Grammelogia, or, The mathematicall ring extracted from the logarythmes, and projected circular : now published in th[e] inlargement thereof unto any magnitude fit for use, shewing any reasonable capacity that hath not arithmeticke, how to resolve and worke, all ordinary operations of arithmeticke : and those that are most difficult with greatest facilitie, the extract on of rootes, the valuation of leases, &c. the measuring of plaines and solids, with the resolution of plaine and sphericall triangles applied to the practicall parts of geometrie, horo[l]ogographic, geographie, fortification, navigation, astronomie, &c, and that onely by an ocular inspection, and a circular motion / invented an[d] first published, by R. Delamain, teacher, and student of the mathematicks.

To the Reader.

NOw by way of advertisment to the Reader, in this Circular pro∣jection of Logarithmes, you may make use of the Projection of the Circles of the Ring upon a Plaine, having the feet of a paire of Compasses (but so that they be flat) to move on the Center of that Plaine, and those feet to open and shut as a paire of Compasses (which some call a Sector abusively) now if the feet bee opened to any two termes or numbers in that Proj••ction, then may you move the first foot to the third number, and the other foot shall give the Answer; and so moving those feet along Circularly, as one foot passeth by any number in the Projection, the other foot shall shew his proportionall number in that Projection; it hath pleased some to make use of this way. But in this there is a double labour in respect of that of the Ring, the one in fitting those feet unto the numbers assigned, and the other by moving them about, in which a man can hardly accom∣date the Instrument with one hand, and expresse the Proportionals in writing with the other. By the Ring you need not but bring one num∣ber to another, and right against any other number is his Answer without any such motion. But this or the former I leave to such as shall best affect them, only the latter for Construction I account most facile, and for expedition most excellent, and upon that I write, shew∣ing some uses of those Circles amongst themselves, and conjoyned with others, in the resolution of such Questions which are ordinarily practised in Astronomy, Horolographie, in plaine Triangles applyed to Dimensions, Navigation, Fortification, &c. as a preparative ground for a more ample worke, and as a declaration of the admirable, and excellent use of this Ring in expedition, and facility. But before I come to Construction, I have thought it convenient by way introdu∣ction, to examine the truth of the graduation of those Circles which may be from the ensuing Tables and directions.