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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.
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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 15, 2025.

Pages

Problem 1.

Two sides with an angle opposite to one of them being given, to find the angle opposite to the other. If it be known whether the angle sought be acute or obtuse.

In the oblique angled Spherical triangle ABC.

The angle BAC is inquired.

The given Sides

  • AB 42.15
  • BC 29.83

The given Angle ACB 36. 14

The Anal. s. BA. s. BC ∷ s. C. s A.

Page 104

[illustration]

For by the Catholick proposition.

  • 1 R. s AB ∷ s A. s BD.
  • 2 R. s BC ∷ s C. s BD.
  • Therefore, s AB. s BC ∷ s C. s A.
Illustration by natural numbers.
  • As the sine of AB 42.15 6710738
  • To the sine of BC 29.83 4974282
  • So is the fine of ACB 36.14 5897603
  • To the sine of BAC 25.92 4371552
Illustration by artificial numbers.
  • As the sine of AB 42.15 9.826770
  • To the sine of BC 29.83 9.696730
  • So the sine of ABC 36.14 9.770675
  • 19.467405
  • To the sine of BAC 25.92 9.640635
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