Geometrical trigonometry, or, The explanation of such geometrical problems as are most useful & necessary, either for the construction of the canons of triangles, or for the solution of them together with the proportions themselves suteable unto every case both in plain and spherical triangles ... / by J. Newton ...

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Title: Geometrical trigonometry, or, The explanation of such geometrical problems as are most useful & necessary, either for the construction of the canons of triangles, or for the solution of them together with the proportions themselves suteable unto every case both in plain and spherical triangles ... / by J. Newton ...
Author: Newton, John, 1622-1678.
Publication: London :: Printed for George Hurlock ... and Thomas Pierrepont ...,; 1659.
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: Trigonometry -- Early works to 1800.
Link to this Item: http://name.umdl.umich.edu/A52262.0001.001
Cite this Item: "Geometrical trigonometry, or, The explanation of such geometrical problems as are most useful & necessary, either for the construction of the canons of triangles, or for the solution of them together with the proportions themselves suteable unto every case both in plain and spherical triangles ... / by J. Newton ..." In the digital collection Early English Books Online. https://name.umdl.umich.edu/A52262.0001.001. University of Michigan Library Digital Collections. Accessed June 14, 2025.

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Problem 12.

An angle and leg conterminate with it gi∣ven, to find the other angle.

In the right angled Spherical Tri∣angle ABC.

The angle comp. A the middle part is inquired.

The given Angle comp. C
The given Leg. BC

Extreames disjunct.

Anal. Rad. sine C ∷ cs BC. cos. A.

Demonst. The triangles CFI and CHG have the same acute angle at the base, therefore by the first axiom•• Rad. FC. sine FI ∷ sine HC. sine HG, and the compl. of HC is the leg BC, & GD the measure of the angle at A is the complement of HG.

Therefore,

R. sine C ∷ co-sine BC. co-sine A.