## Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric Tables |

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**sine**A = 2 ;**sine**C = b h B The tangent of either of the acute angles is the quotient ob- tained by dividing the side opposite the angle by the adjacent side . Thus , tangent A = ; tangent C = b P The secant of either of the acute ... Page 5

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**sine**of that angle . Thus , C , D , is the**sine**of the angle СAC1 . For we have ( §8 ) defined the**sine**of this angle to be the quo- tient obtained by dividing C , D , by AC1 , which quotient be- comes C , D ,, since the divisor is the ... Page 7

... counted in the positive direction ( §9 ) is the arc , CD the

... counted in the positive direction ( §9 ) is the arc , CD the

**sine**, CH the cosine , BE the tangent , GF the cotangent , AE the secant , and AF the cosecant . The algebraic sines of these lines will be as follows § 11. ] 7 TRIGONOMETRY . Page 8

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**Sine**and cosecant , Cosine and secant , • Tangent and cotangent , In In In In 1st quad . 2d quad . 3d quad 4th quad + + + + + 1 + 1 § 12. By carefully inspecting the diagrams of § 11 , we see that denoting any arc when considered as ... Page 9

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**sine**and cosine of the sum and difference of two arcs . Let the angle BAC = a ; that is , let a denote the length of the arc which measures this angle ; also let the an- gle CAD be denoted by b ; then will BAD be denoted by a + b . also ...### Other editions - View all

### Common terms and phrases

a+b+c ACē altitude angles equal apothem bisect centre chord circ circumference cone consequently corresponding cosec Cosine Cotang cylinder decimal denote described diameter dicular distance divided draw drawn equation equivalent exterior angles feet figure formed frustum give given line greater half hence homologous sides hypotenuse inscribed circle intersection logarithm measure middle point multiplied number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right-angled triangle Scholium secant sector similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang tangent THEOREM three sides triangle ABC triangular prism vertex volume