A Synopsis of the Principal Formulae and Results of Pure MathematicsJ. & J.J. Deighton, 1829 - 358 σελίδες |
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Σελίδα vi
... angles of plane tri- angles . ib . 19 . Solution of right - angled plane triangles • 109 20 . Solution of oblique - angled plane triangles 110 • · 21 . 22 . 23 . 24 . General principles of spherical trigonometry Relations between the ...
... angles of plane tri- angles . ib . 19 . Solution of right - angled plane triangles • 109 20 . Solution of oblique - angled plane triangles 110 • · 21 . 22 . 23 . 24 . General principles of spherical trigonometry Relations between the ...
Σελίδα 107
... angles of plane Let A , B , C , be the angles , sin A α a , b , c , the sides subtending them ; s = = ( a + b + c ) . sin B sin C b C cos A = b2 + c2 - a2 2 bc 2 sin 4 = s ( s — a ) ( s — b ) ( s —c ) ] * . bc ( sin 14 ) 2 = ( s — b ) ...
... angles of plane Let A , B , C , be the angles , sin A α a , b , c , the sides subtending them ; s = = ( a + b + c ) . sin B sin C b C cos A = b2 + c2 - a2 2 bc 2 sin 4 = s ( s — a ) ( s — b ) ( s —c ) ] * . bc ( sin 14 ) 2 = ( s — b ) ...
Σελίδα 108
... B.b2 - ( a sin B ) 2 * Analogous formulæ may be obtained by substituting A , a , for B , b , and vice versa , in this , and several of the following formula . Right angled triangles : C , the right angle . 108 TRIGONOMETRY .
... B.b2 - ( a sin B ) 2 * Analogous formulæ may be obtained by substituting A , a , for B , b , and vice versa , in this , and several of the following formula . Right angled triangles : C , the right angle . 108 TRIGONOMETRY .
Σελίδα 109
Charles Brooke. Right angled triangles : C , the right angle . ( 19. ) [ 1 ] Given a , b : tan A = ᄒᄒ a log Tan 4 * = log r + log a log b . c = ( a2 + b2 ) * ; or C = b cos A ; log clog r + log blog Cos A. [ 2 ] Given a , c : b = ( c2 ...
Charles Brooke. Right angled triangles : C , the right angle . ( 19. ) [ 1 ] Given a , b : tan A = ᄒᄒ a log Tan 4 * = log r + log a log b . c = ( a2 + b2 ) * ; or C = b cos A ; log clog r + log blog Cos A. [ 2 ] Given a , c : b = ( c2 ...
Σελίδα 110
... angle . C = 180 ° - ( 4+ B ) . c = b sin C sin B log clog blog Sin C - log Sin B : or c = a cos B + b2— ( a sin B ) o | 3 . [ 3 ] Given C , a , b ; a- .b tan ( 4 - B ) = tan ( A + B ) ; a + b log Tan 1⁄2 ( A – B ) = log ( a − b ) — log ( a ...
... angle . C = 180 ° - ( 4+ B ) . c = b sin C sin B log clog blog Sin C - log Sin B : or c = a cos B + b2— ( a sin B ) o | 3 . [ 3 ] Given C , a , b ; a- .b tan ( 4 - B ) = tan ( A + B ) ; a + b log Tan 1⁄2 ( A – B ) = log ( a − b ) — log ( a ...
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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...