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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"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 May 18, 2024.
Pages
CASE VI. The three Angles being given, to find the other Parts.
IN the Triangle Z E P, if the three Angles E Z P, Z P E, and P E Z, be given, there may be found 3.
1. Z P, the Complement of the Latitude.
2. P E, the Sun's distance from the Pole.
3. Z E, the Complement of the Sun's Altitude.
Thus have you in these six Cases all the Varieties that will arise out of an Oblique-angled Sphericall Triangle, in the Conversion of
descriptionPage 94
which Cases you may observe 60 Questions of the Sphere to be re∣solved; and so many are resolvable in every Oblique-angled Sphe∣ricall Triangle, and 30 in every Right-angled: So that in these two Triangles 90 Questions are resolved. For,
In a Right-angled Sphericall Triangle,
By the
First
Case are resolved
3
Sphericall Questions.
Second
6
Third
6
Fourth
12
Fifth
3
In all 30.
In an Oblique-angled Sphericall Triangle,
By the
First
Case are resolved
3
Sphericall Problems.
Second
9
Third
9
Fourth
18
Fifth
18
Sixth
3
In all 60.
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