A Treatise on Plane and Spherical Trigonometry, and on Trigonometrical Tables and Logarithms: Together with a Selection of Problems and Their Solutions |
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Page 1
... equal to two right angles ) we can form an infinite number of triangles , which are not equal , but only . similar to one another . Geometry furnishes simple construc- tions for each of the cases in which we can determine a triangle by ...
... equal to two right angles ) we can form an infinite number of triangles , which are not equal , but only . similar to one another . Geometry furnishes simple construc- tions for each of the cases in which we can determine a triangle by ...
Page 2
... equal parts called degrees , each degree into 60 equal parts called minutes , each minute into 60 equal parts called seconds ; then an angle is expressed by the number of degrees , minutes , seconds , and decimal parts of a second ...
... equal parts called degrees , each degree into 60 equal parts called minutes , each minute into 60 equal parts called seconds ; then an angle is expressed by the number of degrees , minutes , seconds , and decimal parts of a second ...
Page 3
... equal 2πr , let ACB ( fig . 1 ) be an angle at the centre of a circle subtended by an arc equal to the radius of the circle ; then since ( Euclid , VI . 33 ) angles at the centre of the same circle are to one another as the arcs on ...
... equal 2πr , let ACB ( fig . 1 ) be an angle at the centre of a circle subtended by an arc equal to the radius of the circle ; then since ( Euclid , VI . 33 ) angles at the centre of the same circle are to one another as the arcs on ...
Page 4
... equal to the radius , or = w ; and ACP any other angle Ow ; then ( Euclid , VI . 33 ) = LACP AP AP = = ‹ ACB AB AC ' .. ACP ACB . = 2 - arc = E . ; AP AC radius arc .. 0 = radius = If we suppose the radius of the circle to be taken equal ...
... equal to the radius , or = w ; and ACP any other angle Ow ; then ( Euclid , VI . 33 ) = LACP AP AP = = ‹ ACB AB AC ' .. ACP ACB . = 2 - arc = E . ; AP AC radius arc .. 0 = radius = If we suppose the radius of the circle to be taken equal ...
Page 5
... equal to the radius of the circle , is taken for the unit , and conversely . The numerical value of π , the ratio of the circumference of a circle to its diameter , is 3.14159 . Let r be the radius and c the circumference of a circle ...
... equal to the radius of the circle , is taken for the unit , and conversely . The numerical value of π , the ratio of the circumference of a circle to its diameter , is 3.14159 . Let r be the radius and c the circumference of a circle ...
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angle BAC angular points arcs base bisected calculation circle circular measure circumscribed circumscribed circle cloth consequently corresponding cos³ cosec cosine decimal denoted determined difference digits equal equation expressed formula fraction given triangle Hence History hypothenuse inscribed integer intersection less than 90 log-cos log-sin logarithms magnitude middle points morocco multiple negative obtain perpendicular plane Plates pole positive Post 8vo produced quadrant quantities revised right angles right-angled triangle Second Edition shew Similarly sin a sin sin A+B sin c cos sin³ sine sines and cosines solid angle solution sphere spherical excess spherical triangle subtended suppose tables tan³ tangent three sides triangle ABC TRIG Trigonometrical Ratios values vols Woodcuts zero
Popular passages
Page 182 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 182 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
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