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.

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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.
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http://name.umdl.umich.edu/A48344.0001.001
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"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 16, 2024.

Pages

Page 140

Analogie or Proportion.

(1.) As the Radius 90 degr. is to the Co-sine of the difference of Longitude 40 degr.

So is the Co-tangent of the greater Latitude 50 d. to the Tan∣gent of a fourth Arch 37 d. 10 m. which being substracted out of the other Latitude, and 90 d. added thereto, say,

[illustration] geometrical diagram

Page 141

(2.) As the Co-sine of the Arch found 52 degr. 50 min. is to the Co-sine of the Arch remaining 52 degr. 50 min.

So is the Co-sine of the Latitude first taken 50 degr. 00 min. to the Co-sine of the Distance 40 degr. which taken from 180 degr. there remains 140 degr. for the Distance of the two Places.

So the two Places propounded being the Cape of Good hope, lying in the Latitude of 40 degr. South, and Longitude 50 d. and the other Place Malibrigo, lying in 26 degr. of North La∣titude, and in 180 degr. of Longitude, you may find their Di∣stance by the foregoing Analogie to be 140 degr. which, con∣verted into Miles, make 8400. And such is the Distance of the two Places.

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