The mariners magazine, or, Sturmy's mathematical and practical arts containing the description and use of the scale of scales, it being a mathematical ruler, that resolves most mathematical conclusions, and likewise the making and use of the crostaff, quadrant, and the quadrat, nocturnals, and other most useful instruments for all artists and navigators : the art of navigation, resolved geometrically, instrumentally, and by calculation, and by that late excellent invention of logarithms, in the three principal kinds of sailing : with new tables of the longitude and latitude of the most eminent places ... : together with a discourse of the practick part of navigation ..., a new way of surveying land ..., the art of gauging all sorts of vessels ..., the art of dialling by a gnomical scale ... : whereunto is annexed, an abridgment of the penalties and forfeitures, by acts of parliaments appointed, relating to the customs and navigation : also a compendium of fortification, both geometrically and instrumentally / by Capt. Samuel Sturmy.

CASE IV. The Hypothenusal and Angle at the Base being given, To find the Base.

LEt there be given in the Triangle the Hypothenusal BC, and the Angle at the Base CBA; and by consequence the Angle BCA the Complement of the other to 90 degrees: Then to find BA, the Proportion is,

[illustration]

As the Sine of 90 deg. CAB	10, 000000
To the Hypothenusal CB 478	2, 679428
So is the Sine of the Angle ACB 58	9, 928420
To the Logarithm of the Base AB	12, 607848

The nearest Number answering to 2, 607848, is the Logarithm of 405: And so many Foot or Poles, or if the Question be Miles or Leagues, is the Base or Parallel of Longitude AB.

Now you see the former Figure is turned, and therefore very fitly may have other Denominations (or Names) So that in the Art of Navigation, it will not be unfit to call one of these Sides the Parallel-Side, as AB, or Side of Longitude, or Meridian Distance; the other the Perpendicular-Side, or the Side of Latitude, as CA; and the Hypothenusal, the Side of Distance CB, and the Arches to lay down from the Chords, as before-directed.

By the Line of Sines and Numbers.

THe Angle given, as before, Extend the Compasses from the Sine of 90 deg. unto 478. the same Extent will reach from the Sine of 58 deg. to 405 in the Line of Numbers.

Or, Extend the Compasses from the Sine of 90 deg. to the Sine of 58 deg. the same Extent will reach from 478 to 405, which is the Length of the Base turned up, or Parallel-Line of Longitude, as before said, AB.