The circles of proportion and the horizontal instrument. The former shewing the maner how to work proportions both simple and compound: and the ready and easy resolving of quæstions both in arithmetic, geometrie, & astronomie: and is newly increased with an additament for navigation. All which rules may also be wrought with the penne by arithmetic, and the canon of triangles. The later teaching how to work most quæstions, which may be performed by the globe: and to delineat dialls upon any kind of plaine. Invented, and written in latine by W.O. Translated into English, and set out for the public benefit, by William Forster.

TO THE HONOVRABLE AND RENOWNED FOR vertue, learning, and true valour, Sir KENELME DIGBYE Knight.

SIR,

THE excellent accomplishments wher∣with you are adorned both of vertue, and learning, and particularly in the Mathematicall Sciences, together with the Ho∣nourable respect the Author hereof beareth vnto your Worth, and his desire to testifie the same, hath made mee presume to present vnto you, and vnder the happy auspice of your renowned name, to publish to the world this Treatise: the owning whereof though I may not chalenge to my selfe, yet the birth and production, whereby it hath a being to the benefit of others, is, as vnto a second parent, due vnto me.

For being in the time of the long vacation 1630, in the Country, at the house of the Reue∣rend,

and my most worthy friend, and Teacher, M^r. William Oughtred (to whose instruction I owe both my initiation, and whole progresse in these Sciences.) I vpon occasion of speech told him of a Ruler of Numbers, Sines, & I angents, which one had be spoken to be made (such as is vsu∣ally called M^r. Gunters Ruler) 6 feet long, to be vsed with a payre of beame-compasses.

He an∣swered that was a poore invention, and the per∣formance very troublesome: But, said he, see∣ing you are taken with such mechanicall wayes of Instruments, I will shew you what deuises I haue had by mee these many yeares.

And first, hee brought to mee two Rulers of that sort, to be vsed by applying one to the other, without any compasses: and after that hee shewed mee those lines cast into a circle or Ring, with another moueable circle vpon it. I seeing the great ex∣peditenesse of both those wayes; but especially, of the latter, wherein it farre excelleth any other In∣strument which hath bin knowne; told him, I won∣dered that hee could so many yeares conceale such vsefull inuentions, not onely from the world, but from my selfe, to whom in other parts and myste∣ries of Art, be had bin so liber all.

He answered,

That the true way of Art is not by Instruments, but by Demonstration: and that it is a prepo∣sterous course of vulgar Teachers, to begin with Instruments, and not with the Sciences, and so in-stead of Artists, to make their Schol∣lers only doers of tricks, and as it were Iuglers: to the despite of Art, losse of precious time, and betraying of willing and industrious wits, vnto ignorance, and idlenesse. That the vse of Instru∣ments is indeed excellent, if a man be an Artist: but contemptible, being set and opposed to Art. And lastly, that he meant to commend to me, the skill of Instruments, but first he would haue me well instructed in the Sciences.

He also shewed me many notes, and Rules for the vse of those circles, and of his Horizontall Instrument, (which he had proiected about 30 yeares before) the most part written in Latine. All which I ob∣tained of him leaue to translate into English, and make publique, for the vse, and benefit of such as were studious, & louers of these excellent Sciences.

Which thing while I with mature, and diligent care (as my occasions would giue me leaue) went about to doe: another to whom the Author in a louing confidence discouered this intent, vsing

more hast then good speed, went about to preocu∣pate; of which vntimely birth, and preuenting (if not circumuenting) forwardnesse, I say no more: but aduise the studious Reader, onely so farre to trust, as he shal be sure doth agree to truth & Art.

And thus most noble Sir, without any brauing flourishes, or needlesse multiplying of tautolo∣gized and erroneous praecepts, in naked truth, and in the modest simplicity, of the Author himselfe (whose knowne skill in the whole Systeme of Ma∣thematicall learning, will easily free him from the suspicion of hauing the way made for him, and the subiect vnuailed, to help his sight) I haue not∣withstanding vnder the protection of your courte∣ous fauour, and learned iudgement, persisted in my long conceiued purpose, of presenting this tractate to the publique view, and light. Wishing withall vnto you encrease of deserued honor, and happines.

May the 1. 1632.

By the honourer and admirer of your Worthines, WILLIAM FORSTER.