The Elements of Algebra: Designed for the Use of Students in the UniversityJ. Smith, 1815 - 305 σελίδες |
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Σελίδα 11
... determined . S. d . 9 . Ex . 1. What fraction of a pound is 12 : 7 : 3 ? 12 : 7 : 3 = 607 , and one pound = 960 ; therefore 607 960 d . is the fraction sought . Because the integer being S. d . 9 . divided into 960 equal parts , 12 : 7 ...
... determined . S. d . 9 . Ex . 1. What fraction of a pound is 12 : 7 : 3 ? 12 : 7 : 3 = 607 , and one pound = 960 ; therefore 607 960 d . is the fraction sought . Because the integer being S. d . 9 . divided into 960 equal parts , 12 : 7 ...
Σελίδα 24
... determined quantities are usually repre- sented by the first letters of the alphabet , a , b , c , d , & c . and unknown or undetermined quantities , by the last , y , x , w , & c . The following signs are made use of to express the ...
... determined quantities are usually repre- sented by the first letters of the alphabet , a , b , c , d , & c . and unknown or undetermined quantities , by the last , y , x , w , & c . The following signs are made use of to express the ...
Σελίδα 27
... determined , the quantities are called irrational , or surds . ( 59. ) Points are made use of to denote proportion thus , a : b :: cd , signifies that a bears the same proportion to b that c bears to d . ( 60. ) The number prefixed to ...
... determined , the quantities are called irrational , or surds . ( 59. ) Points are made use of to denote proportion thus , a : b :: cd , signifies that a bears the same proportion to b that c bears to d . ( 60. ) The number prefixed to ...
Σελίδα 37
... determining the sign of a pro- duct from the consideration of abstract quantities , has been found fault with by some algebraical writers , who contend that a , without reference to other quantities , is imaginary , and consequently not ...
... determining the sign of a pro- duct from the consideration of abstract quantities , has been found fault with by some algebraical writers , who contend that a , without reference to other quantities , is imaginary , and consequently not ...
Σελίδα 38
... determine how often the latter is contained in the ・ former , or what quantity multiplied by the latter will produce ... determined by the last rule , is the quotient . abc Thus , ab = c ; because ab multiplied by c gives abc . If we ...
... determine how often the latter is contained in the ・ former , or what quantity multiplied by the latter will produce ... determined by the last rule , is the quotient . abc Thus , ab = c ; because ab multiplied by c gives abc . If we ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
abscissa algebraical quantities annuity arithmetical progression assumed binomial biquadratic coefficients common denominator conic section cube root cubic equation curve decimal Diff difference divided dividend division divisor equa equal expressed factors find the sum former fraction geometrical progression greater greatest common measure greatest root hence impossible roots increment integral last term least common multiple less Let the roots limiting equation logarithm m.m+r m+r.m+2r manner multiplied negative roots nth term numerator and denominator obtained odd number ordinates original equation parabola positive possible roots present value probability proportionals proposed equation quadratic surds quan quotient ratio reduced remainder represented shillings signs simple equation square root substituted subtracted suppose supposition taken tion tities unity unknown quantity vulgar fraction whole number
Δημοφιλή αποσπάσματα
Σελίδα 64 - This process of adding the square of half the coefficient of the first power of the unknown quantity to the first member, in order to make it a perfect square, is called COMPLETING THE SQUARE.
Σελίδα 44 - Divide this quantity, omitting the last figure, by twice the part of the root already found, and annex the result to the root and also to the divisor, then multiply the divisor as it now stands by the part of the root last obtained for the subtrahend.
Σελίδα 52 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Σελίδα 37 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Σελίδα 73 - Ratio is the relation which one quantity bears to another in respect of magnitude, the comparison being made by considering what multiple, part, or parts, one is of the other.
Σελίδα 44 - Divide the number thus formed, omitting the last figure, by twice the part of the root already obtained, and annex the result to the root and also to the divisor. Then multiply the divisor, as it now stands, by the part of the root last obtained, and subtract the product from the number formed, as above mentioned, by the first remainder and second period. If there be more periods- to be brought down, the operation must be repeated.
Σελίδα 13 - Multiply as in whole numbers, and point off as many decimal places in the product as there are in both multiplicand and multiplier. DIVISION. Divide as in whole numbers, and point off...
Σελίδα 73 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.
Σελίδα 73 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Σελίδα 50 - Let the equation first be cleared of fractions ; then transpose all the terms which involve the unknown quantity to one side of the equation, and the known quantities to the other...