Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 |
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Strona 10
... COROLLARY . Hence , in two triangles ABC and Ab¤ , having two sides equal , each to each , it will be ( by equality ) , as tang . Abc + ACb : tang . Abc - ACh 2 ABC + ACB : : tang . : 2 2 tang . ABC ACB - 2 But , if CA be supposed a ...
... COROLLARY . Hence , in two triangles ABC and Ab¤ , having two sides equal , each to each , it will be ( by equality ) , as tang . Abc + ACb : tang . Abc - ACh 2 ABC + ACB : : tang . : 2 2 tang . ABC ACB - 2 But , if CA be supposed a ...
Strona 16
... their dif- ference . But , because of the similar triangles OCF , Omn , and Dom , It will be SOC : Om :: CF : mn OC : Dm :: FO : Dv 2. E. D. COROLLARY I. Because of the foregoing proportions , we have 16 CONSTRUCTION OF THE TABLE.
... their dif- ference . But , because of the similar triangles OCF , Omn , and Dom , It will be SOC : Om :: CF : mn OC : Dm :: FO : Dv 2. E. D. COROLLARY I. Because of the foregoing proportions , we have 16 CONSTRUCTION OF THE TABLE.
Strona 17
... COROLLARY II . = Hence , if the mean arch AC be supposed that of 60 ° ; then , OF being the co - sine of 60 ° , sine 30 ° chord of 60 ° OC , it is manifest that DGBE will , in this case , be barely Dm ; and consequently DG Dm + BE ...
... COROLLARY II . = Hence , if the mean arch AC be supposed that of 60 ° ; then , OF being the co - sine of 60 ° , sine 30 ° chord of 60 ° OC , it is manifest that DGBE will , in this case , be barely Dm ; and consequently DG Dm + BE ...
Strona 26
... , and thereby form two spherical triangles ABC and FCE , the latter of the tri- angles so formed is said to be the complement of the former ; and vice versa . COROLLARIES . 1. It is manifest ( from Def . SPHERICAL TRIGONOMETRY. ...
... , and thereby form two spherical triangles ABC and FCE , the latter of the tri- angles so formed is said to be the complement of the former ; and vice versa . COROLLARIES . 1. It is manifest ( from Def . SPHERICAL TRIGONOMETRY. ...
Strona 27
With the Construction and Application of Logarithms Thomas Simpson. COROLLARIES . 1. It is manifest ( from Def . 1. ) that the section of two great circles ( as it passes through the centre ) will be a diame- ter of the sphere ; and ...
With the Construction and Application of Logarithms Thomas Simpson. COROLLARIES . 1. It is manifest ( from Def . 1. ) that the section of two great circles ( as it passes through the centre ) will be a diame- ter of the sphere ; and ...
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ABDP AC by Theor adjacent angle arch bisecting chord circle passing co-sine AC co-tangent of half common logarithm common section Comp describe the circle E. D. COROLLARY E. D. PROP equal to half extremes gent given angle given circle given point half the difference half the sum half the vertical Hence hyperbolic logarithm hypothenuse inclination intersect leg BC line of measures original circle parallel perpendicular plane of projection plane triangle ABC primitive PROB produced projected circle projected pole projecting point radius rectangle right line right-angled spherical triangle SCHOLIUM secant semi-tangents sides similar triangles sine 59 sine AC sine of half sphere spherical angle SPHERICAL PROJECTIONS spherical triangle ABC sum or difference tangent of half THEOREM THOMAS SIMPSON triangle ABC fig versed sine vertical angle whence
Popularne fragmenty
Strona 69 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Strona 79 - ... projection is that of a meridian, or one parallel thereto, and the point of sight is assumed at an infinite distance on a line normal to the plane of projection and passing through the center of the sphere. A circle which is parallel to the plane of projection is projected into an equal circle, a circle perpendicular to the plane of projection is projected into a right line equal in length to the diameter of the projected circle; a circle in any other position is projected into an ellipse, whose...
Strona 25 - The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference...
Strona 28 - The rectangle of the radius, and sine of the middle part, is equal to the rectangle of the tangents of the two EXTREMES CONJUNCT, and to that of the cosines of the two EXTREMES DISJUNCT.
Strona 7 - 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...
Strona 28 - In a right angled spherical triangle, the rectangle under the radius and the sine of the middle part, is equal to the rectangle under the tangents of the adjacent parts ; or', to the rectangle under the cosines of the opposite parts.