Nine geometricall exercises, for young sea-men and others that are studious in mathematicall practices: containing IX particular treatises, whose contents follow in the next pages. All which exercises are geometrically performed, by a line of chords and equal parts, by waies not usually known or practised. Unto which the analogies or proportions are added, whereby they may be applied to the chiliads of logarithms, and canons of artificiall sines and tangents. By William Leybourn, philomath.

About this Item

Title
Nine geometricall exercises, for young sea-men and others that are studious in mathematicall practices: containing IX particular treatises, whose contents follow in the next pages. All which exercises are geometrically performed, by a line of chords and equal parts, by waies not usually known or practised. Unto which the analogies or proportions are added, whereby they may be applied to the chiliads of logarithms, and canons of artificiall sines and tangents. By William Leybourn, philomath.
Author
Leybourn, William, 1626-1716.
Publication
London :: printed by James Flesher, for George Sawbridge, living upon Clerken-well-green,
anno Dom. 1669.
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.

This text has been selected for inclusion in the EEBO-TCP: Navigations collection, funded by the National Endowment for the Humanities.

Link to this Item
http://name.umdl.umich.edu/A48344.0001.001
Cite this Item
"Nine geometricall exercises, for young sea-men and others that are studious in mathematicall practices: containing IX particular treatises, whose contents follow in the next pages. All which exercises are geometrically performed, by a line of chords and equal parts, by waies not usually known or practised. Unto which the analogies or proportions are added, whereby they may be applied to the chiliads of logarithms, and canons of artificiall sines and tangents. By William Leybourn, philomath." In the digital collection Early English Books Online 2. https://name.umdl.umich.edu/A48344.0001.001. University of Michigan Library Digital Collections. Accessed June 1, 2024.

Pages

PROP. IV. The Latitude of the Place, and the Declination of the Sun, being given, to find the Angle of the Sun's Position at the time of his rising.

THIS Proposition is resolvable upon the Triangle P ☉ O: In which there is given (1.) the Hypotenuse P ☉, the Complement of the Sun's Declination; (2.) the Perpendi∣cular P O, the Latitude: and it is required to find the Angle P ☉ O: which may be found by the 15. Case of Right-angled Sphericall Triangles, and by the following

Analogie or Proportion.

As the Co-sine of the Declination 70 degr. is to the Radius 90 degr.

So is the Sine of the Latitude 51 degr. 30 min. to the Sine of the Angle of the Sun's Position at the time of his rising.

By the Projection.

Lay a Ruler to X, (the Pole of the Hour-Circle P ☉ S,) and the Point ☉; the Ruler so laid will cut the Meridian Circle near the Point ♌: then set 90 degr. from ♌ to x upon the Me∣ridian, and lay the Ruler from X to x; so shall it cut the Hour-Circle

Page 102

S ☉ P (being continued without the Meridian Circle) in the Point Φ. Again, the Ruler laid from ☉ to Φ will cut the Meridian Circle in the Point 2. So the distance O 2, being ta∣ken in the Compasses and applied to the Line of Chords, will be found to contain 56 degr. 29 min. which is the quantity of the Angle P ☉ O.

Do you have questions about this content? Need to report a problem? Please contact us.