Elements of Geometry and Trigonometry |
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Page 214
... sine of an arc is the perpendicular let fall from one extremity of the arc , on the diameter which passes through the other extremity . Thus , MP is the sine of the are AM , or of the angle ACM . The tangent of an arc is a line touching ...
... sine of an arc is the perpendicular let fall from one extremity of the arc , on the diameter which passes through the other extremity . Thus , MP is the sine of the are AM , or of the angle ACM . The tangent of an arc is a line touching ...
Page 215
... sine of an arc , is the part of the diameter inter- cepted between one extremity of the arc and the foot of the sine . Thus , AP is the versed sine of the arc AM , or the angle ACM . These four lines MP , AT , CT , AP , are dependent ...
... sine of an arc , is the part of the diameter inter- cepted between one extremity of the arc and the foot of the sine . Thus , AP is the versed sine of the arc AM , or the angle ACM . These four lines MP , AT , CT , AP , are dependent ...
Page 216
... sine and tangent of an arc S ' S M Q M B N P A N R E zero , are zero , and the cosine and secant of this same arc , are each equal to the radius . Hence if R represents the radius of the circle , we have sin 0 = 0 , tang 0 = 0 , cos 0 ...
... sine and tangent of an arc S ' S M Q M B N P A N R E zero , are zero , and the cosine and secant of this same arc , are each equal to the radius . Hence if R represents the radius of the circle , we have sin 0 = 0 , tang 0 = 0 , cos 0 ...
Page 217
... sine of an arc or of an angle is equal to the sine of the supplement of that arc or angle . 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 ...
... sine of an arc or of an angle is equal to the sine of the supplement of that arc or angle . 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 ...
Page 218
... sine AP is equal to the radius CA minus CP the cosine AM : that is , ver - sin AM = R - c Now when the arc AM be- comes AM ' the versed sine AP , becomes AP ' , that is equal to R + CP ' . But this expression cannot be derived from the ...
... sine AP is equal to the radius CA minus CP the cosine AM : that is , ver - sin AM = R - c Now when the arc AM be- comes AM ' the versed sine AP , becomes AP ' , that is equal to R + CP ' . But this expression cannot be derived from the ...
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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