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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... formula , the formula will be rendered homogeneous . TABLE OF NATURAL SINES . 31. A NATURAL SINE , PLANE 21 TRIGONOMETRY . Plane Trigonometry Defined, 17 Functions of the Arc, 18-22.
... formula , the formula will be rendered homogeneous . TABLE OF NATURAL SINES . 31. A NATURAL SINE , PLANE 21 TRIGONOMETRY . Plane Trigonometry Defined, 17 Functions of the Arc, 18-22.
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... formulas into ordinary language , we have the following PRINCIPLES . 1. The perpendicular of any right - angled triangle is equa to the hypothenuse into the sine of the angle at the base . 2. The base is equal to the hypothenuse into ...
... formulas into ordinary language , we have the following PRINCIPLES . 1. The perpendicular of any right - angled triangle is equa to the hypothenuse into the sine of the angle at the base . 2. The base is equal to the hypothenuse into ...
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... Formulas ( 7 ) and ( 8 ) . α B 1. Given a = 749 , B , b , and C. EXAMPLES . and C 47 ° 31 ' 10 " ; required OPERATION . B = 90 ° 47 ° 03 ' 10 " = 42 ° 56 ' 50 " . ― Applying logarithms to Formula ( 7 ) , remembering that the logarithm ...
... Formulas ( 7 ) and ( 8 ) . α B 1. Given a = 749 , B , b , and C. EXAMPLES . and C 47 ° 31 ' 10 " ; required OPERATION . B = 90 ° 47 ° 03 ' 10 " = 42 ° 56 ' 50 " . ― Applying logarithms to Formula ( 7 ) , remembering that the logarithm ...
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... Formula ( 8 ) , we have , log a log b = log a log cos C ( 749 ) log cos C ( 47 ° 03 ′ 10 ′′ ) 10 ; • 2.874481 9.833354 log b • 2.707835 b = 510.31 1 Ans . B = 42 ° 56 ′ 50 ′′ , b = 510.31 , and c = 548.255 2. Given α = 439 , and B = 27 ...
... Formula ( 8 ) , we have , log a log b = log a log cos C ( 749 ) log cos C ( 47 ° 03 ′ 10 ′′ ) 10 ; • 2.874481 9.833354 log b • 2.707835 b = 510.31 1 Ans . B = 42 ° 56 ′ 50 ′′ , b = 510.31 , and c = 548.255 2. Given α = 439 , and B = 27 ...
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... Formula ( 7 ) , and the unknown side about the right angle , by Formula ( 8 ) . EXAMPLES . 1. Given c56.293 , and C = 54 ° 27 ′ 39 ′′ , to find B , a , and b . B = 90 ° - OPERATION . 54 ° 27 ' 39 " = 35 ° 32 ′ 21 ′′ . Applying ...
... Formula ( 7 ) , and the unknown side about the right angle , by Formula ( 8 ) . EXAMPLES . 1. Given c56.293 , and C = 54 ° 27 ′ 39 ′′ , to find B , a , and b . B = 90 ° - OPERATION . 54 ° 27 ' 39 " = 35 ° 32 ′ 21 ′′ . Applying ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence