A Treatise of Trigonometry: Plane and Spherical, Theoretical and Practical. In which the Several Cases of Plane and Spherical Triangles are Solved, Instrumentally and Arithmetically. ... To which is Added a Correct Table of Logarithms, Sines, Tangents and Secants. By Sam. Heynes, ...

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J. Matthews, 1701 - 8 pages
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Page 11 - Secants, and are to be taken out of your Table. To find a Side, any Side may be made Radius : Then fay, As the Name of the Side given, Is to the Name of the Side required ; So is the Side given, To the Side required. But to find an Angle, one of the given Sides...
Page 2 - Calculation, if, fuppofing the Radius divided into any Number of equal Parts, we know how many of thofe equal Parts are in the Sine, Tangent, or Secant of any Arch propos'd: The Art of inferring which is called Trigonometry, and it is either Plane or Spherical.
Page 1 - Diameter pafling thro' the other End ; or it is half the Chord of twice the Arch ; fo BF is the Sine of the Arches BA, BD. And here it is evident, that the Sine of 90...
Page 12 - But to find an angle, one of the given sides must be made radius: then, as the side made radius is to the other side ; so is the name of the...
Page 33 - DAG, that is, the half of BAC : but HA is half the perimeter of the triangle ABC, and AD is the excess of the same above HD, that is, above the base BC...
Page 79 - The first shows that, the sum of the sines of two arcs is to the difference of those sines, as the tangent of half the sum of the arcs is to the tangent of half their difference.
Page 58 - In spherical triangles, whether right angled or oblique angled, the sines of the sides are proportional to the sines of the angles opposite to them.
Page 32 - ... so is the square of the radius to the square of the sine of half their contained angle, as shown in Leslie's Geometry.
Page 54 - 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 - Solution of Right-angled Triangles, obferve, that as different Sides are made Radius, fo the other Sides acquire different Names, which Names are either Sines, Tangents, or Secants, and are to be taken out of your Table, To find a Side, any Side may be made Radius : Then fay, as the Name of the Side given is to the Name of the Side required ; fo is the Side given to the Side required.

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