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 26
... former from 180 ° . Note 1. Since sines are lines , there can be no impro- priety in comparing them with the sides of triangles ; and the rule is better remembered by young mathema- ticians , than when the sines and sides are compared ...
... former from 180 ° . Note 1. Since sines are lines , there can be no impro- priety in comparing them with the sides of triangles ; and the rule is better remembered by young mathema- ticians , than when the sines and sides are compared ...
Página 27
... former , and to make with BA an angle of 22 ° 37 ' . The intersection c , of these two lines determines the triangle ; and the sides AC , BC , measured upon the scale of equal parts . from which AB was laid down , are found to be 159 ...
... former , and to make with BA an angle of 22 ° 37 ' . The intersection c , of these two lines determines the triangle ; and the sides AC , BC , measured upon the scale of equal parts . from which AB was laid down , are found to be 159 ...
Página 29
... former proportion , and say , As sin A ..... 22 ° 37 ′ .... 9.5849685 To BC .. ... . . 117 . . . . . . . . So is sin ACB ' .. 112 ° 9 ′ .... 2.0681859 9.9667048 TO AB ' ...... 281 · 79 ...... 2 · 4499222 6. Remark . The ambiguity in ...
... former proportion , and say , As sin A ..... 22 ° 37 ′ .... 9.5849685 To BC .. ... . . 117 . . . . . . . . So is sin ACB ' .. 112 ° 9 ′ .... 2.0681859 9.9667048 TO AB ' ...... 281 · 79 ...... 2 · 4499222 6. Remark . The ambiguity in ...
Página 58
... former borrowing 20 for radius squared , gives 19.9071690 . The latter log . by 2 for the √ , gives 9.9535845 . This , by the tables , is nearly tan 41 ° 56 ′ , and by the formula it is tan A ; therefore A 41 ° 56 ' , and the required ...
... former borrowing 20 for radius squared , gives 19.9071690 . The latter log . by 2 for the √ , gives 9.9535845 . This , by the tables , is nearly tan 41 ° 56 ′ , and by the formula it is tan A ; therefore A 41 ° 56 ' , and the required ...
Página 61
... former usually designated by the term alti- metry , the latter by that of longimetry . It is not in- tended to treat them separately here , nor to treat them jointly much in detail ; but simply to present and solve a selection of such ...
... former usually designated by the term alti- metry , the latter by that of longimetry . It is not in- tended to treat them separately here , nor to treat them jointly much in detail ; but simply to present and solve a selection of such ...
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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