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.

PROBL. XV. How to work the Rule of Proportion by a Scale of equal Parts, and such other Conclusions as are usually wrought in Lines and Numbers, as in Mr. Gunter's 10 Prob. 2 Chap.

The Scale of Inches is a Scale of equal Parts, and will perform (by protraction upon a Flat or Paper) such Conclusions as are usually wrought in Lines and Numbers, as in Mr. Gunter's 10 Prob. 2 Chap. Sector, may be seen, and in others that have writ in the same kind. This way Mr. Samuel Foster hath directed in the I Chap. of his Posthumus Fosteri.

An Example in Numbers like his Tenth Probl.

As 16 to 7: So is 8 to what?

Here because the second Term is less than the first, upon the Line AB, I set AC the first Term 16, and the second Term AD 7, both taken out of the Scale of equal parts: thence also the third Number 8 being taken, with it upon the Center C, I de∣scribe the Arke EF, and from A draw the Line AE, which may only touch the same Arke; then from D, I take DG, the least distance from the Line AE, and the same measured in the same Scale of equal parts, gives 3½, the fourth Term required.

[illustration] geometrical diagram

But if the second Term shall be greater than the first, then the form of working must be changed, as in the following Example.

EXAMPLE.

As 7 to 16: So 21 to what? — 48.

Upon the Line AB, I set the second Term 16, which is here supposed to be AD; then with the first Term 7 upon the Center D, I describe the Arke GH, and draw AG that may just touch it: Again, having taken 21 out of the same Scale, I set one Foot of that Extent upon the Line AB, removing it until it fall into such a place, as that the other Foot being turned about, will justly touch the Line AG before-drawn; and where (upon such Conditions) it resteth, I make the Point C; then measuring AC upon your Scale, you shall find it to reach 48 Parts, which is the fourth Num∣ber required.

The form of Works (although not so Geometrical) is here given, because it is here more expedite than the other by drawing Parallel Lines; but in some Practice the other may be used. I have been the more large upon this, because in the following

Treatise I shall quote some more remarkable Places in Posthuma Fosteri: and the So∣lution of Proportions must be referred thither, the form of their Operations being the same with this. In them therefore shall only be intimated what must be done in ge∣neral, the particular way of working being here directed.