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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... of Differential Equa tions for the variations of triangles , are taken , simply with such alterations as fitted them better for general usefulness , from the Chevalier Delambre's admirable treatise on Astronomy A 3 PREFACE .
... of Differential Equa tions for the variations of triangles , are taken , simply with such alterations as fitted them better for general usefulness , from the Chevalier Delambre's admirable treatise on Astronomy A 3 PREFACE .
Página 37
... equa- tions , every other theorem and formula that is likely to be of use , is deduced with great facility by the mere re- duction and transformation of the original equations . This method serves greatly to shorten almost all trigo ...
... equa- tions , every other theorem and formula that is likely to be of use , is deduced with great facility by the mere re- duction and transformation of the original equations . This method serves greatly to shorten almost all trigo ...
Página 48
... from the solution of the equa- tions A2 + 1 = 0 , and в2 + 10 : so that , though these roots , A = ± √− 1 , and в = ± √ - 1 , are in- -- 5 dications of an absurd supposition , they still serve as 48 Plane Trigonometry .
... from the solution of the equa- tions A2 + 1 = 0 , and в2 + 10 : so that , though these roots , A = ± √− 1 , and в = ± √ - 1 , are in- -- 5 dications of an absurd supposition , they still serve as 48 Plane Trigonometry .
Página 51
... equa . s ) , there will result , 1 cot A cot B + cot B cot c + cot a cot c .... ( 5. ) If the sum of A , B , and C , instead of being 180 ° , were 360 ° , the same formulæ would result , as is evident from the consideration , that in ...
... equa . s ) , there will result , 1 cot A cot B + cot B cot c + cot a cot c .... ( 5. ) If the sum of A , B , and C , instead of being 180 ° , were 360 ° , the same formulæ would result , as is evident from the consideration , that in ...
Página 52
... equa . o . ) or , tan - A tan c + tan B tan c = 1 - tan A tan B ( by mul . ) tan A tan B + tan - A tan c + tan B tan c ( by trans . ) : or , 1 and cot A cot B cot ccot A + cot B + cot c ......... . ( 6 . ) → And this formula will ...
... equa . o . ) or , tan - A tan c + tan B tan c = 1 - tan A tan B ( by mul . ) tan A tan B + tan - A tan c + tan B tan c ( by trans . ) : or , 1 and cot A cot B cot ccot A + cot B + cot c ......... . ( 6 . ) → And this formula 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