Higher Algebra: A Sequel to Elementary Algebra for SchoolsMacmillan, 1891 - 557 páginas |
Dentro del libro
Resultados 1-5 de 40
Página ix
... greatest and least of fractions Eliminant of three linear equations Examples I .. CHAPTER II . PROPORTION . Definitions and Propositions Comparison between algebraical and geometrical definitions . Case of incommensurable quantities ...
... greatest and least of fractions Eliminant of three linear equations Examples I .. CHAPTER II . PROPORTION . Definitions and Propositions Comparison between algebraical and geometrical definitions . Case of incommensurable quantities ...
Página xii
... greatest · 127 Ab initio proof of the formula for the number of combinations of n things r at a time • 128 Total number of selections of p + q + r + ... things , whereof p are alike of one kind , q alike of a second kind , & c . 129 ...
... greatest · 127 Ab initio proof of the formula for the number of combinations of n things r at a time • 128 Total number of selections of p + q + r + ... things , whereof p are alike of one kind , q alike of a second kind , & c . 129 ...
Página xiii
... greatest term Expansion of ( x + a ) " , when n is a positive integer General term of the expansion The expansion may be made to depend upon the case in which the first term is unity . Second proof of the binomial theorem The ...
... greatest term Expansion of ( x + a ) " , when n is a positive integer General term of the expansion The expansion may be made to depend upon the case in which the first term is unity . Second proof of the binomial theorem The ...
Página xv
... greatest when they are equal : product being given , the sum is least when they are equal • The arithmetic mean of a number of positive quantities is greater than the geometric mean Given sum of a , b , c , ; to find the greatest value ...
... greatest when they are equal : product being given , the sum is least when they are equal • The arithmetic mean of a number of positive quantities is greater than the geometric mean Given sum of a , b , c , ; to find the greatest value ...
Página 6
... greatest and least of them . a Suppose that all the denominators are positive . Let be t least fraction , and denote it by k ; then b r = * > * ; k ; .. a = kb ,; k ; ... a1 > kb1 ; agk ; .. a2 > kb ̧ ; b2 .. by addition , 3 and so on ...
... greatest and least of them . a Suppose that all the denominators are positive . Let be t least fraction , and denote it by k ; then b r = * > * ; k ; .. a = kb ,; k ; ... a1 > kb1 ; agk ; .. a2 > kb ̧ ; b2 .. by addition , 3 and so on ...
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Otras ediciones - Ver todas
Higher Algebra: A Sequel to Elementary Algebra for Schools H. S. Hall,S. R. Knight Sin vista previa disponible - 2017 |
Higher Algebra: A Sequel to Elementary Algebra for Schools (Classic Reprint) H. S. Hall Sin vista previa disponible - 2017 |
Higher Algebra: A Sequel to Elementary Algebra for Schools H. S. Hall,S. R. Knight Sin vista previa disponible - 2018 |
Términos y frases comunes
a+b+c a₁ Algebra annuity arithmetic mean arithmetical progression ax² b₁ balls Binomial Theorem C₁ C₂ CAMB COLL common difference common ratio complete quotient contains continued fraction decimal denominator denote digits divided divisible equal event Example expansion expression factors find the chance find the number Find the sum find the value finite geometric Geometrical Progression given series greater harmonic means hence In+1 infinite series less letters logarithms multiplying negative nth term number of shot number of solutions number of terms obtain P₁ partial fractions positive integers preceding article prime number proper fraction prove quadratic quadratic equation quantities radix recurring decimal result scale of relation series is convergent shew shillings Similarly Solve the equations suppose U₁ U₂ unity varies whence zero
Pasajes populares
Página 55 - ... any number divided by 9 will leave the same remainder as the sum of its digits divided by 9.
Página 169 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Página 111 - The number of combinations of n things г at a time is equal to the number of combinations of n things n—r at a time.
Página 488 - At the 50th mile stone from London, A overtook a drove of geese which were proceeding at the rate of three miles in two hours ; and two hours afterwards met a stage waggon, which was moving at the rate of 9 miles in 4 hours.
Página 450 - If then we suppose the factors corresponding to the negative and imaginary roots to be already multiplied together, each factor x— a corresponding to a positive root introduces at least one change of sign ; therefore no equation can have more positive roots than it has changes of sign. To prove the second part of Descartes...
Página 109 - Pr always denotes the number of factors in the formula we are using. Ex. 1. Four persons enter a carriage in which there are six seats : in how many ways can they take their places ? The first person may seat himself in 6 ways ; and then the second person in 5 ; the third in 4 ; and the fourth in 3 ; and since each of these ways may be associated with each of the others, the required answer is б x 5 x 4 x 3, or 360.
Página 13 - Hence if any three terms of a proportion are given, the fourth may be found. Thus if...
Página 172 - The integral part of a logarithm is called the characteristic, and the decimal part is called the mantissa.
Página 482 - A railway train after travelling for one hour meets with an accident which delays it one hour, after which it proceeds at three-fifths of its former rate, and arrives at the terminus...
Página 455 - Every equation of an odd degree has at least one real root whose sign is opposite to that of its last term.