Algebra for the Use of Colleges and Schools: With Numerous ExamplesMacmillan, 1866 - 553 σελίδες |
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Αποτελέσματα 1 - 5 από τα 64.
Σελίδα 20
... of two dimensions , and the multiplier is homogeneous and of two dimensions ; the product is homogeneous and of four dimensions . The law here stated and exemplified is of great importance as it serves 20 MULTIPLICATION .
... of two dimensions , and the multiplier is homogeneous and of two dimensions ; the product is homogeneous and of four dimensions . The law here stated and exemplified is of great importance as it serves 20 MULTIPLICATION .
Σελίδα 33
... four factors . - 49. Resolve 4 ( ad + bc ) 2 — ( a2 — b2 — c2 + d2 ) 2 into four factors . - - 50. Shew that ( ay — bx ) 2 + ( bz — cy ) 2 + ( cx − az ) 2 + ( ax + by + cz ) 3 livisible by a2 + b2 + c2 and by x2 + y2 + z2 . - V ...
... four factors . - 49. Resolve 4 ( ad + bc ) 2 — ( a2 — b2 — c2 + d2 ) 2 into four factors . - - 50. Shew that ( ay — bx ) 2 + ( bz — cy ) 2 + ( cx − az ) 2 + ( ax + by + cz ) 3 livisible by a2 + b2 + c2 and by x2 + y2 + z2 . - V ...
Σελίδα 39
... four cases to consider in multiplication . Let a and b denote any two numbers , then we have to consider + ax + b , - − a x + b , + ax - b , -a × — b . - The first case is that of common Arithmetic and needs NEGATIVE QUANTITIES . 39.
... four cases to consider in multiplication . Let a and b denote any two numbers , then we have to consider + ax + b , - − a x + b , + ax - b , -a × — b . - The first case is that of common Arithmetic and needs NEGATIVE QUANTITIES . 39.
Σελίδα 40
... four results obtained are true ; that is , + ax + b = + ab , - ax + b — ab , + a × −b = -ab , - a × -b = + ab . - - Take , for example , the last of these , and suppose that a is a negative quantity , and so may be denoted by -a ; then ...
... four results obtained are true ; that is , + ax + b = + ab , - ax + b — ab , + a × −b = -ab , - a × -b = + ab . - - Take , for example , the last of these , and suppose that a is a negative quantity , and so may be denoted by -a ; then ...
Σελίδα 52
... four algebraical expressions . Or we may find the G. C. M. of two of the given expressions and also the G. C. M. of the other two ; then the G. C. M. of the two expressions thus found will be the G. C. M. of the four given expressions ...
... four algebraical expressions . Or we may find the G. C. M. of two of the given expressions and also the G. C. M. of the other two ; then the G. C. M. of the two expressions thus found will be the G. C. M. of the four given expressions ...
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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.