## Elements of Plain and Spherical Trigonometry: Together with the Principles of Spherick Geometry, and the Several Projections of the Sphere in Plano. The Whole Demonstrated and Illustrated with Useful Cases and Examples |

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Elements of Plain and Spherical Trigonometry: Together with the Principles ... John Harris No preview available - 2017 |

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alſo apply Axiom Baſe becauſe called Caſe Center Chords common Complement conſequently conſidered Declination DEMONSTRATION deſcribe the Circle determin Diameter Difference Diſtance divide draw drawn eaſily Ecliptick Elevation equal Equinoctial evident fall fame firſt give given greater half Horizon Hour Hour-Circles laſt Latitude Legs Lemma length leſs likewiſe Line of Meaſures Logarithm manner meet muſt North Number number of Degrees oblique Circle oppoſite Angles parallel paſs thro paſſing perpendicular placed Plain Pole Primitive Prob produced Projection Prop proper Proportions Quadrant Radius repreſent Repreſentation right Angles right Circle right Line ſame ſay Secant ſet ſhall Sides ſimilar ſince Sine South Sphere Spherick Supplement ſuppoſe Tables Tangent ther theſe thing thoſe thro Triangle Uſe Weſt wherefore whoſe

### Popular passages

Page 162 - 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 c _ sin A sin B sin C...

Page 41 - As the base or sum of the segments Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base.

Page 161 - BD ; the co-fine of the angle B will be to the co-fine of the angle D, as the fine of the angle BCA to the fine of the angle DCA. For by 22. the co-fine of the angle B is to the fine of the angle...

Page 11 - If either of the legs, including the right angle, be made the radius of a circle, the other leg will be the tangent of its oppofite angle, and the hypothenufe the fecant of the fame angle, E For TRIGONOMETRY.

Page 35 - 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 40 - Sum of fs'' \ the Legs, as the Difference of the Legs is to the Difference of the Segments of the Bafe made by a Perpendicular let fall from the Angle oppofite to the Bafe.

Page 168 - Angle oppoflte call the Bafe ; then work as in the nth Cafe. For fuch is the Operation in the Supplemental Triangle, whofe Angles and Sides are equal to the Supplements of the Sides and Angles of the Triangle propnk'd ; and Arcs and their Supplements have the fame Sines and Tangents.

Page 58 - Projeftiott the Angles made by the Circles on the Surface of the Sphere are equal to the Angles made by their Reprefentatiyes on the plane of the Projection.

Page 38 - FA : FG ; that is in Words, half the Sum of the Legs is to half their Difference, as the Tangent of half the Sum of the oppofite Angles is to the Tangent of half their Difference : But Wholes are as their Halves ; wherefore the Sum of the Legs...

Page 160 - OBlique Spherical Triangles may be reduced to two Right-angled Spherical Triangles, by letting fall a Perpendicular, which Perpendicular eiPlate V.