There is yet another way of disposing of this Line of Proportion, by having one Line of the full length of the Ruler, and another Line of the same Radius broken in two parts between 3 and 4; so that in working your Compasses never go off of the Line: This is one of the best contrivances, but here Compasses must be used. These are all the Contrivances that I have hitherto seen of these Lines: That which I here speak of, and will shew how to use, is only two Lines of one and the same Radius, being set upon a plain Ruler of any length (the larger the better) having the beginning of one Line, at the end of the other, the divisions of each Line being set so close together, that if you find any number upon one of the Lines, you may easily see what number stands against it on the other Line. This is all the Variation. . . .
Example 1. If a Board be 1 Foot 64 parts broad, how much in length of that Board will make a Foot Square? Look upon one of your Lines (it matters not which) for 1 Foot 64 parts, and right against it on the other Line you shall find 61; and so many parts of a Foot will make a Foot square of that Board.
This contrivance solves the equation 1.64x=1, yielding centesimal parts of a foot.
James Atkinson[15] speaks of “Gunter’s scale” as “usually of Boxwood . . . commonly 2 ft. long, 1½ inch broad” and “of two kinds: long Gunter or single Gunter, and the sliding Gunter. It appears that during the seventeenth century (and long after) the Gunter’s scale was a rival of the slide rule.
III. RICHARD DELAMAIN’S GRAMMELOGIA
We begin with a brief statement of the relations between Oughtred and Delamain. At one time Delamain, a teacher of mathematics in London, was assisted by Oughtred in his mathematical studies. In 1630 Delamain published the Grammelogia, a pamphlet describing a circular slide rule and its use. In 1631 he published another tract, on the Horizontall Quadrant.[16] In 1632 appeared Oughtred’s Circles of Proportion[17] translated into English from Oughtred’s Latin manuscript by another pupil, William Forster, in the preface of which Forster makes the charge (without naming Delamain) that “another . . . went about to pre-ocupate” the new invention. This led to verbal disputes and to the publication by Delamain of several additions to the Grammelogia, describing further designs of circular slide rules and also stating his side of the bitter controversy, but without giving the name of his antagonist. Oughtred’s Epistle was published as a reply. Each combatant accuses the other of stealing the invention of the circular slide rule and the horizontal quadrant.
The two title-pages of the edition of the Grammelogia in the British Museum in London which we have called “Grammelogia IV.”
Different editions or impressions
There are at least five different editions, or impressions, of the Grammelogia which we designate, for convenience, as follows:
Grammelogia I, 1630. One copy in the Cambridge University Library.[18]
Grammelogia II, I have not seen a copy of this.
Grammelogia III, One copy in the Cambridge University Library.[19]
Grammelogia IV, One copy in the British Museum, another in the Bodleian Library, Oxford.[20]
Grammelogia V, One copy in the British Museum.