An Elementary Treatise on Algebra: Theoretical and PracticalCollins and Hannay, 1824 - 516 σελίδες |
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Σελίδα 12
... evident truth , or a propo- sition universally assented to , or which requires no formal proof . 45. As axioms are the first principles upon which all mathematical demonstrations are founded , I will point out those that are necessary ...
... evident truth , or a propo- sition universally assented to , or which requires no formal proof . 45. As axioms are the first principles upon which all mathematical demonstrations are founded , I will point out those that are necessary ...
Σελίδα 15
... evident that 5 ( A — α ) +3 ( A - a ) , or ( 5A - 5a ) + ( 3A - 3a ) = 8A - 8a ; and therefore the sum of the quantities -5a and -3a , when taken in their isolated state , will by a ne- cessary extension of the proposition be - Sa . A ...
... evident that 5 ( A — α ) +3 ( A - a ) , or ( 5A - 5a ) + ( 3A - 3a ) = 8A - 8a ; and therefore the sum of the quantities -5a and -3a , when taken in their isolated state , will by a ne- cessary extension of the proposition be - Sa . A ...
Σελίδα 25
... evident from the following consideration ; Thus , if it were required to sub- tract 6 from 9 , the difference is properly 9-6 , which is 3 ; and if 6-2 were subtracted from 9 , it is plain , that the remainder would be greater by 2 ...
... evident from the following consideration ; Thus , if it were required to sub- tract 6 from 9 , the difference is properly 9-6 , which is 3 ; and if 6-2 were subtracted from 9 , it is plain , that the remainder would be greater by 2 ...
Σελίδα 31
... evident , from the nature of multiplica- tion , that the product contains either of the factors as many times as the other contains an unit . There- fore , the product ab contains a as many times as contains an unit , that is , b times ...
... evident , from the nature of multiplica- tion , that the product contains either of the factors as many times as the other contains an unit . There- fore , the product ab contains a as many times as contains an unit , that is , b times ...
Σελίδα 44
... evident , from various instances , in the following part of the work . Ex . 16. Required the product of a + b + c by a- b + c . Ans . a2ac - b2 + c2 . Ex . 17. Required the product of x + y + z by x - y - z . Ans . x - y - 2yz - 22 . Ex ...
... evident , from various instances , in the following part of the work . Ex . 16. Required the product of a + b + c by a- b + c . Ans . a2ac - b2 + c2 . Ex . 17. Required the product of x + y + z by x - y - z . Ans . x - y - 2yz - 22 . Ex ...
Άλλες εκδόσεις - Προβολή όλων
An Elementary Treatise on Algebra: Theoretical and Practical James Ryan,Robert Adrain Πλήρης προβολή - 1824 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a²+ab+b² added adfected algebraic quantities becomes binomial changing the signs coefficient common denominator completing the square compound quantity consequently cube root difference digits divi dividend division enunciation equa equal example exponent expressed extracting the root factors find the values formula fourth gives greater greatest common divisor greatest common measure Hence least common multiple less letter logarithm lowest terms lues magnitudes manner method miles multiplied negative observed operation positive preceding Prob problem proportion proposed equation quadratic equations quadratic surds quan quotient radical quantities radical sign ratio Reduce remainder Required the cube Required the square required to find result RULE second equation shillings side simple equations solution square root substituting subtracted third tion tity transposition travelled unity unknown quantity values of x whence whole number
Δημοφιλή αποσπάσματα
Σελίδα iv - In conformity to the act of Congress of the United States, entitled, " An act for the encouragement of learning, by securing the copies of maps, charts and books, to the authors and proprietors of such copies, during the times therein mentioned ;
Σελίδα 498 - IF any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents.
Σελίδα 57 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Σελίδα 162 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Σελίδα 489 - The first of four magnitudes is said to have the same ratio to the second which the third has to the. fourth, when any equimultiples...
Σελίδα 239 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Σελίδα 503 - THEOB.—If four magnitudes be proportionals, they are also proportionals by conversion; that is, the first is to its excess above the second, as the third to its excess above the fourth. Let AB be to BE, as CD to DF: then BA shall be to AE, as DC to CF.
Σελίδα 496 - Equal magnitudes have the same ratio to the same magnitude; and the same has the same ratio to equal magnitudes.
Σελίδα 318 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Σελίδα 7 - NB When four magnitudes are proportionals, it is usually expressed by saying, the first is to the second, as the third to the fourth.' VII. When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater than that of the second...