Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsJ. Nourse, 1748 - 77 sider |
Inni boken
Resultat 6-10 av 26
Side 25
... Sin . DC :: Sin . D : Sin . AC . COROLLARY 2 . It follows , moreover , that , in right - angled fpherical Triangles ABC , DBC , having one Leg BC common , the Tangents of the Hypothenuses are to each other , inversely , as the Co ...
... Sin . DC :: Sin . D : Sin . AC . COROLLARY 2 . It follows , moreover , that , in right - angled fpherical Triangles ABC , DBC , having one Leg BC common , the Tangents of the Hypothenuses are to each other , inversely , as the Co ...
Side 26
... Sine F :: Sine CF : Sine CE ; that is , Radius Co - fine BA :: Co - fine CB : Co fine AC ( See Cor . 4. p . 23. ) 2. E. D. : COROLLAR Y. B Hence , if two right- angled spherical Trian- gles ABC , CBD have the fame Perpendicular D BC , the ...
... Sine F :: Sine CF : Sine CE ; that is , Radius Co - fine BA :: Co - fine CB : Co fine AC ( See Cor . 4. p . 23. ) 2. E. D. : COROLLAR Y. B Hence , if two right- angled spherical Trian- gles ABC , CBD have the fame Perpendicular D BC , the ...
Side 28
... Sine DB :: Tang . D : Tang . BC we fhall ( by reafoning as in Cor . 1. Theor . 1. ) have Sine AB : Sine DB :: Tang . D : Tang . A. THEOREM V. In any right - angled Spherical Triangle it will be , as Radius is to the Co ... AC :: Tang . C : Co ...
... Sine DB :: Tang . D : Tang . BC we fhall ( by reafoning as in Cor . 1. Theor . 1. ) have Sine AB : Sine DB :: Tang . D : Tang . A. THEOREM V. In any right - angled Spherical Triangle it will be , as Radius is to the Co ... AC :: Tang . C : Co ...
Side 32
... AC and one Angle A The oppo- fite Leg BC The Hyp . 2 AC and one Angle A Solution As Radius : Sine Hyp . AC :: Sine A : Sine BC ( by the for- mer Part of Theor . 1. ) The adja - As Radius : Co - fine of A :: Tang . AC : Tang . AB ( by ...
... AC and one Angle A The oppo- fite Leg BC The Hyp . 2 AC and one Angle A Solution As Radius : Sine Hyp . AC :: Sine A : Sine BC ( by the for- mer Part of Theor . 1. ) The adja - As Radius : Co - fine of A :: Tang . AC : Tang . AB ( by ...
Side 33
... Sine A :: Co- fite Angle fine of AB : Co - fine of C ( by C Theor . 3. ) The Hyp . As Co - fine of A : Radius :: AC Tang . AB : Tang . AC ( by ) Theor . I. ) The other As Tang . A : Tang BC :: Leg AB Radius : Sine AB ( by Theor . 4 ...
... Sine A :: Co- fite Angle fine of AB : Co - fine of C ( by C Theor . 3. ) The Hyp . As Co - fine of A : Radius :: AC Tang . AB : Tang . AC ( by ) Theor . I. ) The other As Tang . A : Tang BC :: Leg AB Radius : Sine AB ( by Theor . 4 ...
Andre utgaver - Vis alle
Trigonometry, Plane and Spherical;: With the Construction and Application of ... Thomas Simpson Uten tilgangsbegrensning - 1765 |
Trigonometry, Plane and Spherical: With the Construction and Application of ... Thomas Simpson Uten tilgangsbegrensning - 1765 |
Trigonometry, Plane and Spherical: With the Construction and Application of ... Thomas Simpson Uten tilgangsbegrensning - 1765 |
Vanlige uttrykk og setninger
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Populære avsnitt
Side 1 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees; and each degree into 60 minutes, each minute into 60 seconds, and so on.
Side 3 - Canon, is a table showing the length of the sine, tangent, and secant, to every degree and minute of the quadrant, with respect to the radius, which is expressed by unity or 1, with any number of ciphers.
Side 6 - In every plane triangle, it will be, as the sum of any two sides is to their difference...
Side 41 - The sum of the logarithms of any two numbers is equal to the logarithm of their product. Therefore, the addition of logarithms corresponds to the multiplication of their numbers.
Side 13 - If the sine of the mean of three equidifferent arcs' dius being unity) be multiplied into twice the cosine of the common difference, and the sine of either extreme be deducted from the product, the remainder will be the sine of the other extreme. (B.) The sine of any arc above 60°, is equal to the sine of another arc as much below 60°, together with the sine of its excess above 60°. Remark. From this latter proposition, the sines below 60° being known, those of arcs above 60° are determinable...
Side 31 - ... is the tangent of half the vertical angle to the tangent of the angle which the perpendicular CD makes with the line CF, bisecting the vertical angle.
Side 73 - BD, is to their Difference ; fo is the Tangent of half the Sum of the Angles BDC and BCD, to the Tangent of half their Difference.
Side 28 - As the sum of the sines of two unequal arches is to their difference, so is the tangent of half the sum of those arches to the tangent of half their difference : and as the sum...
Side 68 - In any right lined triangle, having two unequal sides ; as the less of those sides is to the greater, so is radius to the tangent of an angle ; and as radius is to the tangent of the excess of...