Algebra for the Use of Colleges and Schools: With Numerous ExamplesMacmillan, 1866 - 553 σελίδες |
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Σελίδα
... Greatest Common Measure 45 VIII . Fractions · VII . Least Common Multiple IX . Equations of the First Degree X. Problems which lead to Simple Equations with one Un- 54 57 70 known Quantity .80 • · · · XI . Simultaneous Equations of the ...
... Greatest Common Measure 45 VIII . Fractions · VII . Least Common Multiple IX . Equations of the First Degree X. Problems which lead to Simple Equations with one Un- 54 57 70 known Quantity .80 • · · · XI . Simultaneous Equations of the ...
Σελίδα 45
... GREATEST COMMON MEASURE . 105. In Arithmetic the greatest common measure of two or more whole numbers is the greatest number which will divide each of them without remainder . The term is also used in Algebra , and its meaning in this ...
... GREATEST COMMON MEASURE . 105. In Arithmetic the greatest common measure of two or more whole numbers is the greatest number which will divide each of them without remainder . The term is also used in Algebra , and its meaning in this ...
Σελίδα 46
... P divides A and B , we may suppose A = aP , and B = bP , then ma ± nB = ( ma ± nb ) P ; thus P divides mA ± nB . We can now prove the rule given in Art . 107 . PB 110. Let A and B denote the two expres- 46 GREATEST COMMON MEASURE .
... P divides A and B , we may suppose A = aP , and B = bP , then ma ± nB = ( ma ± nb ) P ; thus P divides mA ± nB . We can now prove the rule given in Art . 107 . PB 110. Let A and B denote the two expres- 46 GREATEST COMMON MEASURE .
Σελίδα 47
... greatest common measure . By Art . 109 every expression which divides A and B divides A - pB , that is , C ; thus every expression which is a measure of A and B is a measure of B and C. Similarly every expression which is a measure of B ...
... greatest common measure . By Art . 109 every expression which divides A and B divides A - pB , that is , C ; thus every expression which is a measure of A and B is a measure of B and C. Similarly every expression which is a measure of B ...
Σελίδα 48
... + 6 is the G. C. M. of the two given expressions , we merely mean that no measure can be found which contains higher powers of x than 6x + 6 . Other measures may be found which differ from this so 48 GREATEST COMMON MEASURE . Fractions.
... + 6 is the G. C. M. of the two given expressions , we merely mean that no measure can be found which contains higher powers of x than 6x + 6 . Other measures may be found which differ from this so 48 GREATEST COMMON MEASURE . Fractions.
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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.