A Synopsis of the Principal Formulae and Results of Pure MathematicsJ. & J.J. Deighton, 1829 - 358 σελίδες |
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Αποτελέσματα 1 - 5 από τα 12.
Σελίδα 101
... ( cosec a ) 2 . vers a = 1 - cos a . covers a 1- sin a . = suvers a = 1 + cos a . ( L. 35. ) ( 5. ) The sine is ... cosec 2n = ∞ . cos ( 2n + 1 ) = 0 , cot ( 2n + 1 ) π = 0 , cosec ( 2n + 1 ) = 1 . cos ( 2n + 1 ) π = −1 , cot ( 2n + 1 ) ...
... ( cosec a ) 2 . vers a = 1 - cos a . covers a 1- sin a . = suvers a = 1 + cos a . ( L. 35. ) ( 5. ) The sine is ... cosec 2n = ∞ . cos ( 2n + 1 ) = 0 , cot ( 2n + 1 ) π = 0 , cosec ( 2n + 1 ) = 1 . cos ( 2n + 1 ) π = −1 , cot ( 2n + 1 ) ...
Σελίδα 103
... ̄ * . 1 — ( cos a ) 2 | * . cos a 2 tana sin 2 a sin 2 a 1+ cos 2 a 1 . cos 2 a - • - 1 + cos 2 a 12 { tan ( 45 ° + 1⁄2 a ) — tan ( 45 ° —— a ) } . 1 — ( tan 1a ) 2 ( 10. ) sec 2a = ( cosec a ) ( cot a FORMULE RELATING TO TWO ARCS . 103.
... ̄ * . 1 — ( cos a ) 2 | * . cos a 2 tana sin 2 a sin 2 a 1+ cos 2 a 1 . cos 2 a - • - 1 + cos 2 a 12 { tan ( 45 ° + 1⁄2 a ) — tan ( 45 ° —— a ) } . 1 — ( tan 1a ) 2 ( 10. ) sec 2a = ( cosec a ) ( cot a FORMULE RELATING TO TWO ARCS . 103.
Σελίδα 105
... 1 — ( tan a ) 2 ; 2 cot a ( cot a ) 2 - 1 ( cot a ) 2 - 1 2 cot a ; = ( cot a― tan a ) . ( sec a ) 2 1 — ( tan a ) 2 2 1 + ( tan a ) 2 1- ( tan a ) e ' sec 2a = cosec 2α = cota seca = = coseca = ( FORMULE RELATING TO TWO ARCS . 105.
... 1 — ( tan a ) 2 ; 2 cot a ( cot a ) 2 - 1 ( cot a ) 2 - 1 2 cot a ; = ( cot a― tan a ) . ( sec a ) 2 1 — ( tan a ) 2 2 1 + ( tan a ) 2 1- ( tan a ) e ' sec 2a = cosec 2α = cota seca = = coseca = ( FORMULE RELATING TO TWO ARCS . 105.
Σελίδα 106
... cosec 2a = ( cosec a ) 2 2 cot a = ( tan a + cot a ) . 2 cot a sina ( 1 = - cos a ) 1 + cos a = ; sin a a ) ] 2 . COS a = ( 1 + cos a ) tana : α = = sin a 1 + cos a 1 - 1 . - cos a ; sin a cos a 1 + cos a tan a sec a + 1 sec a 1 ; = = 1 ...
... cosec 2a = ( cosec a ) 2 2 cot a = ( tan a + cot a ) . 2 cot a sina ( 1 = - cos a ) 1 + cos a = ; sin a a ) ] 2 . COS a = ( 1 + cos a ) tana : α = = sin a 1 + cos a 1 - 1 . - cos a ; sin a cos a 1 + cos a tan a sec a + 1 sec a 1 ; = = 1 ...
Σελίδα 128
... Cosec = - x + + 1.2.3 3.1 .... 5 3.1 .... 7 + + 5.1 .... 9 + + tanax + 5.7.73x9 1414477x11 3.1 .... 11 3.5.7.1 .... 13 • 11 X3 2x5 17x7 62x9 · 1382 x11 + + + + 3 3.5 32.5.7 3.5.7 3.52.7.11 + & c . δ + 21844x13 35.52.7.11.13 + 929569x15 ...
... Cosec = - x + + 1.2.3 3.1 .... 5 3.1 .... 7 + + 5.1 .... 9 + + tanax + 5.7.73x9 1414477x11 3.1 .... 11 3.5.7.1 .... 13 • 11 X3 2x5 17x7 62x9 · 1382 x11 + + + + 3 3.5 32.5.7 3.5.7 3.52.7.11 + & c . δ + 21844x13 35.52.7.11.13 + 929569x15 ...
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Άλλες εκδόσεις - Προβολή όλων
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A Synopsis of the Principal Formulae and Results of Pure Mathematics Charles Brooke Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a-log a.sin a₁ a² a² angle arcs Assume ax² axis ay² B.cos B.sin b₁ Biot Bour c₁ centre circle co-ordinates conjugate diameters const continued fraction converging fraction cosec cosine curve cx² determined differential coefficients e₁ ellipse formula functions G. G. A. Ch given equation hyperbola integral intersection Let the equation log Cot log Sin log Sin Blog logarithmic m₁ method modulus negative obtained parabola perpendicular plane possible root prime number primitive equation quadratic divisor quadratic equation quotients R₁ radius reduced remainders sin x sine solution square straight line substituting subtangent Suppose surface tana tangent ternary divisor ternary form theorem triangle u₁ unknown quantities values vers x₁ y-y₁ y₁ απ
Δημοφιλή αποσπάσματα
Σελίδα 112 - THEOREM. Every section of a sphere, made by a plane, is a circle.
Σελίδα 4 - Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Σελίδα 4 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Σελίδα 347 - Si, the formula assigned by Thomson to the mineral from Ireland, named " Anhydrous silicate of iron." Now, this slag had evidently been in a position favourable to the absorption of oxygen, namely, the...
Σελίδα 4 - To reduce a fraction to its lowest terms, divide both the numerator and denominator by their greatest common divisor.
Σελίδα 4 - The same quantity may be added to, or subtracted from, both sides of an equation. To...
Σελίδα 343 - The immutability, no less than the symmetry of its notation, (which should ever be guarded with a jealousy commensurate to its vital importance,) facilitates the translation of an expression into common language at any stage of an operation, - disburdens the memory of all the load of the previous steps, - and at the same time, affords it a considerable assistance in retaining the results.
Σελίδα 46 - These criteria were derived by a new transformation, namely the one which yields an equation whose roots are the squares of the differences of the roots of the given...
Σελίδα 161 - Straight line and circle. A straight line cannot cut a circle in more than two points. In fact, an unlimited straight line may (i) cut a circle in two points, eg AB or CD in fig.
Σελίδα 2 - Tiie square root of a quantity cannot be partly rational and partly a quadratic surd. If possible, let...