Elements of Plane and Spherical Trigonometry: With Their Applications to Heights and Distances Projections of the Sphere, Dialling, Astronomy, the Solution of Equations, and Geodesic OperationsBaldwin, Cradock, and Joy, 1816 - 244 páginas |
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Página 1
... sections of three or more planes , form plane angles and triedral or polyedral surfaces , the determination of the magnitudes and relations of which is facilitated by re- B ference to the surface of a sphere . Hence mathemati-
... sections of three or more planes , form plane angles and triedral or polyedral surfaces , the determination of the magnitudes and relations of which is facilitated by re- B ference to the surface of a sphere . Hence mathemati-
Página 2
... Hence mathemati- cians have been led to attempt the solution of two general problems . I. Knowing three of the six things , whether angles or sides , which enter the constitution of a rectilinear tri- angle , to determine the other ...
... Hence mathemati- cians have been led to attempt the solution of two general problems . I. Knowing three of the six things , whether angles or sides , which enter the constitution of a rectilinear tri- angle , to determine the other ...
Página 7
... Hence , when the sine and radius are known , the cosine is determined by Euc . i . 47. The same may be said of the determination of the secant , from the tangent and radius , & c . & c . & c . ( G ) . Further , since CD : DB :: CA : AT ...
... Hence , when the sine and radius are known , the cosine is determined by Euc . i . 47. The same may be said of the determination of the secant , from the tangent and radius , & c . & c . & c . ( G ) . Further , since CD : DB :: CA : AT ...
Página 10
... Hence , the triangles BDA , LBA , are similar , and we have AD : AB :: AB : AL . PROP . II . L CD A 2. As radius : cosine of any arc :: twice the sine of that are the sine of double the arc . In the preceding figure CH is the cosine of ...
... Hence , the triangles BDA , LBA , are similar , and we have AD : AB :: AB : AL . PROP . II . L CD A 2. As radius : cosine of any arc :: twice the sine of that are the sine of double the arc . In the preceding figure CH is the cosine of ...
Página 11
... Hence BD DE = comp . AB , and AS = tan AB + Sec AB = tan AD = tan ( AB + 3 comp AB ) . PROP . V. 5. The chord of 60 ° is equal to the radius of the cir- cle ; the versed sine , and cosine of 60 ° are each equal to half the radius ; and ...
... Hence BD DE = comp . AB , and AS = tan AB + Sec AB = tan AD = tan ( AB + 3 comp AB ) . PROP . V. 5. The chord of 60 ° is equal to the radius of the cir- cle ; the versed sine , and cosine of 60 ° are each equal to half the radius ; and ...
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Términos y frases comunes
altitude angled spherical triangle azimuth base becomes bisect centre chap chord circle circle of latitude computation consequently cos² cosec cosine cotangent declination deduced determine dial diameter difference distance draw earth ecliptic equa equal equation Example find the rest formulæ given side h cos h half Hence horizon hour angle hypoth hypothenuse intersecting latitude logarithmic longitude measured meridian obliq oblique opposite angle parallel perpendicular plane angles plane triangle pole problem prop quadrant radius right angled spherical right angled triangle right ascension right line sec² secant sin A sin sin² sine solid angle sphere spherical excess spherical trigonometry star substyle sun's supposed surface tan² tangent theorem three angles three sides tion triangle ABC values versed sine versin vertical angle whence zenith