A Treatise on Plane and Spherical Trigonometry: Including the Construction of the Auxiliary Tables ; a Concise Tract on the Conic Sections, and the Principles of Spherical Projection |
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Page 32
... cosine , cotangent or cosecant of an arc , is the sine , tangent or secant of the complement of that arc . Thus BI , HK and CK , the sine , tangent and secant of HB , are termed the cosine , cotangent and cosecant of AB . 9. What an arc ...
... cosine , cotangent or cosecant of an arc , is the sine , tangent or secant of the complement of that arc . Thus BI , HK and CK , the sine , tangent and secant of HB , are termed the cosine , cotangent and cosecant of AB . 9. What an arc ...
Page 33
... cosine : rad . :: radius : sec't . 3. As CI : CB :: CH : CK , or as sine : radius :: radius : cosec . 4. As AG : CA ... cosine sine = tangent ; sine = cosine.tangent ; cosine tan 1 1 1 2 . secant ; cosine.secant = 1 ; cos = - cosine sec ...
... cosine : rad . :: radius : sec't . 3. As CI : CB :: CH : CK , or as sine : radius :: radius : cosec . 4. As AG : CA ... cosine sine = tangent ; sine = cosine.tangent ; cosine tan 1 1 1 2 . secant ; cosine.secant = 1 ; cos = - cosine sec ...
Page 34
... cosine 4. = cotan ; tan.cotan = 1 ; cotan tan sine 1 tan Hence , taking P and Q any arcs , tan P. cotan P = tan Q. , cotan Q ; consequently ( 16.6 ) , 5. sine = tan P tan Q :: cotan Q : cotan P. tangent tangent = secant ✓1 + tan2 ART ...
... cosine 4. = cotan ; tan.cotan = 1 ; cotan tan sine 1 tan Hence , taking P and Q any arcs , tan P. cotan P = tan Q. , cotan Q ; consequently ( 16.6 ) , 5. sine = tan P tan Q :: cotan Q : cotan P. tangent tangent = secant ✓1 + tan2 ART ...
Page 35
... cosine CM also negative , the tangent AG positive ; but the secant CG , not being produced through N , but in the opposite direction , is negative . If we take the arc more than three quadrants , but less than four , as AHDE ; the sine ...
... cosine CM also negative , the tangent AG positive ; but the secant CG , not being produced through N , but in the opposite direction , is negative . If we take the arc more than three quadrants , but less than four , as AHDE ; the sine ...
Page 37
... is to the base , so is radius to the cosine of the angle at the base ; and as the base is to the perpendicular , so is radius to the tangent of the angle at the base . D GI F C Let ABC be a triangle , right SECTION I. 37.
... is to the base , so is radius to the cosine of the angle at the base ; and as the base is to the perpendicular , so is radius to the tangent of the angle at the base . D GI F C Let ABC be a triangle , right SECTION I. 37.
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Common terms and phrases
ABDP adjacent angle angled spherical triangle base bisect C.cos c.sin centre circle Art common section Comp AC cone conical surface consequently construction cosec cosine cotan directrix distance EB² EC² ecliptic ED² ellipse equal equation given angle greater axis Hence hyperbola hypothenuse join latus rectum less circle Let ABC line of measures logarithms meet opposite ordinate original circle parabola parallel perpendicular plane of projection primitive circle projected circle projected pole projecting point Q. E. D. ART Q. E. D. Cor quadrant radius right angled spherical right ascension right line secant semicircle semitangent sides similar triangles sine sphere spherical angle tangent tangent of half touches the circle triangle ABC vertex vertical angle whence wherefore