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 22
... natural sinės , tangents , & c . To glance , for a moment , at this application , in passing , suppose it were required to find the natural sines to each of the 10 first minutes of the quadrant . The radius of a circle being 1 , the ...
... natural sinės , tangents , & c . To glance , for a moment , at this application , in passing , suppose it were required to find the natural sines to each of the 10 first minutes of the quadrant . The radius of a circle being 1 , the ...
Página 32
... natural tangent is unity ; and the sum and the difference of the given sides are 72 and 8 respectively . Hence - 8 As 72 : 8 :: 1 : = 72 = · 1111111 = nat . tan . 6 ° 20 ′ . - Therefore 45 ° + 6 ° 20 ′ 51 ° 20 , and 45 ° 6 ° 20 ′ 38 ...
... natural tangent is unity ; and the sum and the difference of the given sides are 72 and 8 respectively . Hence - 8 As 72 : 8 :: 1 : = 72 = · 1111111 = nat . tan . 6 ° 20 ′ . - Therefore 45 ° + 6 ° 20 ′ 51 ° 20 , and 45 ° 6 ° 20 ′ 38 ...
Página 45
... the sum of all the natural cosines of every minute in the quadrant , gives sin 45 x cos 45 ° 0 ′ 30 ′′ sin 30 " 3437 2470374 . 23. Otherwise , in order to obtain expressions for the Analytical Investigation of Properties . 45.
... the sum of all the natural cosines of every minute in the quadrant , gives sin 45 x cos 45 ° 0 ′ 30 ′′ sin 30 " 3437 2470374 . 23. Otherwise , in order to obtain expressions for the Analytical Investigation of Properties . 45.
Página 50
... natural sine and cosine of such arc . C3 C5 sin c = c + 1.2.3 1.2.3.4.5 C7 1.2.3.4.5.6.7 + & c . Cosc = 1- + 1.2 * C4 1.2.3.4 C6 ( Y. ) + & c . 1.2.3.4.5.6 These series will converge rapidly when the arc is small 50 Plane Trigonometry .
... natural sine and cosine of such arc . C3 C5 sin c = c + 1.2.3 1.2.3.4.5 C7 1.2.3.4.5.6.7 + & c . Cosc = 1- + 1.2 * C4 1.2.3.4 C6 ( Y. ) + & c . 1.2.3.4.5.6 These series will converge rapidly when the arc is small 50 Plane Trigonometry .
Página 55
... natural sines and tangents , the subject need not be resumed here . We shall merely subjoin the values of a few of the sines , cosines , & c in surd expressions , and a few formulæ of verification , such as may readily be reduced to ...
... natural sines and tangents , the subject need not be resumed here . We shall merely subjoin the values of a few of the sines , cosines , & c in surd expressions , and a few formulæ of verification , such as may readily be reduced to ...
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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