Algebra for the Use of Colleges and Schools: With Numerous ExamplesMacmillan, 1866 - 553 σελίδες |
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Σελίδα
... Quadratic Equations 155 167 · 173 XXI . Equations which may be solved like Quadratics XXII . Theory of Quadratic Equations and Quadratic Expressions 187 XXIII . Simultaneous Equations involving Quadratics XXIV . Problems which lead to ...
... Quadratic Equations 155 167 · 173 XXI . Equations which may be solved like Quadratics XXII . Theory of Quadratic Equations and Quadratic Expressions 187 XXIII . Simultaneous Equations involving Quadratics XXIV . Problems which lead to ...
Σελίδα
... Quadratic Surd to a continued Fraction XLVI . Indeterminate Equations of the First Degree 369 • • 377 XLVIII . XLVII . Indeterminate Equations of a Degree higher than the first . 385 Partial Fractions and Indeterminate Coefficients 390 ...
... Quadratic Surd to a continued Fraction XLVI . Indeterminate Equations of the First Degree 369 • • 377 XLVIII . XLVII . Indeterminate Equations of a Degree higher than the first . 385 Partial Fractions and Indeterminate Coefficients 390 ...
Σελίδα 158
... quadratic surds . For So also α a ( √b = √c ) F √6 ± √c ( √6 ± √c ) ( √b = √c ) α - a ( b = √c ) b ± √c ( b ± √c ) ( b = √c ) a ( √b = √c ) . b - c = a ( b = √c ) . b2 - c 294. By two operations we may rationalise the ...
... quadratic surds . For So also α a ( √b = √c ) F √6 ± √c ( √6 ± √c ) ( √b = √c ) α - a ( b = √c ) b ± √c ( b ± √c ) ( b = √c ) a ( √b = √c ) . b - c = a ( b = √c ) . b2 - c 294. By two operations we may rationalise the ...
Σελίδα 159
... quadratic surds . For suppose the denominator to be a + √b + √c ; first multiply both numerator and denominator by Ja + b - c , thus the denominator becomes a + b - c + 2 ( ab ) ; then multiply both numerator and denominator by a + b ...
... quadratic surds . For suppose the denominator to be a + √b + √c ; first multiply both numerator and denominator by Ja + b - c , thus the denominator becomes a + b - c + 2 ( ab ) ; then multiply both numerator and denominator by a + b ...
Σελίδα 160
... quadratic surds cannot be reduced to others which have the same irrational part , their product is irrational . Let x and y be the two quadratic surds , and if possible let ( xy ) = rx , where r is a whole number or a fraction . Then xy ...
... quadratic surds cannot be reduced to others which have the same irrational part , their product is irrational . Let x and y be the two quadratic surds , and if possible let ( xy ) = rx , where r is a whole number or a fraction . Then xy ...
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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.