A Treatise on AlgebraHarper & brothers, 1846 - 346 páginas |
Dentro del libro
Resultados 1-5 de 24
Página viii
... taken away The Limits of a Root determined Derived Polynomials . - Equal Roots Theorem of Sturm Page 259 · 260 265 267 • 268 · 270 • 271 272 273 278 • 279 280 283 285 • 286 . 286 287 • 289 • 290 • 291 292 295 SECTION XX . SOLUTION OF ...
... taken away The Limits of a Root determined Derived Polynomials . - Equal Roots Theorem of Sturm Page 259 · 260 265 267 • 268 · 270 • 271 272 273 278 • 279 280 283 285 • 286 . 286 287 • 289 • 290 • 291 292 295 SECTION XX . SOLUTION OF ...
Página 13
... taken from the num- ber 8 , which leaves a remainder of 3. In like manner , 12 — 7 is equal to 5 ; and 2014 is equal to 6 , etc. Sometimes we may have several numbers to subtract from a single one . Thus , 1654 signifies that 5 is to be ...
... taken from the num- ber 8 , which leaves a remainder of 3. In like manner , 12 — 7 is equal to 5 ; and 2014 is equal to 6 , etc. Sometimes we may have several numbers to subtract from a single one . Thus , 1654 signifies that 5 is to be ...
Página 15
... taken as many times as there are units in m . If m stands for 5 , then mn is 5 times n . In 4abc , 4 may be considered as the coefficient of abc ; or 4a may be considered as the coefficient of bc ; or 4ab the coeffi- cient of c . ( 20 ...
... taken as many times as there are units in m . If m stands for 5 , then mn is 5 times n . In 4abc , 4 may be considered as the coefficient of abc ; or 4a may be considered as the coefficient of bc ; or 4ab the coeffi- cient of c . ( 20 ...
Página 25
... less than 5a by 3b , too much has been taken away by 36 ; and therefore , the true remainder will be greater than 8a + 56-5a by 36 , and will hence be expressed by 8a + 5b - 5a + 3b , where the signs of the last two terms are both 4.
... less than 5a by 3b , too much has been taken away by 36 ; and therefore , the true remainder will be greater than 8a + 56-5a by 36 , and will hence be expressed by 8a + 5b - 5a + 3b , where the signs of the last two terms are both 4.
Página 34
... taken twice is obviously - 2a , taken three times is -3a , etc. hence if - a is repeated b times , it will make - ba orab . That is , a minus quantity multiplied by a plus quan- tity gives minus . Thirdly , if a is to be multiplied by ...
... taken twice is obviously - 2a , taken three times is -3a , etc. hence if - a is repeated b times , it will make - ba orab . That is , a minus quantity multiplied by a plus quan- tity gives minus . Thirdly , if a is to be multiplied by ...
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.