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. XIV. Three Right Lines being given, To find a fourth in proportion to them.

THe three Lines given are ABC, unto which it is required to find a fourth Pro∣portional Line. This is to perform the Rule of Three. As in the last Problem, you must draw two Right Lines, making any Angle at pleasure, as the Angle EFG; then take the Line A in your Compass, and set it from F to I; then take the Line B in your Compas∣ses, and set that from F to K; then take the third given Line in your Com∣passes, and set that from F to H, and from that Point H draw the Line H L, parallel to IK; So shall the Line FL be the third Proportional required.

[illustration] geometrical diagram

Note, That these Lines are taken off a Scale, that is divided into 20 parts to an Inch: To do it Arithmetically say,

As FI is to FK: So is FH to FI.

〈 math 〉〈 math 〉

Here note, That in performance of the last Problem, That the first and third Terms, namely the Lines A and C, must be set upon one and the same Line, as here upon the Line FE, and the second Line B must be set upon the other Line FG, upon which Line also the fourth Proportion will be found.