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 arc AM , or of the angle ACM . The tangent of an arc is a line ...
... 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 arc AM , or of the angle ACM . The tangent of an arc is a line ...
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 T B P A N R V 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 = R ...
... sine and tangent of an arc S ' S M T B P A N R V 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 = R ...
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 - cos AM . 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 ...
... sine AP is equal to the radius CA minus CP the cosine AM : that is , ver - sin AM - R - cos AM . 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 ...
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Common terms and phrases
adjacent altitude angle ACB ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang 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 greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment side BC similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Popular passages
Page 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 18 - If two triangles have two sides of the one equal to two sides of the...
Page 233 - It is, indeed, evident, that the negative characteristic will always be one greater than the number of ciphers between the decimal point and the first significant figure.
Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Page 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 159 - S-o6c be the smaller : and suppose Aa to be the altitude of a prism, which having ABC for its base, is equal to their difference. Divide the altitude AT into equal parts Ax, xy, yz, &c. each less than Aa, and let k be one of those parts ; through the points of division...
Page 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.