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... Continued Fractions • XLV . Reduction of a Quadratic Surd to a continued Fraction XLVI . Indeterminate Equations of the First Degree XLVII . Indeterminate Equations of a Degree higher than the first XLVIII . Partial Fractions and ...
... Continued Fractions • XLV . Reduction of a Quadratic Surd to a continued Fraction XLVI . Indeterminate Equations of the First Degree XLVII . Indeterminate Equations of a Degree higher than the first XLVIII . Partial Fractions and ...
Page 216
... continued proportion . 403. Similarly we may shew that if a b :: b c cd , then ad : a3 b3 . Here the four quantities ... fraction formed by taking one of the quantities as a numerator , and the other as a denominator , is a determinate ...
... continued proportion . 403. Similarly we may shew that if a b :: b c cd , then ad : a3 b3 . Here the four quantities ... fraction formed by taking one of the quantities as a numerator , and the other as a denominator , is a determinate ...
Page 339
... constant ratio to its value at that instant , prove that its value at any time t will be a t XLIV . CONTINUED FRACTIONS . 600. Every expression of the form a- b is called d C ± e ± & c . a continued fraction . We shall confine our ...
... constant ratio to its value at that instant , prove that its value at any time t will be a t XLIV . CONTINUED FRACTIONS . 600. Every expression of the form a- b is called d C ± e ± & c . a continued fraction . We shall confine our ...
Page 340
... fraction into a continued fraction , we have to proceed as if we were finding the greatest common measure of the numerator and denominator , and we must therefore at last arrive at a point where the remainder is zero and the operation ...
... fraction into a continued fraction , we have to proceed as if we were finding the greatest common measure of the numerator and denominator , and we must therefore at last arrive at a point where the remainder is zero and the operation ...
Page 341
... fraction may be formed in a similar manner by multiplying the denominator of the second by the third quotient , and adding the denominator of the first . We shall now shew by induction that such a law holds ... CONTINUED FRACTIONS . 341.
... fraction may be formed in a similar manner by multiplying the denominator of the second by the third quotient , and adding the denominator of the first . We shall now shew by induction that such a law holds ... CONTINUED FRACTIONS . 341.
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arithmetic mean arithmetical Arithmetical Progression ax² binomial Binomial Theorem black balls Cambridge chance cloth coefficient College contains continued fraction convergent Crown 8vo cube root digits divided divisible divisor equal event example expansion Extract the square factors Fcap find the number Geometrical Progression given equations Hence least common multiple less than unity letters logarithm mean miles multiply negative quantity number of combinations number of terms obtain P₁ P₂ positive integers positive quantity preceding article prime number probability prove quadratic equation quadratic surd quotient radix ratio remainder respectively result scale shew shillings Similarly solution square root subtraction suppose surd theorem things taken third unknown quantities white balls whole number zero
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Page 53 - Hence if the numerator and denominator of a fraction be multiplied by the same number the value of the fraction is not altered.
Page 494 - NEWMAN'S Essay on Development. 8vo. cloth, 10s. 6d. CAMBRIDGE.— Cambridge Theological Papers. Comprising those given at the Voluntary Theological and Crosse Scholarship Examinations. Edited, with References and Indices, by AP MOOR, MA of Trinity College, Cambridge, and Sub-warden of St. Augustine's College, Canterbury. 8vo. cloth, Is.
Page 497 - Worship. 18mo. cloth, 2s. 6d. HARE.— Two Sermons preached in Herstmonceux Church, on Septuagesima Sunday, 1855, being the Sunday after the Funeral of the Venerable Archdeacon Hare. By the Rev. H. VENN ELLIOTT, Perpetual Curate of St. Mary's, Brighton, late Fellow of Trinity College, Cambridge, and the Rev. JN SIMPKINSON, Rector of Brington, Northampton, formerly Curate of Herstmonceux. 8vo.