Elements of Geometry and Trigonometry |
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Page 6
Division of the Circumference , 207 General Ideas relating to the Trigonometrical Lines , 208 Theorems and Formulas relating to the Sines , Cosines , Tan- gents , & c . · 215 Construction and Description of the Tables , 223 Description ...
Division of the Circumference , 207 General Ideas relating to the Trigonometrical Lines , 208 Theorems and Formulas relating to the Sines , Cosines , Tan- gents , & c . · 215 Construction and Description of the Tables , 223 Description ...
Page 209
For the sake of brevity , they are called the cosine , cotangent , and cosecant , of the arc AM , and are thus designated : MQ = cos AM , or cos ACM , DS = cot AM , or cot ACM , CS cosec AM , or cosec ACM . In general , A being any arc ...
For the sake of brevity , they are called the cosine , cotangent , and cosecant , of the arc AM , and are thus designated : MQ = cos AM , or cos ACM , DS = cot AM , or cot ACM , CS cosec AM , or cosec ACM . In general , A being any arc ...
Page 210
When the point M is at A , or when the arc AM is zero , the three points T , M , P , are confounded with the point A ; whence it appears that the sine and tangent of an arc B M M R E P zero , are zero , and the cosine and secant of this ...
When the point M is at A , or when the arc AM is zero , the three points T , M , P , are confounded with the point A ; whence it appears that the sine and tangent of an arc B M M R E P zero , are zero , and the cosine and secant of this ...
Page 211
X. The point M continuing to advance from D towards B , the sines diminish and the cosines increase . Thus M'P ' is the sine of the arc AM ' , and M'Q , or CP ' its cosine . But the arc M'B is the supplement of AM ' , since AM ' + M'B ...
X. The point M continuing to advance from D towards B , the sines diminish and the cosines increase . Thus M'P ' is the sine of the arc AM ' , and M'Q , or CP ' its cosine . But the arc M'B is the supplement of AM ' , since AM ' + M'B ...
Page 212
The versed sine AP is equal to the radius CA minus CP the cosine AM : that is , ver - sin AM - R - cos AM . Now when the arc AM be- comes AM ' the versed sine AP , becomes AP ' , that is equal to R + CP ' . But this expression cannot be ...
The versed sine AP is equal to the radius CA minus CP the cosine AM : that is , ver - sin AM - R - cos AM . Now when the arc AM be- comes AM ' the versed sine AP , becomes AP ' , that is equal to R + CP ' . But this expression cannot be ...
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ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole