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.

CASE IV. The Hypotenuse C B 225, the Angle C 53 degr. 7 min. and the Angle at B 36 degr. 53 min. given, to finde the Base B A, and the Perpendicular C A.

[illustration] geometrical diagram

DRaw a right Line C B containing 225 of your Line of equal parts; then taking 60 deg. out of your Line of Chords, set one foot of the Compasses in B, and with the other describe the Arch e d; also (the Compasses continuing at the same distance) place one foot in C, and with the other describe the

Arch g f. Then from the Point B, and through the Point d, draw a right Line; also from the Point C, and through the Point f, draw another right Line: these two Lines will intersect or cross each other in the Point A, forming the Triangle C A B. Lastly, take the Line A B in your Com∣passes, and applying it to your Scale of equal parts, you shall finde it to contain 180; and that is the length of the Base A B. Likewise A C being taken in the Compasses, and measured upon the Line of equal parts, will be found to contain 135, which is the length of the Perpendicular C A.

The Analogie or Proportion is,

As the Radius is to the Logarithm of C B,

So is the Sine of C to the Logarithm of A B,

And the Sine of B to the Logarithm of C A.