The semicircle on a sector in two books. Containing the description of a general and portable instrument; whereby most problems (reducible to instrumental practice) in astronomy, trigonometry, arithmetick, geometry, geography, topography, navigation, dyalling, &c. are speedily and exactly resolved. By J. T.

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Title: The semicircle on a sector in two books. Containing the description of a general and portable instrument; whereby most problems (reducible to instrumental practice) in astronomy, trigonometry, arithmetick, geometry, geography, topography, navigation, dyalling, &c. are speedily and exactly resolved. By J. T.
Author: Taylor, John, 1666 or 7-1687.
Publication: London :: printed for William Tompson, bookseller at Harborough in Leicestershire,; 1667.
Rights/Permissions: To the extent possible under law, the Text Creation Partnership has waived all copyright and related or neighboring rights to this keyboarded and encoded edition of the work described above, according to the terms of the CC0 1.0 Public Domain Dedication (http://creativecommons.org/publicdomain/zero/1.0/). This waiver does not extend to any page images or other supplementary files associated with this work, which may be protected by copyright or other license restrictions. Please go to http://www.textcreationpartnership.org/ for more information.
Subject terms: Mathematics -- Early works to 1800.; Navigation -- Early works to 1800.; Dialing -- Early works to 1800.
Cite this Item: "The semicircle on a sector in two books. Containing the description of a general and portable instrument; whereby most problems (reducible to instrumental practice) in astronomy, trigonometry, arithmetick, geometry, geography, topography, navigation, dyalling, &c. are speedily and exactly resolved. By J. T." In the digital collection Early English Books Online. https://name.umdl.umich.edu/A64223.0001.001. University of Michigan Library Digital Collections. Accessed May 18, 2024.

Pages

PROBL. 4.

By the Lines of Natural Sines to lay down any Tangent, or Secant required to a Radius given.

In some Cases, especially for Dyalling, your Instrument may be defective of a Tan∣gent, or Secant for your purpose, Ex. gr. when the Tangent exceeds 76, or the Secant is more than 60. In these extremities use the following Remedies. First, for a Tangent.

As the cosine of the Ark is to the Radius given, so is the sine of the Ark to the length of the Tangent required. Secondly, for a Secant.

As the cosine of the Ark is to the Radius given, so is the Sine 90 to the length of the Secant required.