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.

As for Example.

The Right-Range being all the Right-Line AB which is properly called his Violent Motion, and BC will be the mixt or Crooked-Range, and CD the Natural Motion, wherein from A to B is the furthest part of the Violent Motion, and from C to d the end of the Natural Motion.

And in the seventh Proposition of the same Book, he proveth that every Shot equal∣ly heavy, great or little, equally elevated above the Horizon, or equally Oblique or Levelly directed, are among themselves like and proportional in their Distances, as the Figure following sheweth, as A:E:F is like and proportional in the Right and Crooked-Ranges unto H:I, and in their Distance or Dead-Ranges AF unto A:I.

And in his fourth and sixth Propositions of the same Book, he proveth that every Shot made upon the Level hath the mixt or Crooked-Range thereof, equal to the Arch of a Quadrant 90 degr. and if it be made upon any Elevation above the Level, that then it will make the Crooked-Range, to be more than the Quadrant.

And if that be made Imbased under the Level, that then the Crooked-Range thereof will be an Arch less than a Quadrant.

And lastly, in his ninth Proposition of the same Book, he undertakes to prove if one Piece be Shot off twice, the one Level, and the other at the best of the Random at 42½ degr. Mounture, that the Right-Range of the length is but ¼ of the Right-Range of the best of the Randoms, and that the Dead-Range of the Level is but 1/20 of the Dead-Range of the best Random, whereto he that desires a further Demonstration of these Propositions in his said second Book of Nova Scientia.

[illustration] geometrical diagram