A Treatise on Trigonometry, Plane and Spherical: With Its Application to Navigation and Surveying, Nautical and Practical Astronomy and Geodesy : with Logarithmic, Trigonometrical, and Nautical Tables, for the Use of Schools and Colleges |
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Page xii
... sides , Formulas for the sine and tangent of half an angle in terms of the three sides of a spherical triangle , . Ā· Blank form for the application of one of these formulas , Derivation of the formulas for sine and cosine of a side in ...
... sides , Formulas for the sine and tangent of half an angle in terms of the three sides of a spherical triangle , . Ā· Blank form for the application of one of these formulas , Derivation of the formulas for sine and cosine of a side in ...
Page 1
... sides and angles , though trigonometry properly includes the measurement of the surface also . There will accordingly be ... side , because if the three angles only were equal respectively in the two triangles they would be but similar ...
... sides and angles , though trigonometry properly includes the measurement of the surface also . There will accordingly be ... side , because if the three angles only were equal respectively in the two triangles they would be but similar ...
Page 2
... sides and included angle of a triangle being given , let it be required to find the remaining side and the other two angles . Let A and B be the two given sides , and c the given included angle . Draw two lines DH and DG of indefinite ...
... sides and included angle of a triangle being given , let it be required to find the remaining side and the other two angles . Let A and B be the two given sides , and c the given included angle . Draw two lines DH and DG of indefinite ...
Page 3
... side towards which the line is to be drawn ; then from a draw the line in the proper direction , terminating it at ... sides of an angle are proportional to the parts into which they divide the sides . ( See Plane Geom . , Theorems 61 ...
... side towards which the line is to be drawn ; then from a draw the line in the proper direction , terminating it at ... sides of an angle are proportional to the parts into which they divide the sides . ( See Plane Geom . , Theorems 61 ...
Page 4
... sides , the arcs being described with equal radii , and it is also there stated that hence such arcs are properly the measures of angles . So that if an arc included between two sides of one angle be double , or triple , or sextuple ...
... sides , the arcs being described with equal radii , and it is also there stated that hence such arcs are properly the measures of angles . So that if an arc included between two sides of one angle be double , or triple , or sextuple ...
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Common terms and phrases
A.M. Hour P.M. altitude azimuth centre circle colatitude collimation column comp cosĀ² cosc Cosecant Cotangent Diff Cotangent Secant course decimal declination departure determined diagram difference of latitude difference of longitude distance divided equal equation error EXAMPLE expressed feet formula Geom given number hence horizontal Hour A.M. Cosine Hour A.M. Hour hour angle hypothenuse instrument Logarithms of Numbers longitude meridian miles multiplied Napier's rules Natural Sines Nautical Almanac negative number of degrees observed obtained parallel parallel sailing perpendicular plane sailing plane triangle Prop proportion quadrant quotient radius right angled triangle right ascension sailed screw second member ship side opposite siderial sin a cos sin a sin sinĀ² sine and cosine solution sphere spherical triangle spherical trigonometry spirit level star subtracting supporting axis TABLE XXVII tangent telescope transit trigonometrical lines vertical zenith