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 2
... included between the radii which limit such arcs . 5. By means of this happy invention of intermediate quantities , the business of trigonometry is greatly facili- tated . For , by imagining a perpendicular let fall from the vertical ...
... included between the radii which limit such arcs . 5. By means of this happy invention of intermediate quantities , the business of trigonometry is greatly facili- tated . For , by imagining a perpendicular let fall from the vertical ...
Página 25
... included angle are given ; they , therefore , constitute a second case . The example marked 3 , has three sides given , but no angle ; this makes a third case : and the remaining variety in which the three angles are given , but no side ...
... included angle are given ; they , therefore , constitute a second case . The example marked 3 , has three sides given , but no angle ; this makes a third case : and the remaining variety in which the three angles are given , but no side ...
Página 30
... included angle are given . The solution is effected by means of chap . ii . prop . 15 . Take the given angle from 180 ° , the remainder will be the sum of the other two angles , Then say , -As the sum of the given sides , Is to their ...
... included angle are given . The solution is effected by means of chap . ii . prop . 15 . Take the given angle from 180 ° , the remainder will be the sum of the other two angles , Then say , -As the sum of the given sides , Is to their ...
Página 31
... included angle c = 80 ° ; to find the remaining angles and side . Leaving the construction to be effected by the pupil , I shall proceed to the computation . BC AC 990 , BC - AC 90 , 180 ° — c = 100 ° . ... 990 .. 2-9956352 90 ...
... included angle c = 80 ° ; to find the remaining angles and side . Leaving the construction to be effected by the pupil , I shall proceed to the computation . BC AC 990 , BC - AC 90 , 180 ° — c = 100 ° . ... 990 .. 2-9956352 90 ...
Página 32
... included angle 128 ° 4 ′ ; to find the rest . Ans . Angles 33 ° 35 ' , 18 ° 21 ' , side 2400 . CASE III . 10. When the three sides of a plane triangle are given , to find the angles . 1st Method . Assume the longest of the three sides ...
... included angle 128 ° 4 ′ ; to find the rest . Ans . Angles 33 ° 35 ' , 18 ° 21 ' , side 2400 . CASE III . 10. When the three sides of a plane triangle are given , to find the angles . 1st Method . Assume the longest of the three sides ...
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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