The elements of algebra |
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Página ix
... questions in Compound Interest , and in Certain and Contingent Annuities , and in various other important branches . The ... question . About the middle of the fourth century , the arithmetic of the ancients contained only the four ...
... questions in Compound Interest , and in Certain and Contingent Annuities , and in various other important branches . The ... question . About the middle of the fourth century , the arithmetic of the ancients contained only the four ...
Página xx
... Questions producing these Equations 204 Simple Equations containing three Unknown Quantities 212 Questions producing these Equations 222 QUADRATIC EQUATIONS . Definitions 225 Pure Quadratics 226 Questions producing Pure Quadratics 230 ...
... Questions producing these Equations 204 Simple Equations containing three Unknown Quantities 212 Questions producing these Equations 222 QUADRATIC EQUATIONS . Definitions 225 Pure Quadratics 226 Questions producing Pure Quadratics 230 ...
Página 2
... questions , a theo- rem and a problem . ( 10. ) In a theorem , it is proposed to demonstrate some relation or property of numbers or abstract quantities . ( 11. ) In a problem , the object is to find the value of some unknown numbers or ...
... questions , a theo- rem and a problem . ( 10. ) In a theorem , it is proposed to demonstrate some relation or property of numbers or abstract quantities . ( 11. ) In a problem , the object is to find the value of some unknown numbers or ...
Página 159
... question is unknown , only one relation or condition must be given . " For example , if a number is required , such that being increased by 3 , the sum shall be 12 , then if x be that num- ber , the equation x + 3 = 12 expresses this ...
... question is unknown , only one relation or condition must be given . " For example , if a number is required , such that being increased by 3 , the sum shall be 12 , then if x be that num- ber , the equation x + 3 = 12 expresses this ...
Página 160
... question becomes impossible , as the con- ditions would be inconsistent were x to be = 9 , and , at the same time , equal to some other number , while by the ques- tion only one number is sought . If , therefore , when only one unknown ...
... question becomes impossible , as the con- ditions would be inconsistent were x to be = 9 , and , at the same time , equal to some other number , while by the ques- tion only one number is sought . If , therefore , when only one unknown ...
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Términos y frases comunes
a²x a²x² a³x algebraical Algebraical Fractions annuity assumed ax² ax³ binomial coefficients continued fraction cube root cubic equation denote Divide dividend divisible divisor equa equal equations containing equidifferent evident EXAMPLES EXERCISES exponent expressed factors Find a number Find the cube Find the least Find the square Find the sum Find the value Find two numbers former given equations given quantity greatest common measure harmonic mean hence last term latter least common multiple Let the number logarithms method Multiply nth root number of terms permutations positive preceding prefixed proportional equation quadratic quan quotient radical sign ratio Rationalise the denominator Reduce relatively prime remainder required the numbers result rule second term solution square root subtract system of values taken theorem third tion tity unknown quantities vulgar fraction ах
Pasajes populares
Página 76 - Multiply each numerator by all the denominators except its own, for the new numerators ; and all the denominators together for A COMMON denominator. NOTE 1.
Página 317 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Página 339 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.
Página 309 - Find the nth term, and the sum of n terms of the natural series of numbers 1, 2, 3, 4 . . . . Ans.
Página 223 - If A and В together can perform a piece of work in 8 days, A and С together in 9 days, and В and С in 10 days; how many days would it take each person to perform the same work alone?
Página 353 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 286 - If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Página 178 - A man was hired 50 days on these conditions. — that, for every day he worked, he should receive $ '75, and, for every day he was idle, he should forfeit $ '25 ; at the expiration of the time, he received $ 27'50 ; how many days did he work...
Página 176 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare?
Página 352 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.