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. XXXI. To enlarge or diminish a Plot given, according to any Proportion required.

LEt ABCDE be a Plot given, to be diminished in Power as L to K.

Divide one of the Sides, as AB in Power as L to K, in such sort that the Power of AF may be to the Power of AB, as L to K; then from the Angle A draw Lines to the Point C and D. That done, by F draw a Parallel to BC, to cut AC in G, as FG: again, from G draw a Parallel to DC, to cut AD in H. Lastly, from H draw a Parallel to DE, to cut AE in I: So shall the Plot AFGHI be like ABCDE, and in proportion to it, as the Line L to the Line K, which was required.

Also if the lesser Plot was given, and it was required to make it in proportion to it as K to L; then from the Point A draw the Lines AC and AD at length; also increase AF and AI: That done, enlarge AF in Power as K to L, which set from A to B; then by B draw a Parallel to FG, to cut AC in C, as B C: likewise from C draw a Parallel to GH, to cut AD in D: Lastly, a Parallel from D to HI, as DE, to cut AI being increased in E; so shall you include the Plot ABC DE, like AFGHI, and in proportion thereunto, as the Line K is to the Line L, which was required.

[illustration] geometrical diagram