Elements of Geometry and TrigonometryWiley & Long, 1836 - 359 σελίδες |
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Σελίδα 215
... cotangent , and cosecant , of the arc AM and are thus designated : MQ = cos AM , or coş ACM , DS - cot AM , or cot ACM , CS cosec AM , or cosec ACM . In general , A being any arc or angle , we have cos A = sin ( 90 ° —A ) ,, cot A tang ...
... cotangent , and cosecant , of the arc AM and are thus designated : MQ = cos AM , or coş ACM , DS - cot AM , or cot ACM , CS cosec AM , or cosec ACM . In general , A being any arc or angle , we have cos A = sin ( 90 ° —A ) ,, cot A tang ...
Σελίδα 216
... cotangent , and the cosecant , diminish . When the point M is at the middle of AD , or when the arc AM is 45 ° , in which case it is equal to its complement MD , the sine MP is equal to the cosine MQ or CP ; and the trian- gle CMP ...
... cotangent , and the cosecant , diminish . When the point M is at the middle of AD , or when the arc AM is 45 ° , in which case it is equal to its complement MD , the sine MP is equal to the cosine MQ or CP ; and the trian- gle CMP ...
Σελίδα 219
... cotangent is infinite ; when at E it is zero : hence , cot 180 ° ∞ ; cot 270 ° = 0 . Let q stand for a quadrant ; then the following table will show the signs of the trigonometrical lines in the different quadrants . Sine Cosine ...
... cotangent is infinite ; when at E it is zero : hence , cot 180 ° ∞ ; cot 270 ° = 0 . Let q stand for a quadrant ; then the following table will show the signs of the trigonometrical lines in the different quadrants . Sine Cosine ...
Σελίδα 222
... cotangent , and cosecant of the same arc . The triangles CPM , CAT , CDS , being similar , we have the proportions : CP : PM :: CA : AT ; or cos A : sin A :: R : tang A : - CP : CM :: CA : CT ; or cos A : R :: R : sec A = PM : CP :: CD ...
... cotangent , and cosecant of the same arc . The triangles CPM , CAT , CDS , being similar , we have the proportions : CP : PM :: CA : AT ; or cos A : sin A :: R : tang A : - CP : CM :: CA : CT ; or cos A : R :: R : sec A = PM : CP :: CD ...
Σελίδα 223
... cotangent to R.Cos COS sin it follows that tangent and cotangent will both be positive when the sine and cosine have like algebraic signs , and both negative , when the sine and cosine have contrary algebraic signs . Hence , the tangent ...
... cotangent to R.Cos COS sin it follows that tangent and cotangent will both be positive when the sine and cosine have like algebraic signs , and both negative , when the sine and cosine have contrary algebraic signs . Hence , the tangent ...
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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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 18 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Σελίδα 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 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'.
Σελίδα 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...
Σελίδα 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.