Florian Cajori - On the History of Gunter's Scale and the Slide Rule during the Seventeenth Century

R. Delamain, The Making, Description, and Use of a small portable Instrument.. called a Horizontall Quadrant , etc., London, 1631.

Oughtred’s description of his circular slide rule of 1632 and his rectilinear slide rule of 1633, as well as a drawing of the circular slide rule, are reproduced in Cajori’s History of the Slide Rule , Addenda, pp. ii-vi.

The full title of the Grammelogia I is as follows:

Gram̄elogia | or, | The Mathematicall Ring. | Shewing (any reasonable Capacity that hath | not Arithmeticke) how to resolve and worke | all ordinary operations of Arithmeticke. | And those which are most difficult with greatest | facilitie: The extraction of Roots, the valuation of | Leases, &c. The measuring of Plaines | and Solids. | With the resolution of Plaine and Sphericall | Triangles. | And that onely by an Ocular Inspection, | and a Circular Motion. | Naturae secreta tempus aperit. | London printed by John Haviland, 1630.

Grammelogia III is the same as Grammelogia I , except for the addition of an appendix, entitled:

De la Mains | Appendix | Vpon his | Mathematicall | Ring. Attribuit nullo (praescripto tempore) vitae | vsuram nobis ingeniique Deus. | London, |

.. The next line or two of this title-page which probably contained the date of publication, were cut off by the binder in trimming the edges of this and several other pamphlets for binding into one volume.

Grammelogia IV has two title pages. The first is Mirifica Logarithmoru’ Projectio Circularis . There follows a diagram of a circular slide rule, with the inscription within the innermost ring: Nil Finis, Motvs, Circvlvs vllvs Habet . The second title page is as follows:

Grammelogia | Or, the Mathematicall Ring. | Extracted from the Logarythmes, and projected Circular: Now published in the | inlargement thereof unto any magnitude fit for use: shewing any reason- | able 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 extracti- | 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, Horologographie, Geographie | Fortification, Navigation, Astronomie, &c. | And that onely by an ocular inspection, and a Circular motion, Invented and first published, by R. Delamain, Teacher, and Student of the Mathematicks. | Naturae secreta tempus aperit. |

There is no date. There follows the diagram of a second circular slide rule, with the inscription within the innermost ring: Typus proiectionis Annuli adaucti vt in Conslusione Lybri praelo commissi, Anno 1630 promisi . There are numerous drawings in the Grammelogia , all of which, excepting the drawings of slide rules on the engraved title-pages of Grammelogia IV and V , were printed upon separate pieces of paper and then inserted by hand into the vacant spaces on the printed pages reserved for them. Some drawings are missing, so that the Bodleian Grammelogia IV differs in this respect slightly from the copy in the British Museum and from the British Museum copy of Grammelogia V .