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 V. The Hypotenuse C B 225, and the Base A B 180, being given, to finde the Perpendicular C A.

DRaw a right Line A B containing 180 of your Scale of equal parts, and upon the end A erect a Perpendicular A C. Then take out of your Scale of equal parts 225, (the length of your Hypotenuse given,) and setting one foot of the Compasses in B, with the other describe the Arch h k, cut∣ting the Perpendicular A C in C, then draw the Line C B: so have you constituted the Triangle C A B. Lastly, take in your Compasses the length of the Line A C, and apply it to your Line of equal parts, where you shall finde that it will contain 135: and that is the length of the Perpendicular C A.

The Analogie or Proportion is,

1. Operation.

As the Logarithm of C B is to the Radius,

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

2. Operation.

As the Radius is to the Logarithm of C B,

So is the Sine of B (the Complement of C) to the Log. of C A.