A Synopsis of the Principal Formulae and Results of Pure MathematicsJ. & J.J. Deighton, 1829 - 358 σελίδες |
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Σελίδα viii
... tangent plane DIFFERENTIAL CALCULUS . Differentiation of algebraic functions Differentiation of exponential functions • · Differentiation of functions of superior orders Development of functions . Implicit functions . 1 . 2 . 3-6 ...
... tangent plane DIFFERENTIAL CALCULUS . Differentiation of algebraic functions Differentiation of exponential functions • · Differentiation of functions of superior orders Development of functions . Implicit functions . 1 . 2 . 3-6 ...
Σελίδα 131
... tangents , then tan ( a , + a2 + & c . + a „ ) : = If a1 = a2 = & c . = an then 1 T1 - T , + T- & c . Ꭲ 3 1 - T + T- & c . n ( n − 1 ) ( n - 2 ) sin na = n ( cos a ) " -1 sin a—— ( cos a ) -3 ( sin a ) 3 + & c . 1. 2 3 • to ( ...
... tangents , then tan ( a , + a2 + & c . + a „ ) : = If a1 = a2 = & c . = an then 1 T1 - T , + T- & c . Ꭲ 3 1 - T + T- & c . n ( n − 1 ) ( n - 2 ) sin na = n ( cos a ) " -1 sin a—— ( cos a ) -3 ( sin a ) 3 + & c . 1. 2 3 • to ( ...
Σελίδα 135
... Tangents of multiple arcs . tan 2x = tan 3x = tan 4x = 2 tan x 1 — ( tan x ) 2 - 3 3 tan x- ( tan x ) 3 1-3 ( tana ) - 4 tan x 4 ( tan x ) 3 1-6 ( tan x ) 2 + ( tan x ) * ¿ If n is odd , N- m 2 sin nx = n Sm ( − 1 ) m + § ( n + 1 ) m ...
... Tangents of multiple arcs . tan 2x = tan 3x = tan 4x = 2 tan x 1 — ( tan x ) 2 - 3 3 tan x- ( tan x ) 3 1-3 ( tana ) - 4 tan x 4 ( tan x ) 3 1-6 ( tan x ) 2 + ( tan x ) * ¿ If n is odd , N- m 2 sin nx = n Sm ( − 1 ) m + § ( n + 1 ) m ...
Σελίδα 147
... the method of differences , which will be explained hereafter . Series for calculating the tangent and cotangent , inde- pendently of the sine and cosine . m π 2mn - tan n'2 n2 m2 m n SERIES FOR THE CONSTRUCTION OF TABLES . 147.
... the method of differences , which will be explained hereafter . Series for calculating the tangent and cotangent , inde- pendently of the sine and cosine . m π 2mn - tan n'2 n2 m2 m n SERIES FOR THE CONSTRUCTION OF TABLES . 147.
Σελίδα 149
... tangent . 1002 2276 28 log , sin x = log , x - + + + + + x10 34.52.7.11 2.37.53.72.11.13 3617x16 12.3 22.32.5 34.5.7 23.33.52.7 + 691x12 + 2x14 36.52.79.11.13 + & c . 2.3.5.7.11.13.17 & c . } 17x8 31a10 log , cos x = - + + SERIES FOR ...
... tangent . 1002 2276 28 log , sin x = log , x - + + + + + x10 34.52.7.11 2.37.53.72.11.13 3617x16 12.3 22.32.5 34.5.7 23.33.52.7 + 691x12 + 2x14 36.52.79.11.13 + & c . 2.3.5.7.11.13.17 & c . } 17x8 31a10 log , cos x = - + + SERIES FOR ...
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Άλλες εκδόσεις - Προβολή όλων
A Synopsis of the Principal Formulae and Results of Pure Mathematics ... Charles Brooke Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
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...