A Treatise on AlgebraHarper & brothers, 1846 - 346 páginas |
Dentro del libro
Resultados 1-5 de 30
Página 14
... dividend above the divisor , and drawing a line between them . Thus 24 ÷ 6 and ab are usually written and % . = ( 17. ) The sign ( two horizontal lines ) when placed between two quantities denotes that they are equal to each other ...
... dividend above the divisor , and drawing a line between them . Thus 24 ÷ 6 and ab are usually written and % . = ( 17. ) The sign ( two horizontal lines ) when placed between two quantities denotes that they are equal to each other ...
Página 43
... dividend ab . It is plain also that if we have to divide ab by b , the quotient will be a . Again the dividend abc divided by a gives bc ; for a multiplied by bc gives abc . So also 12mn divided by 3m gives 4n ; for 3m multiplied by 4n ...
... dividend ab . It is plain also that if we have to divide ab by b , the quotient will be a . Again the dividend abc divided by a gives bc ; for a multiplied by bc gives abc . So also 12mn divided by 3m gives 4n ; for 3m multiplied by 4n ...
Página 44
... dividend , by 5 the coefficient of the divisor ; and have subtracted the exponent of the divisor from the exponent of the dividend . ( 67. ) Hence for the division of monomials , we have the fol- lowing RULE . 1. Divide the coefficient ...
... dividend , by 5 the coefficient of the divisor ; and have subtracted the exponent of the divisor from the exponent of the dividend . ( 67. ) Hence for the division of monomials , we have the fol- lowing RULE . 1. Divide the coefficient ...
Página 45
... dividend . We thus obtain = a a3 ; and since the value But a3 divided by a3 may be written of a fraction is not altered by dividing both numerator and denom- inator by the same quantity , this expression is equivalent to Hence a - 2 is ...
... dividend . We thus obtain = a a3 ; and since the value But a3 divided by a3 may be written of a fraction is not altered by dividing both numerator and denom- inator by the same quantity , this expression is equivalent to Hence a - 2 is ...
Página 46
... dividend are the same as in the divisor . Let it be required to divide a2 by a2 . The quotient is obvi- ously 1 , for every number is contained in itself once . But if we apply the rule of exponents , Art . 66 , we shall have a2 - 2 or ...
... dividend are the same as in the divisor . Let it be required to divide a2 by a2 . The quotient is obvi- ously 1 , for every number is contained in itself once . But if we apply the rule of exponents , Art . 66 , we shall have a2 - 2 or ...
Otras ediciones - Ver todas
Términos y frases comunes
according to Art algebraic arithmetical arithmetical progression binomial cents Charles Anthon coefficients Completing the square contrary sign cube root denotes derived polynomial Divide the number dividend divisible equal roots equation whose roots equation x³ example exponent expression Extract the square factors find the square find the values following RULE fourth power fourth root fraction geometrical geometrical progression given equation greater greatest common divisor Hence infinite series irreducible fraction last term less letters taken method miles monomial mth degree multiplied negative nth root number of permutations number of terms obtain order of differences preceding Prob problem proportion PROPOSITION quadratic equations quotient ratio real roots Reduce remainder represent Required the square Required the sum result second degree second term Sheep extra square root subtract suppose surd theorem unity unknown quantity variation whence whole number
Pasajes populares
Página 344 - Sallust's Jugurthine War and Conspiracy of Catiline. With an English Commentary, and Geographical and Historical Indexes. Portrait. 12mo, Sheep extra, 75 cents. Anthon's Horace. The Works of Horace. With English Notes, Critical and Explanatory. A new Edition, corrected and enlarged...
Página 343 - Latin Grammar, Part I. Containing the most important Parts of the Grammar of the Latin Language, together with appropriate Exercises in the translating and writing of Latin.
Página 345 - OF CHEMISTRY ; Including the most Recent Discoveries and Applications of the Science to Medicine and Pharmacy, and to the Arts. By ROBERT KANE, MDMRIA, Professor of Natural Philosophy to the Royal Dublin Society.
Página 341 - Elements of Rhetoric and Literary Criticism, with copious Practical Exercises and Examples : including, also, a succinct History of the English Language, and of British and American Literature, from the earliest to the present Times.
Página 32 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Página 343 - Commentaries on the Gallic War, and the First Book of the Greek Paraphrase ; with English Notes, Critical and Explanatory, Plans of Battles, Sieges, &c., and Historical, Geographical, and Archaeological Indexes.
Página 162 - A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons ; and then filling the vessel with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left. How much wine did he draw each time ? 50.
Página 189 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Página 345 - Schmucker's Psychology ; Or, Elements of a new System of Mental Philosophy, on the Basis of Consciousness and Common Sense.
Página 43 - 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.