Elements of Geometry and Trigonometry |
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Page 38
... equation to , or subtract it from M.P , and we shall have , M.P + N.P - M.P + M.Q ; or ( M ± N ) × P ( P ± Q ) × M. But M ± N and P , may be considered the two extremes , and P + Q and M , the two means of a proportion : hence , M ± N ...
... equation to , or subtract it from M.P , and we shall have , M.P + N.P - M.P + M.Q ; or ( M ± N ) × P ( P ± Q ) × M. But M ± N and P , may be considered the two extremes , and P + Q and M , the two means of a proportion : hence , M ± N ...
Page 128
... equation from the second , and observing that the triangles APC , APB , which are both right angled at P , give AC - PC - AP2 , and AB2 - PB2 = AP2 ; we shall have AP2 + AP2-2AQ2 - 2PQ2 . Therefore , by taking the halves of both , we ...
... equation from the second , and observing that the triangles APC , APB , which are both right angled at P , give AC - PC - AP2 , and AB2 - PB2 = AP2 ; we shall have AP2 + AP2-2AQ2 - 2PQ2 . Therefore , by taking the halves of both , we ...
Page 211
... 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 217
... equation sin A + cos 2A = R2 , furnish some others worthy of attention . First we have R2 + tang2 A = R2 + Ꭱ cos A R2 sin2 A - ; hence R2 + tang ? A cos2 A sec2 A , a R2 ( sin3 A + cos2 A ) _____ R1 cos 2A formula which might be ...
... equation sin A + cos 2A = R2 , furnish some others worthy of attention . First we have R2 + tang2 A = R2 + Ꭱ cos A R2 sin2 A - ; hence R2 + tang ? A cos2 A sec2 A , a R2 ( sin3 A + cos2 A ) _____ R1 cos 2A formula which might be ...
Page 236
... equation c = 10 - b , we have c - 10 -- b : hence if we substitute for b its value , we shall have a - b = a + c - 10 , which agrees with the enunciation . When we wish the arithmetical complement 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 a - b = a + c - 10 , which agrees with the enunciation . When we wish the arithmetical complement 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 centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines 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 sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex