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.

QUEST. VI. From the Port at A I Sail S. S. W. unto B, and from B I Sail N. W. b. W. unto C, and from C I Sailed unto my first Port at A, E. b. N. Now having Sailed in all 120 Leagues, I would know how many Leagues I have Sailed upon each Point.

FIrst draw AB a S. S. VV. Course, at any convenient distance; then from B draw a N. VV b. VV. Course, and from A draw the opposite Course of E. b. N. which is VVest by South, which will cut BC in C; so continue the Sides of the Tri∣angle AB unto E, and AC unto F. Then lay BC from B unto D, and AC from D unto E. Then take 120 Leagues, and lay the same from A unto F: Next draw the Line EF, and from D and B draw Parallels thereunto, which will cut AF in G and H. Lastly, measuring AH, you shall have 33 ⅔ Leagues that you have Sailed S. S. VV. And measuring HG, you shall have 39 Leagues 6/10 parts that you have Sailed N. VV. b. VV. Also measuring GF, you shall have 46 ¾ Leagues near, that you have Sailed E. b. N. which makes in all near 120 Leagues.

[illustration] geometrical diagram

Arithmetically, By the Table of Natural Sines in the Sea-mans Kalendar.

First, Add up all the Sines of the Angles together, Which is

deg.	min.
45	00	7071
56	15	8314
78	45	9790
		25175

Then by the Rule of Three,

As 25194, to 120 Leagues: So	45	00	To the Distan∣ces sailed	S. S. W. 33 68/106 AB.
56	15	N. W. b. W. 39 60/100 Leag.
78	45	E. b. N. 46 72/100 CA.

I might have added several other Questions of this nature, but I hold these sufficient; for those that understand how these are done, may do any of the like nature: But the way of demonstrating and laying of them down, as you see in the Figures, I ne∣ver saw before of any other Mans Work. Therefore now we will come to the true way of Sailing, and Use of the true Sea-Chart.