Elements of Geometry and Trigonometry |
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Page 209
... equations we obtain , y = { a ± √1⁄2d2 — a2 = 8 or 6 , A B and x = { a = √√ď2— ↓ a2 = 6 or 8 . PROBLEM IV . Having given the base and perpendicular of a triangle , to find the side of an inscribed square . Let ABC be the triangle ...
... equations we obtain , y = { a ± √1⁄2d2 — a2 = 8 or 6 , A B and x = { a = √√ď2— ↓ a2 = 6 or 8 . PROBLEM IV . Having given the base and perpendicular of a triangle , to find the side of an inscribed square . Let ABC be the triangle ...
Page 217
... equation sin ( 90 ° + B ) = sin ( 90 ° —B ) , B being the arc DM or its equal DM ' . XI . The same arcs AM , AM ' , which are supplements of each other , and which have equal sines , have also equal co- sines CP , CP ; but it must be ...
... equation sin ( 90 ° + B ) = sin ( 90 ° —B ) , B being the arc DM or its equal DM ' . XI . The same arcs AM , AM ' , which are supplements of each other , and which have equal sines , have also equal co- sines CP , CP ; but it must be ...
Page 223
... equation sin 2A + cos 2A - R2 . furnish some others worthy of attention . First we have R2 + tang2 A = R2 + R2 sin2 A R2 ( sin2 A + cos2 A ) . cos 2A R4 cos A hence R2 + tang2 A sec2 A , a cos A formula which might be immediately ...
... equation sin 2A + cos 2A - R2 . furnish some others worthy of attention . First we have R2 + tang2 A = R2 + R2 sin2 A R2 ( sin2 A + cos2 A ) . cos 2A R4 cos A hence R2 + tang2 A sec2 A , a cos A formula which might be immediately ...
Page 225
... equations cos la + sin a = R2 , and cos a - sin2 ja R cos a , there results by adding and subtracting whence cosa R2 + R cos a , and sina R2 - R cos a : = sin a = √ ( } R2 — R cos a ) = √2R2 — 2R cos a . cos ļa = √ ( R2 + R cos a ) ...
... equations cos la + sin a = R2 , and cos a - sin2 ja R cos a , there results by adding and subtracting whence cosa R2 + R cos a , and sina R2 - R cos a : = sin a = √ ( } R2 — R cos a ) = √2R2 — 2R cos a . cos ļa = √ ( R2 + R cos a ) ...
Page 242
... equation c = 10 - b , we have c - 10 -- b : hence if we substitute for -b its value , we shall have ab = a + c - 10 , which agrees with the enunciation . When we wish the arithmetical compleinent of a logarithm , we may write it ...
... equation c = 10 - b , we have c - 10 -- b : hence if we substitute for -b its value , we shall have ab = a + c - 10 , which agrees with the enunciation . When we wish the arithmetical compleinent of a logarithm , we may write it ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex