Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 páginas |
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Página 7
... co - secant of an arch are the tan- gent and secant of the complement of that arch . Thus HK and CK are the co - tangent and co - secant of AB . 12. A trigonometrical canon is a table exhibiting the length of the sine ... AC : BC :: AE ED ( ...
... co - secant of an arch are the tan- gent and secant of the complement of that arch . Thus HK and CK are the co - tangent and co - secant of AB . 12. A trigonometrical canon is a table exhibiting the length of the sine ... AC : BC :: AE ED ( ...
Página 15
... co - tangent is known . 4. EF : EC ( CD ) :: CD : CH ; whence the co - secant is known . Hence it appears , 1. That the tangent is a fourth proportional to the co - sine ... AC :: CD ( AC ) ; DH ) , that the rectangle of the tangent and co ...
... co - tangent is known . 4. EF : EC ( CD ) :: CD : CH ; whence the co - secant is known . Hence it appears , 1. That the tangent is a fourth proportional to the co - sine ... AC :: CD ( AC ) ; DH ) , that the rectangle of the tangent and co ...
Página 16
... co - tang . Q : : tang . Q : tang . P ; or as co - tang . P : tang . Q : co - tang . Q : tang . P ( by 16. 6. ) . PROP . II . If there be three equidifferent arches AB , AC , AD ( fig . 10. ) , it will be , as radius is to the co - sine ...
... co - tang . Q : : tang . Q : tang . P ; or as co - tang . P : tang . Q : co - tang . Q : tang . P ( by 16. 6. ) . PROP . II . If there be three equidifferent arches AB , AC , AD ( fig . 10. ) , it will be , as radius is to the co - sine ...
Página 17
... 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 . From whence , and the preceding corollary ...
... 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 . From whence , and the preceding corollary ...
Página 28
... sine of the hy- pothenuse to the sine of the perpendicular ; and as radius to the co - sine of the angle at the base ... AC the hypothenuse , and BAC ( ar DAE = DE DOE ) the angle at the base : moreover , let CG be the sine of the ...
... sine of the hy- pothenuse to the sine of the perpendicular ; and as radius to the co - sine of the angle at the base ... AC the hypothenuse , and BAC ( ar DAE = DE DOE ) the angle at the base : moreover , let CG be the sine of the ...
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Términos y frases comunes
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
Pasajes populares
Página 69 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 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...
Página 25 - The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference...
Página 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.
Página 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...
Página 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.