Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 277
... supplemental triangle , and the angles of each of its polar triangles . 2. Find the area of a tri - rectangular triangle , on a sphere whose diameter is 8 feet . 3. Find the area of a tri - rectangular triangle , on a sphere whose ...
... supplemental triangle , and the angles of each of its polar triangles . 2. Find the area of a tri - rectangular triangle , on a sphere whose diameter is 8 feet . 3. Find the area of a tri - rectangular triangle , on a sphere whose ...
Page 18
... supplement of an arc is the difference between that arc and 180 ° . The supplement of an angle is the difference between that angle and two right angles . Thus , EC is the supplement of AE , and FC the supple- ment of AF . In like ...
... supplement of an arc is the difference between that arc and 180 ° . The supplement of an angle is the difference between that angle and two right angles . Thus , EC is the supplement of AE , and FC the supple- ment of AF . In like ...
Page 19
... supplements of each other ; and because MM ' is parallel to AC , PM is equal to P'M ' ( B. I. , P. XXIII . ) : hence , the sine of an arc is equal to the sine of its supplement . T " B N a 10 D P MT A T ' 27. The cosine of an arc is the ...
... supplements of each other ; and because MM ' is parallel to AC , PM is equal to P'M ' ( B. I. , P. XXIII . ) : hence , the sine of an arc is equal to the sine of its supplement . T " B N a 10 D P MT A T ' 27. The cosine of an arc is the ...
Page 20
... supplement . 29. The cotangent of an arc is the tangent of its complement , " complement tangent " being contracted ... supplement . an When it is stated that the cotangent , tangent , & c . , of arc are equal respectively to the ...
... supplement . 29. The cotangent of an arc is the tangent of its complement , " complement tangent " being contracted ... supplement . an When it is stated that the cotangent , tangent , & c . , of arc are equal respectively to the ...
Page 25
... supplement ( Arts . 26 and 28 ) . 3. Find the logarithmic tangent of 118 ° 18 ′ 25 ′′ . · • Given arc Supplement log tan 61 ° 41 ' • • Tabular difference No. of seconds Operation . 5.04 35 180 ° 118 ° 18 ' 25 " 61 ° 41 ′ 35 ...
... supplement ( Arts . 26 and 28 ) . 3. Find the logarithmic tangent of 118 ° 18 ′ 25 ′′ . · • Given arc Supplement log tan 61 ° 41 ' • • Tabular difference No. of seconds Operation . 5.04 35 180 ° 118 ° 18 ' 25 " 61 ° 41 ′ 35 ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence