same opera- tions as on numerical ones ; we add ...
... letters of the alphabet , which , having no determined value , are thereby very proper to re- present all kinds of magnitude or quantities . We perform upon algebraical quantities , the same opera- tions as on numerical ones ; we add ...
Page 97
... letter or a quantity , is called the coefficient of that letter or of that quantity . We shall remark , that the unit is always supposed to be the coefficient of every quantity which has none , for a or 1 Xa , is the same thing ...
... letter or a quantity , is called the coefficient of that letter or of that quantity . We shall remark , that the unit is always supposed to be the coefficient of every quantity which has none , for a or 1 Xa , is the same thing ...
Page 98
... letters . The rule of multiplication for the Letters , is to write them one after another ; but when a same letter is to be taken several times as a factor in a monomial 98 ALGEBRA .
... letters . The rule of multiplication for the Letters , is to write them one after another ; but when a same letter is to be taken several times as a factor in a monomial 98 ALGEBRA .
Page 99
... letter but once , with a little figure raised above it on the right hand , which expresses the number of times that this ... letters or quantities , is per- formed by adding together their exponents ; thus a * bc3d ab2 c2 = a5b3c5d ...
... letter but once , with a little figure raised above it on the right hand , which expresses the number of times that this ... letters or quantities , is per- formed by adding together their exponents ; thus a * bc3d ab2 c2 = a5b3c5d ...
Page 102
... letters . Thus 6a 3a 2a 26 b 5a a 4 1 • ; but . 46 66 36 8a2a not admit any change . - will For the rule of Letters , we must efface the 102 ALGEBRA .
... letters . Thus 6a 3a 2a 26 b 5a a 4 1 • ; but . 46 66 36 8a2a not admit any change . - will For the rule of Letters , we must efface the 102 ALGEBRA .
Common terms and phrases
aliquot annum antecedents arithmetic progression arithmetic proportion binomial bottles calculation called cent coefficient comma common divisor complete the square composed consequently contains cost cube root cyphers decimals denominator difference divide division dollars double sign equal ratios evident example exponent expressed factors fath fathoms feet figures follows fourth fractional number gain gallons geometric progression geometric proportion gives greatest common divisor hundred hundredth INCOMPLEX NUMBERS INDETERMINATE PROBLEMS interest last term logarithms means method Mixed Number mixture monomial months multiplicand multiply necessary number of terms operation orifice partial dividend pence pounds problem proof quan question quotient reduced remainder remark rule of three second degree second equation shillings solution solve square root substituting subtract tables taken tens third tion tity treme unity unknown quantity whole number write yards
Popular passages
Page 33 - Multiply the whole number by the numerator of the fraction, and divide the product by the denominator ; or divide the whole number by the denominator of the fraction, and multiply the quotient by the numerator.
Page 224 - The earth being 360 degrees in circumference, turns round on its axis in 24 hours ; how far does it turn in one minute, in the 43d parallel of latitude; the degree of longitude, in this latitude, being about 51 statute miles?
Page 104 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 202 - OF TIME. 60 Seconds = 1 Minute 60 Minutes =± 1 Hour 24 Hours = 1 Day 7 Days = 1 Week 28 Days = 1 Lunar Month...
Page 203 - The fourth, eleventh, ninth, and sixth, Have thirty days to each affix'd: And every other thirty-one, Except the second month alone, Which has but twenty-eight in fine, Till leap year gives it twenty-nine.
Page 59 - The first term of a ratio is called the antecedent, and the second term the consequent.
Page 34 - It will be seen that we multiply the denominator of the dividend by the numerator of the divisor for the denominator of the quotient, and the numerator of the dividend by the denominator of the divisor for the numerator of the quotient.
Page 245 - TARE AND TRET. Tare and Tret are allowances made by the seller to the buyer, on some particular commodities. Tare is an allowance made for the weight of the barrel, box, bag, or whatever contains the commodity. Tret is an allowance of 4 Ib.
Page 85 - Considering, then, the proposed number 6084 as composed of the square of the tens of the root sought, twice the product of the tens by the units, and the square of the units, if we can discover in this number the first of these parts, viz.