A Treatise on Higher TrigonometryMacmillan, 1884 - 208 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 31.
Σελίδα 2
... x . + etc. is conver- ( 6 ) Prove that the series x - x2 + } x3 − x2 + etc . is con- -- + 2 vergent if x is greater than - 1 and is not greater than 1 . 2. Expansion of e * in ascending powers of x 27 TRIGONOMETRY .
... x . + etc. is conver- ( 6 ) Prove that the series x - x2 + } x3 − x2 + etc . is con- -- + 2 vergent if x is greater than - 1 and is not greater than 1 . 2. Expansion of e * in ascending powers of x 27 TRIGONOMETRY .
Σελίδα 3
John Bascombe Lock. 2. Expansion of e * in ascending powers of x . Since nx ( 1 + 1 ) = { ( 1 + 1 ) * } * always ; and since by the binomial theorem nT ( 1 ... expand a * in ascending powers of x 1-2 ON EXPONENTIAL AND LOGARITHMIC SERIES . 3.
John Bascombe Lock. 2. Expansion of e * in ascending powers of x . Since nx ( 1 + 1 ) = { ( 1 + 1 ) * } * always ; and since by the binomial theorem nT ( 1 ... expand a * in ascending powers of x 1-2 ON EXPONENTIAL AND LOGARITHMIC SERIES . 3.
Σελίδα 4
John Bascombe Lock. 3. To expand a * in ascending powers of x . e * x x2 X3 We have ~ 2 = 1 + 1 + 12 + etc. 13 Let a ... EXPANSION . 4. In the above expansion put 1 + y for a , and we obtain x log . ( 1 + y ) , x3 { log 。( 1 + y ) } 2 + ...
John Bascombe Lock. 3. To expand a * in ascending powers of x . e * x x2 X3 We have ~ 2 = 1 + 1 + 12 + etc. 13 Let a ... EXPANSION . 4. In the above expansion put 1 + y for a , and we obtain x log . ( 1 + y ) , x3 { log 。( 1 + y ) } 2 + ...
Σελίδα 5
... Expansion . EXAMPLES . II . ( 1 ) Calculate the numerical value of twelve terms of the x2 X03 series 1 ++ ; + 12 3 + etc. when x = -1 , and show that it Prove the following statements : = 1 e ( 2 ) 12/13 + 4 6 + etc. 5 ' 7 1 1 1 1 + + ...
... Expansion . EXAMPLES . II . ( 1 ) Calculate the numerical value of twelve terms of the x2 X03 series 1 ++ ; + 12 3 + etc. when x = -1 , and show that it Prove the following statements : = 1 e ( 2 ) 12/13 + 4 6 + etc. 5 ' 7 1 1 1 1 + + ...
Σελίδα 11
... expanding the right- hand side that where a2 = 1 + 4x + Aqx2 + A3x3 + etc. , = A1 ( a - 1 ) - ( a − 1 ) 2 + } ( a ... Expand a " , and by equating the coefficients of the various powers of y find A ,, A3 , etc. in terms of A1 . Result ...
... expanding the right- hand side that where a2 = 1 + 4x + Aqx2 + A3x3 + etc. , = A1 ( a - 1 ) - ( a − 1 ) 2 + } ( a ... Expand a " , and by equating the coefficients of the various powers of y find A ,, A3 , etc. in terms of A1 . Result ...
Άλλες εκδόσεις - Προβολή όλων
TREATISE ON HIGHER TRIGONOMETR J. B. (John Bascombe) 1849-1921 Lock Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a+ẞ Algebra angular points arithmetical ascending powers calculated Cambridge centre circular measure circumscribing circle Classical Series coefficients cos² cos³ cosec cosh nx cosine Crown 8vo deduce different values distance Edited by Rev equal escribed circles Eton College EXAMPLES Expand expression Extra fcap fcap Fellow of St Find form A+iB formula GRAMMAR greater Hence inscribed inscribed circle integer Introductions and Notes J. P. MAHAFFY John's College King's College late Fellow less limit LIVY logarithms MACMILLAN'S CLASSICAL CATALOGUE Moivre's Theorem nine-points circle nth roots obtain Oxford P₁ perpendiculars positive integer Prove the following quadratic factors radii radius right angle roots School sec² Shew sides sin n sin² sin³ sine sinh Sum the series Tables tan-¹ tan² tangent triangle ABC Trigonometry Trinity College Vocabulary whole number
Δημοφιλή αποσπάσματα
Σελίδα 7 - THE SEVEN KINGS OF. ROME. An Easy Narrative, abridged from the First Book of Livy by the omission of Difficult Passages; being a First Latin Reading Book, with Grammatical Notes and Vocabulary.
Σελίδα 150 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Σελίδα 19 - Whitney and Edgren. — A COMPENDIOUS GERMAN AND ENGLISH DICTIONARY, with Notation of Correspondences and Brief Etymologies. By Professor WD WHITNEY, assisted by AH EDGREN.
Σελίδα 4 - England. — EXERCISES ON LATIN SYNTAX AND IDIOM, ARRANGED WITH REFERENCE TO ROBY'S SCHOOL LATIN GRAMMAR. By EB ENGLAND, MA, Assistant Lecturer at the Owens College, Manchester. Crown 8vo.
Σελίδα 6 - Works by ALEXANDER W. POTTS, MA, LL.D., late Fellow of St. John's College, Cambridge; Head Master of the Fettes College, Edinburgh. HINTS TOWARDS LATIN PROSE COMPOSITION. New Edition. Extra fcap. 8vo.
Σελίδα 4 - HODGSON -MYTHOLOGY FOR LATIN VERSIFICATION. A brief Sketch of the Fables of the Ancients, prepared to be rendered into Latin Verse for Schools. By F. HODGSON, BD, late Provost of Eton. New Edition, revised by FC HODGSON, MA i8mo. 3*.
Σελίδα 4 - GREENWOOD— THE ELEMENTS OF GREEK GRAMMAR, including Accidence, Irregular Verbs, and Principles of Derivation and Composition ; adapted to the System of Crude Forms. By JG GREENWOOD, Principal of Owens College, Manchester. New Edition. Crown 8vo.
Σελίδα 4 - Blackie. — GREEK AND ENGLISH DIALOGUES FOR USE IN SCHOOLS AND COLLEGES. By JOHN STUART BLACK.IE, Emeritus Professor of Greek in the University of Edinburgh.
Σελίδα 19 - Part II.— SECOND YEAR. Conversational Lessons in Systematic Accidence and Elementary Syntax. With Philological Illustrations and Etymological Vocabulary.
Σελίδα 17 - Kiepert. — MANUAL OF ANCIENT GEOGRAPHY, Translated from the German of Dr. HEINRICH KIEPERT. Crown 8vo. 5*. Mahaffy. — Works by JP MAHAFFY, MA, Professor of Ancient History in Trinity College, Dublin, and Hon. Fellow of Queen's College, Oxford. SOCIAL LIFE IN GREECE; from Homer to Menander.