This plane is represented by the prickt circle in the fundamental Diagram ECW, and is intersected by the hour circles from the pole P, as by the Scheme appeareth, and therefore the Diall proper to this plane must have a center, above which the South pole is elevated; and therefore the stile must look downwards, as in South direct planes; to calculate which Dials there must be given the Poles elevation, and the quantity of reclination, by which to finde the hour distances from the meridian, and thus in the triangle PC 1, having the poles elevation 51 degr. 53 min. and the reclina∣tion 25 degr. PC is given, by substracting 25 degr. from PZ 38 degr. 47 min. the complement of the poles height, the angle CP 1 is 15 degrees, one hours distance, and
Institutio mathematica, or, A mathematical institution shewing the construction and use of the naturall and artificiall sines, tangents, and secants in decimal numbers, and also of the table of logarithms in the general solution of any triangle, whether plain or spherical, with their more particular application in astronomie, dialling, and navigation / by John Newton.
About this Item
- Title
- Institutio mathematica, or, A mathematical institution shewing the construction and use of the naturall and artificiall sines, tangents, and secants in decimal numbers, and also of the table of logarithms in the general solution of any triangle, whether plain or spherical, with their more particular application in astronomie, dialling, and navigation / by John Newton.
- Author
- Newton, John, 1622-1678.
- Publication
- London :: Printed by R. & W. Leybourn, for George Hurlock ... and Robert Boydel ...,
- 1654.
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- Subject terms
- Geometry -- Early works to 1800.
- Trigonometry -- Early works to 1800.
- Logarithms.
- Mathematics -- Problems, exercises, etc.
- Cite this Item
-
"Institutio mathematica, or, A mathematical institution shewing the construction and use of the naturall and artificiall sines, tangents, and secants in decimal numbers, and also of the table of logarithms in the general solution of any triangle, whether plain or spherical, with their more particular application in astronomie, dialling, and navigation / by John Newton." In the digital collection Early English Books Online. https://name.umdl.umich.edu/A52264.0001.001. University of Michigan Library Digital Collections. Accessed May 18, 2024.
Pages
Page 346
the angle at C right, we may finde C 1, by the first case of right angled spherical trian∣gles: for,
| As the Radius 90, | 10.000000 |
| Is to the sine of PC 13.47. | 9.367237 |
| So is the tangent of CP 1. 15. | 9.428052 |
| To the tangent of C 1 3.57. | 8.795289 |
And this being all the varieties, save one∣ly increasing the angle at P, I need not re∣iterate the work.