## Elements of Geometry and Trigonometry |

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Page 38

... then will M ± N : M :: P ± Q : P . For , from the first proportion , we have MxQ = NxP , or NxP = MxQ ; Add each of the members of the last

... then will M ± N : M :: P ± Q : P . For , from the first proportion , we have MxQ = NxP , or NxP = MxQ ; Add each of the members of the last

**equation**to , or subtract it from M.P , and we shall have , M.P ± N.P = M.P ± M.Q ; or ( MN ) ... Page 128

Taking the first

Taking the first

**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 ... Page 211

The arc or angle A has for its supplement 180 ° -A : hence generally , we have sin A sin ( 180 ° -A . ) The same property might also be expressed by the

The arc or angle A has for its supplement 180 ° -A : hence generally , we have sin A sin ( 180 ° -A . ) The same property might also be expressed by the

**equation**sin ( 90 ° + B ) = sin ( 90 ° -B ) , B being the arc DM or its equal DM ' ... Page 217

The formulas of the preceding Article , combined with each other and with the

The formulas of the preceding Article , combined with each other and with the

**equation**sin 2A + cos 2A = R2 , furnish some others worthy of attention . First we have R2 + tang2 AR2 + R1 R2 ( sin2 A + cos2 A ) . cos 2A cos A cos2 A R2 ... Page 236

But from the

But from the

**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 ...### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole