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 29
... give .... AB = 117 .... ACB = 2210 ABC 13430 AB ' = 282 .... ACB ' 112 ° = .... Computation . To find the angle в . AB'C = 4510 . As BC .... 117 ...... 2.0681859 To sin A 22 ° 37 ' .... .. So is AC .. 9.5849685 216 ...... 2 : 3344538 To ...
... give .... AB = 117 .... ACB = 2210 ABC 13430 AB ' = 282 .... ACB ' 112 ° = .... Computation . To find the angle в . AB'C = 4510 . As BC .... 117 ...... 2.0681859 To sin A 22 ° 37 ' .... .. So is AC .. 9.5849685 216 ...... 2 : 3344538 To ...
Página 31
... gives the greater of them ; and taken from half the sum , leaves the less * .- All the angles becoming known by this process , the third side is found by the rule in case 1 . Example I. 8. Let there be given in a plane triangle ABC , AC ...
... gives the greater of them ; and taken from half the sum , leaves the less * .- All the angles becoming known by this process , the third side is found by the rule in case 1 . Example I. 8. Let there be given in a plane triangle ABC , AC ...
Página 32
... gives the greater segment , and made less by it gives the less ; and thus , by means of the perpendicular from the ver- tical angle , divides the original triangle into two , each of which falls under the first case . 2d Method . Find ...
... gives the greater segment , and made less by it gives the less ; and thus , by means of the perpendicular from the ver- tical angle , divides the original triangle into two , each of which falls under the first case . 2d Method . Find ...
Página 44
... theorems : thus make 2 cos A = z + 2 - then 2 cos 2a = 2 ( 2 cos 2A − 1 ) = 2 [ } ( ≈ + 4 ) * − 1 ] = x2 + A like substitution in the forms for 2 cos 3A , 2 cos 4a , & o . will give 2 cos 3A 23 + 2 cos 4A = 24 4.4 Plane Trigonometry .
... theorems : thus make 2 cos A = z + 2 - then 2 cos 2a = 2 ( 2 cos 2A − 1 ) = 2 [ } ( ≈ + 4 ) * − 1 ] = x2 + A like substitution in the forms for 2 cos 3A , 2 cos 4a , & o . will give 2 cos 3A 23 + 2 cos 4A = 24 4.4 Plane Trigonometry .
Página 45
... determine 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.
... determine 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.
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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