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 XI. Two Sides and their Containing Angle given, To find the third Side.

THere is given RS 406 Paces, and RQ 185 Paces, and the Angle at R 45 deg. 20 min. which is by the 10 Case,

As the Sum of the Sides given RS + RQ 594 p.	2771587
Is in proportion to their Difference RS + RQ 221	2344392
So is the Tangent of the Half Sum of the 67 deg. 20 min.	10••79213
Two opposite Angles Q and S unknown, 2, 3 Numb.	1••723605
To the Tangent of the Angle	41 d.	50 m.	9952018
Which added to the Half Sum	67	20
Leaves the greater Angle at Q required	109	10
Whose Complement to 180 deg. is	70	50

Then say,

As the Sine of the Angle found 109, or 70 deg. 50 min.	9,975233
Is in proportion to his opposite Side RS 406 Paces	2,608526
So the Sine of the Angle given at R 45 deg. 20 min.	9,851997
To his opposite Side required QS 305 Paces	12,464523
The Logarithm of the Side required	2, 485290

By the Line of Sines and Numbers.

EXtend the Compasses from the Sine of 70 deg. 50 min. to the Logarithm-Side RS 406 Paces; the same Extent will reach from the Sine of 45 deg. 20 min. to the Side 305.

Or, Extend the Compasses from the Sine of 70 deg. 50 min. to the Sine of 45 deg. 20 min. the same Distance will reach from 406, to 305 Paces, which is the Length of the Side QS, which is required.