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 6
... preceding diagram , the circular sector CAB is less than the triangle CAT , the former being con- tained within the latter . That is , by the rules for men- suration of surfaces , ¿ CA × arc AB is less than ¿ CA × tan AT ; whence ...
... preceding diagram , the circular sector CAB is less than the triangle CAT , the former being con- tained within the latter . That is , by the rules for men- suration of surfaces , ¿ CA × arc AB is less than ¿ CA × tan AT ; whence ...
Página 7
... preceding . 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 ...
... preceding . 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 ...
Página 10
... preceding figure CH is the cosine of the arc BN , AB is twice the sine вH of that arc , and BD is the sine of AB the double arc . From the similar triangles ACH , ABD , we have AC : CH :: AB : BD . PROP . III . 3. The secant of any arc ...
... preceding figure CH is the cosine of the arc BN , AB is twice the sine вH of that arc , and BD is the sine of AB the double arc . From the similar triangles ACH , ABD , we have AC : CH :: AB : BD . PROP . III . 3. The secant of any arc ...
Página 13
... preceding rectangles may , therefore , be expressed thus , CB . E'K ' BH . CF , and CB . D'E ′ = CH . DF , of which the difference is CB . D'K ' BH.CF which is the second part of the proposition . --- CH . DF , Cor . If the two arcs ...
... preceding rectangles may , therefore , be expressed thus , CB . E'K ' BH . CF , and CB . D'E ′ = CH . DF , of which the difference is CB . D'K ' BH.CF which is the second part of the proposition . --- CH . DF , Cor . If the two arcs ...
Página 16
... preceding proportions , we have FG ( DK + D'K ' ) = CF.BH CB , and DE = ( DK - D'K ' ) = Therefore DK + D'K ' = 2CF.BH CB and DK · D'K ' = ― DF.CH CB 2DF.CA - CB Cor . 2. Hence , if the mean arc AB be one of 60 ° , its cosine CH , will ...
... preceding proportions , we have FG ( DK + D'K ' ) = CF.BH CB , and DE = ( DK - D'K ' ) = Therefore DK + D'K ' = 2CF.BH CB and DK · D'K ' = ― DF.CH CB 2DF.CA - CB Cor . 2. Hence , if the mean arc AB be one of 60 ° , its cosine CH , will ...
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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