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.

Geometrical Theoremes.

I. ANY two Right Lines crossing one another, make the contrary or vertical Angles equal. Euclid. 15. 1.

II. If any Right Lines fall upon two parallel Right Lines, it maketh the outward Angles of the one, equal to the inward Angles of the other; and the two inward opposite Angles, on contrary sides of the falling Line, also equal. Euclid 29. 1.

III. If any Side of a Triangle be produced, the outward Angle is equal to the in∣ward opposite Angles, and all the three Angles of any Triangle are equal to two Right Angles. Euclid 32. 1.

IV. In Aequi-angled Triangles all their Sides are proportioned, as well such as con∣tain the equal Angles, as also the subtendent Sides.

V. If any four Quantities be proportional, the first multiplied in the fourth, produceth a Quantity equal to that which is made by multiplication of the second in the third.

VI. In all Right-angled Triangles, the Square of the Side subtending the Right Angle, is equal to both the Squares of the containing sides. Euclid 47.1.

VII. All Parallellograms are double to the Triangles that are described upon their Basis, their Altitudes being equal. Euclid 41.1.

VIII. All Triangles that have one and the same Base, and lie between two Parallel Lines, are equal one to the other. Euclid 37.1.