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 1
... Equations 121 Alligation 53 Equations of the 1st degree 123 28 Formation of Powers 32 Extraction { of square root 84 of cube root 192 Examples 33 Tare and Trett 193 Barter 34 Exchange 193 194 Addition 39 Subtraction Multiplication 196 ...
... Equations 121 Alligation 53 Equations of the 1st degree 123 28 Formation of Powers 32 Extraction { of square root 84 of cube root 192 Examples 33 Tare and Trett 193 Barter 34 Exchange 193 194 Addition 39 Subtraction Multiplication 196 ...
Page 2
... EQUATIONS of any Degree 147 259 Examples 272 $ 26 ARITHMETIC PRO- PORTIONS } - 150 · 151 • 268 Geometric Proportions 269 Arithmetic Progressions - 134 Problems 138 Geometric Progressions Problems Problems 272 - 160 - 273 154 · 278 140 ...
... EQUATIONS of any Degree 147 259 Examples 272 $ 26 ARITHMETIC PRO- PORTIONS } - 150 · 151 • 268 Geometric Proportions 269 Arithmetic Progressions - 134 Problems 138 Geometric Progressions Problems Problems 272 - 160 - 273 154 · 278 140 ...
Page 3
... equation . 1989 product . S = ( 2a - d.n = 1 ) progression . for Example . pass through . 2,262451 2655214 See the note , page 275 . Ans 1104 885,1030 2.30 + 20 · 1811/6 10x - 13dwt . § } d . 3d 44d 65450827 ERRAT A.
... equation . 1989 product . S = ( 2a - d.n = 1 ) progression . for Example . pass through . 2,262451 2655214 See the note , page 275 . Ans 1104 885,1030 2.30 + 20 · 1811/6 10x - 13dwt . § } d . 3d 44d 65450827 ERRAT A.
Page 119
... equations of the second degree , and therefore deserves great attention . The general rule , just given , can be followed , when an exact root is required ; but when the quantity is such , that an exact root cannot be obtained , but ...
... equations of the second degree , and therefore deserves great attention . The general rule , just given , can be followed , when an exact root is required ; but when the quantity is such , that an exact root cannot be obtained , but ...
Page 120
... expeditious , and even , if the number is not an exact square , or cube , it is even better for obtaining a proximate root to make use of the decimal parts . EQUATIONS . An Equation is the equality of two or 120 ALGEBRA .
... expeditious , and even , if the number is not an exact square , or cube , it is even better for obtaining a proximate root to make use of the decimal parts . EQUATIONS . An Equation is the equality of two or 120 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.