Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 19
... cosine of an arc is the sine of the complement of the arc . Thus , NM is the cosine of AM , and NM ' is the cosine of AM ' . These lines are respectively equal to OP and OP ' . It is evident , from the equal triangles of the PLANE 19 ...
... cosine of an arc is the sine of the complement of the arc . Thus , NM is the cosine of AM , and NM ' is the cosine of AM ' . These lines are respectively equal to OP and OP ' . It is evident , from the equal triangles of the PLANE 19 ...
Page 20
... cosine of an arc is equal to the cosine of its supple- ment . 28. The tangent of an arc is the perpendicular to the radius at one extremity of the arc , limited by the prolon- gation of the diameter through the other extremity Thus , AT ...
... cosine of an arc is equal to the cosine of its supple- ment . 28. The tangent of an arc is the perpendicular to the radius at one extremity of the arc , limited by the prolon- gation of the diameter through the other extremity Thus , AT ...
Page 21
... cosine , tangent , and cotangent of the angle AOM , as well as of the arc AM . 30. It is often convenient to use some other radius than 1 ; in such case , the functions of the arc , to the radius 1 , may be reduced to corresponding ...
... cosine , tangent , and cotangent of the angle AOM , as well as of the arc AM . 30. It is often convenient to use some other radius than 1 ; in such case , the functions of the arc , to the radius 1 , may be reduced to corresponding ...
Page 22
... 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 , may be ...
... 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 , may be ...
Page 23
... cosine and the cotangent of an arc are , respectively , the sine and the tangent of the complement of that arc ( Arts . 26 and 28 ) : hence , the columns designated sine and tang , at the top of the page , are designated cosine and ...
... cosine and the cotangent of an arc are , respectively , the sine and the tangent of the complement of that arc ( Arts . 26 and 28 ) : hence , the columns designated sine and tang , at the top of the page , are designated cosine and ...
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Common terms and phrases
ABē 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