Elements of Geometry and Trigonometry |
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Page 237
... . comp . log . 0.000000 To tang . C 16 ° 15 ′ 37 ′′ So is side b 240 9.464889 2.380211 To side c 70.0003 # 1.845100 Or the side c might be found from the equation PLANE TRIGONOMETRY . 237 Solution of Right angled Triangles,
... . comp . log . 0.000000 To tang . C 16 ° 15 ′ 37 ′′ So is side b 240 9.464889 2.380211 To side c 70.0003 # 1.845100 Or the side c might be found from the equation PLANE TRIGONOMETRY . 237 Solution of Right angled Triangles,
Page 238
Adrien Marie Legendre Charles Davies. Or the side c might be found from the equation For , hence , a2 = b2 + c2 . c2 = a2_b2 = ( a + b ) × ( a — b ) : 2 log . c = log . ( a + b ) + log . ( a - b ) , or log . c = log . ( a + b ) + log ...
Adrien Marie Legendre Charles Davies. Or the side c might be found from the equation For , hence , a2 = b2 + c2 . c2 = a2_b2 = ( a + b ) × ( a — b ) : 2 log . c = log . ( a + b ) + log . ( a - b ) , or log . c = log . ( a + b ) + log ...
Page 246
... R × AD = AK sin C. Hence , R2 × AD = AO sin b sin C , by substituting for AK its value taken from the first equation . In like manner the triangles AHO , ADH , right 246 SPHERICAL TRIGONOMETRY . SPHERICAL TRIGONOMETRY First principles,
... R × AD = AK sin C. Hence , R2 × AD = AO sin b sin C , by substituting for AK its value taken from the first equation . In like manner the triangles AHO , ADH , right 246 SPHERICAL TRIGONOMETRY . SPHERICAL TRIGONOMETRY First principles,
Page 247
... b cos C R2 and 9 : therefore R2 OA sin a sin b cos C OA cos a cos b AO sin a sin b cos C R + R2 R2 cos c = R cos a cos b + sin a sin b cos C. or Similar equations may be deduced for each of the other SPHERICAL TRIGONOMETRY . 247.
... b cos C R2 and 9 : therefore R2 OA sin a sin b cos C OA cos a cos b AO sin a sin b cos C R + R2 R2 cos c = R cos a cos b + sin a sin b cos C. or Similar equations may be deduced for each of the other SPHERICAL TRIGONOMETRY . 247.
Page 248
... equation , we have cos A R2 cos a - R cos b cos c sin b sin c Adding R to each member , we have R + cos A = R2 cos a ... equation from 248 SPHERICAL TRIGONOMETRY .
... equation , we have cos A R2 cos a - R cos b cos c sin b sin c Adding R to each member , we have R + cos A = R2 cos a ... equation from 248 SPHERICAL TRIGONOMETRY .
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex