Hence from the forme, I have called it a Ring, and Grammelogia by annoligie of a Lineary speech; which Ring, if it were projected in the convex unto two yards Diameter, or thereabouts, and the line Decupled, it would worke Trigonometrie unto seconds, and give proportionall numbers unto six places only by an ocular inspection, which would compendiate Astronomicall calculations, and be sufficient for the Prosthaphaeresis of the Motions: But of this as God shall give life and ability to health and time. The unnumbered page following page 22 contains the patent and copyright on the instrument and book: Whereas Richard Delamain, Teacher of Mathematicks, hath presented vnto Vs an Instrument called Grammelogia, or The Mathematicall Ring, together with a Booke so intituled, expressing the use thereof, being his owne Invention; we of our Gracious and Princely favour have granted unto the said Richard Delamain and his Assignes, Privilege, Licence, and Authority, for the sole Making, Printing and Selling of the said Instrument and Booke: straightly forbidding any other to Make, Imprint, or Sell, or cause to be Made, or Imprinted, or Sold, the said Instrument or Booke within any our Dominions, during the space of ten yeares next ensuing the date hereof, upon paine of Our high displeasure. Given under our hand and Signet at our Palace of Westminster, the fourth day of January, in the sixth yeare of our Raigne. Delamain’s later designs, and directions for using his instruments In the Appendix of Grammelogia III, on page 52 is given a description of an instrument promised near the end of Grammelogia I: That which I have formerly delivered hath been onely upon one of the Circles of my Ring, simply concerning Arithmeticall Proportions, I will by way of Conclusion touch upon some uses of the Circles, of Logarithmall Sines, and Tangents, which are placed on the edge of both the moveable and fixed Circles of the Ring in respect of Geometricall Proportions, but first of the description of these Circles. First, upon the side that the Circle of Numbers is one, are graduated on the edge of the moveable, and also on the edge of the fixed the Logarithmall Sines, for if you bring 1. in the moveable amongst the Numbers to 1. in the fixed, you may on the other edge of the moveable and fixed see the sines noted thus 90. 90. 80. 80. 70. 70. 60. 60. &c. unto 6.6. and each degree subdivided, and then over the former divisions and figures 90. 90. 80. 80. 70. 70. &c. you have the other degrees, viz. 5. 4. 3. 2. 1. each of those divided by small points. Secondly, (if the Ring is great) neere the outward edge of this side of the fixed against the Numbers, are the usuall divisions of a Circle, and the points of the Compasse: serving for observation in Astronomy, or Geometry, and the sights belonging to those divisions, may be placed on the moveable Circle.