Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 7
... Sine of Half an Angle ,. Area of a Trapezoid , Area of a Quadrilateral , Area of a Polygon , 105 106 106 108 112 112 113 114 . Area of a Regular Polygon , To find the Circumference of a Circle , To find the Diameter of a Circle , To ...
... Sine of Half an Angle ,. Area of a Trapezoid , Area of a Quadrilateral , Area of a Polygon , 105 106 106 108 112 112 113 114 . Area of a Regular Polygon , To find the Circumference of a Circle , To find the Diameter of a Circle , To ...
Page 19
... sine of AM , and P'M ' is the sine of AM ' . If AM is equal to M'C , AM and AM ' will be supple- ments of each other ; and be- cause MM ' is parallel to AC , PM will be equal to P'M ' ( B. I. , P. XXIII . ) : hence , the sine of an arc ...
... sine of AM , and P'M ' is the sine of AM ' . If AM is equal to M'C , AM and AM ' will be supple- ments of each other ; and be- cause MM ' is parallel to AC , PM will be equal to P'M ' ( B. I. , P. XXIII . ) : hence , the sine of an arc ...
Page 20
... is the cotangent of the are AM ' . The sine , cosine , tangent , and cotangent of an arc , a , are , for convenience , written sin a , cos a , tan a , and cot a . These functions of an arc have been defined on the 20 TRIGONOMETRY . PLANE.
... is the cotangent of the are AM ' . The sine , cosine , tangent , and cotangent of an arc , a , are , for convenience , written sin a , cos a , tan a , and cot a . These functions of an arc have been defined on the 20 TRIGONOMETRY . PLANE.
Page 21
... sine , cosine , tangent , and cotangent of the angle AOM , as well as of the arc AM . 30. It is often convenient to ... sine ; A'M ' an arc described from 0 as a centre , with any ra- radius R , and and P'M ' its sine . Then , because ...
... sine , cosine , tangent , and cotangent of the angle AOM , as well as of the arc AM . 30. It is often convenient to ... sine ; A'M ' an arc described from 0 as a centre , with any ra- radius R , and and P'M ' its sine . Then , because ...
Page 22
... SINE , COSINE , TANGENT , OR COTANGENT , is the sine , cosine , tangent , or cotangent of an arc whose radius is 1 . A TABLE OF NATURAL SINES is a table by means of which the natural sine , cosine , tangent , or sotangent of any arc ...
... SINE , COSINE , TANGENT , OR COTANGENT , is the sine , cosine , tangent , or cotangent of an arc whose radius is 1 . A TABLE OF NATURAL SINES is a table by means of which the natural sine , cosine , tangent , or sotangent of any arc ...
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Common terms and phrases
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following