Algebra for the Use of Colleges and Schools: With Numerous ExamplesMacmillan, 1866 - 553 σελίδες |
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Σελίδα 18
... increased by twice their product . Again we have ( a - b ) 2 = a2 - 2ab + b2 . Thus the square of the difference of two numbers is equal to the sum of the squares of the two numbers diminished by twice their product . Also we have ( a + ...
... increased by twice their product . Again we have ( a - b ) 2 = a2 - 2ab + b2 . Thus the square of the difference of two numbers is equal to the sum of the squares of the two numbers diminished by twice their product . Also we have ( a + ...
Σελίδα 34
... increased by a - b pounds . If however b is greater than a the capital has been diminished by b - a pounds . In this latter case a -b is the indication of what would be pronounced in Arithmetic to be an impossible subtraction ; but yet ...
... increased by a - b pounds . If however b is greater than a the capital has been diminished by b - a pounds . In this latter case a -b is the indication of what would be pronounced in Arithmetic to be an impossible subtraction ; but yet ...
Σελίδα 87
... increases one - half , but the revenue falls one - third . Find the duty per cwt . after the reduction . 38. A ship sails with a supply of biscuit for 60 days , at a daily allowance of 1 lb. a head ; after being at sea 20 days she ...
... increases one - half , but the revenue falls one - third . Find the duty per cwt . after the reduction . 38. A ship sails with a supply of biscuit for 60 days , at a daily allowance of 1 lb. a head ; after being at sea 20 days she ...
Σελίδα 99
... increased by 6 , and equal to when its denom- inator is diminished by 2 ? Let x denote the numerator and y the denominator of the fraction ; then by the question , x + 6 y - 3 and , 90 y - 2 = 112 Clear the first equation of fractions ...
... increased by 6 , and equal to when its denom- inator is diminished by 2 ? Let x denote the numerator and y the denominator of the fraction ; then by the question , x + 6 y - 3 and , 90 y - 2 = 112 Clear the first equation of fractions ...
Σελίδα 100
... increased by one its value becomes one - third ; if the denominator is increased by one its value becomes one - fourth . What is the fraction ? 4. Find two numbers such that if the first be added to four times the second , the sum is 29 ...
... increased by one its value becomes one - third ; if the denominator is increased by one its value becomes one - fourth . What is the fraction ? 4. Find two numbers such that if the first be added to four times the second , the sum is 29 ...
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Άλλες εκδόσεις - Προβολή όλων
Algebra for the Use of Colleges and Schools: With Numerous Examples Isaac Todhunter Πλήρης προβολή - 1866 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a+b+c arithmetical arithmetical mean ax² b₁ Binomial Theorem black balls chance coefficient common measure contains continued fraction convergent cube root digits divided divisible divisor equal event example expansion Extract the square factors find the number given equations given number greater than unity greatest Hence least common multiple less than unity letters logarithm meaning multiply negative quantity nth term number of combinations number of terms obtain occur P₁ P₂ positive integers positive quantity preceding Article prime number probability prove quadratic equation quadratic surd quotient radix ratio remainder respectively result scale shew shewn shillings Similarly solution square number square root subtraction suppose surd unknown quantities white balls whole number zero
Δημοφιλή αποσπάσματα
Σελίδα 511 - Prelector of St. John's College, Cambridge. AN ELEMENTARY TREATISE ON MECHANICS. For the Use of the Junior Classes at the University and the Higher Classes in Schools.
Σελίδα 55 - If the numerator and denominator be divided by the same number, the value of the fraction is not altered.
Σελίδα 512 - HODGSON -MYTHOLOGY FOR LATIN VERSIFICATION. A brief Sketch of the Fables of the Ancients, prepared to be rendered into Latin Verse for Schools.
Σελίδα 319 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Σελίδα 277 - To find the number of permutations of n things taken r at a time. Suppose...
Σελίδα 130 - Separate the given number into periods, by pointing every second figure, beginning with the units' place. find the greatest square in the left-hand period, and...
Σελίδα 12 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
Σελίδα 15 - The product of the sum and difference of two numbers is equal to the difference of their squares.
Σελίδα 331 - An infinite series is said to be divergent when the sum of the first n terms can be made numerically greater than any finite quantity by taking n sufficiently great.
Σελίδα 83 - В contains 9 gallons of wine and 3 gallons of water ; how many gallons must be drawn from each cask so as to produce by their mixture 7 gallons of wine and 7 gallons of water ? 33.