A Treatise on Algebra: By Charles SmithMacmillan and Company, 1888 - 571 sider |
Inni boken
Resultat 1-5 av 14
Side 16
... column , and there are a columns ; thus the whole number of dots is b repeated a times , that is b xa . Hence , when a and b are integers , abba . When the numbers are fractions , for example and , we prove as in Art . 28 that above ...
... column , and there are a columns ; thus the whole number of dots is b repeated a times , that is b xa . Hence , when a and b are integers , abba . When the numbers are fractions , for example and , we prove as in Art . 28 that above ...
Side 34
... columns . The following are examples of multiplication arranged as above described : a + b a + b a- - b a2 + ab + b2 a + b a - b a2 + ab a2 + ab a3 + a2b + ab2 + ab + b2 -ab - b2 -a2b- ab2 - b3 a2 + 2ab + b2 a2 - b2 a3 -b3 a + b + c a + ...
... columns . The following are examples of multiplication arranged as above described : a + b a + b a- - b a2 + ab + b2 a + b a - b a2 + ab a2 + ab a3 + a2b + ab2 + ab + b2 -ab - b2 -a2b- ab2 - b3 a2 + 2ab + b2 a2 - b2 a3 -b3 a + b + c a + ...
Side 35
... columns will thus be avoided . 60 . Definitions . A term which is the product of n letters is said to be of n dimensions , or of the nth degree . Thus 3abc is of three dimensions , or of the third degree ; and 5a b'c , that is 5aaabbc ...
... columns will thus be avoided . 60 . Definitions . A term which is the product of n letters is said to be of n dimensions , or of the nth degree . Thus 3abc is of three dimensions , or of the third degree ; and 5a b'c , that is 5aaabbc ...
Side 230
... column , so that in every case the first term of the remainder is obvious . 197. The square root of an algebraical expression may also be obtained by means of the theorem of Art . 91 . Take for example the case just considered . The ...
... column , so that in every case the first term of the remainder is obvious . 197. The square root of an algebraical expression may also be obtained by means of the theorem of Art . 91 . Take for example the case just considered . The ...
Side 522
... columns , will be Let now these products be considered to be positive or negative according as there is an even or an odd number of inversions of the natural order in the suffixes ; then the algebraic sum of all the products will be - a ...
... columns , will be Let now these products be considered to be positive or negative according as there is an even or an odd number of inversions of the natural order in the suffixes ; then the algebraic sum of all the products will be - a ...
Innhold
53 | |
64 | |
70 | |
87 | |
104 | |
112 | |
118 | |
124 | |
133 | |
139 | |
143 | |
149 | |
156 | |
169 | |
176 | |
184 | |
199 | |
201 | |
209 | |
213 | |
216 | |
222 | |
228 | |
235 | |
242 | |
254 | |
261 | |
267 | |
274 | |
275 | |
326 | |
334 | |
342 | |
348 | |
356 | |
362 | |
372 | |
379 | |
385 | |
422 | |
429 | |
444 | |
452 | |
460 | |
474 | |
481 | |
487 | |
491 | |
495 | |
498 | |
502 | |
508 | |
510 | |
517 | |
518 | |
524 | |
531 | |
535 | |
537 | |
Andre utgaver - Vis alle
Vanlige uttrykk og setninger
a+b+c a₁ arithmetic mean arithmetical progression ax² b₁ binomial Binomial Theorem C₁ Cambridge coefficient contain continued fraction Crown 8vo denominator determinant digits divergent divide divisible divisor Edition equal equation ax example expansion Extra fcap Fcap Find the number Find the sum follows geometrical progression given expression Globe 8vo greater Hence the required infinity letters logarithm MACMILLAN'S Multiply negative nth convergent nth root nth term number of terms obtained P₁ periodic continued fraction positive integer powers prime number Professor prove quadratic equation quadratic surd quotient ratio remainder School Shew Solve the equation square root subtract suppose Theorem Trinity College u₁ unknown quantities white ball whole number zero
Populære avsnitt
Side 76 - OF NEW TESTAMENT HISTORY, for National and Elementary Schools. With Map. i8mo, cloth.
Side 63 - HISTORICAL OUTLINES OF ENGLISH ACCIDENCE, comprising Chapters on the History and Development of the Language, and on Word-formation. New Edition. Extra fcap. 8vo. 6s. ELEMENTARY LESSONS IN HISTORICAL ENGLISH GRAMMAR, containing Accidence and Wordformation. New Edition.
Side 61 - HALES— LONGER ENGLISH POEMS, with Notes, Philological and Explanatory, and an Introduction on the Teaching of English. Chiefly for Use in Schools. Edited by JW HALES, MA, Professor of English Literature at King's College, London.
Side 57 - ANALYSIS OF ENGLISH HISTORY, based on Green's "Short History of the English People.
Side 49 - HUXLEY, FRS With numerous Illustrations, and Coloured Plates. New and Cheaper Edition. Crown 8vo. 6s.
Side 36 - MATHEMATICAL PROBLEMS, on Subjects included in the First and Second Divisions of the Schedule of Subjects for the Cambridge Mathematical Tripos Examination. Devised and arranged by JOSEPH WOLSTENHOLME, late Fellow of Christ's College, sometime Fellow of St.
Side 63 - The Golden Treasury of the Best Songs and Lyrical Poems in the English Language. Selected and arranged, with Notes, by FRANCIS TURNER PALGRAVE.
Side 20 - ROBY— A GRAMMAR OF THE LATIN LANGUAGE, from Plautus to Suetonius. By HJ ROBY, MA, late Fellow of St. John's College, Cambridge. In Two Parts. Third Edition. Part I. containing : — Book I. Sounds. Book II. Inflexions. Book III. Word-formation. Appendices. Crown 8vo.
Side 58 - EUROPEAN HISTORY. Narrated in a Series of Historical Selections from the Best Authorities. Edited and arranged by EM SEWELL and CM YONGE. First Series, 1003 — 1154. Third Edition. Crown 8vo. 6s. Second Series, 1088—1228. Crown 8vo. 6s. Third Edition. " We know of scarcely anything which is so likely to raise to a higher level the average standard of English education.
Side 60 - Among the numerous sets of readers before the public the present series is honourably distinguished by the marked superiority of its materials and the careful ability with which they have been adapted to the growing capacity of the pupils. The plan of the two primers is excellent for facilitating the child's first attempts to read. In the first three following books there is abundance of entertaining reading. .... Better food for young minds could hardly be found.