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added againſt alſo Angle Arch Arithmetical Baſe becauſe Cafe called Cape Caſe Chart Chord Circle Column Compaſſes Courſe and Diſtance Current Declination Degrees demand Dep Lat Dep Diff Difference of Latitude Difference of Longitude divide draw draw the Line Eaſt equal Example Extent fall fame Figure firſt Foot given Number gives half Hour Hypotenuſe Latitude and Departure Line meaſured Mercator's Meridian Method Middle Latitude Miles Minutes Minutes Sine Tangent Moon Motion muſt North Note Oblique obſerve Operation oppoſite Parallel Perpendicular Place Plane Sailing Point Pole Port Projection proper Proportion Queſtion Radius Reckoning Remainder Right Right-angled Rule ſaid ſame ſecond ſet ſhall Ship fails Side Sine Comp Sine Tangent Secant ſome South Square ſubtract Sun's ſuppoſe Table theſe third Tide Triangle Trigonometrical true tude Uſe Weſt whole
Page xiv - In any plane triangle, the sum of tfte two sides containing either angle, is to their difference, as the tangent of half the sum of the other two angles, to the tangent of half their difference.
Page xiv - Then as the sum of the sides is to their difference, so is the tangent of half the sum of the unknown angles to the tangent of half their difference (Theor.
Page xiv - ... the sum of the segments of the base is to the sum of the sides as the difference of the sides to the difference of the segments of the base.
Page 231 - ... of the opposite parts. All of the ten formulas just listed can easily be derived from these rules. Oblique Spherical Triangles.— Formulas for the solution of oblique spherical triangles are developed from those for right spherical triangles. The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a sin b sin с...
Page xi - Circumference of every Circle is fuppofed to be Divided into 360 equal Parts called Degrees, and each Degree...
Page 24 - Then radius : log. 179-3 :: s. 8° 31' : log. ofi6'5i; which doubled is the diftance between Edyftone and Lizard 53-04 miles. For the other two, there are 2 fides, and an angle oppofite to one of them, given, to find the other fide.
Page 232 - Day, fubtradt the Complement of the Sun's Altitude, noting the half Sum, and the Remainder. 3. Then to find the Sun's Azimuth, it's thus ; to the Complement Arithmetic of the Sines of the Complement of the Latitude, and Complement of the Sun's Altitude, add the Sines of the aforefaid...
Page 231 - Perpendicular, let it fall from the End of a given Side, and oppofite to a given Angle...