Forster's 1632 Dedication to an Oughtred Book with Implications for Slide Rule History

Tom and Lu Wetmore

There has been debate over the invention of the slide rule for centuries.

Evidence that Wm. Oughtred was the inventor comes from the dedication Wm. Forster wrote for "The Circles of Proportion and the Horizontal Instrument," first published in 1632. The author on the title page is Forster, though in E.G.R. Taylor's "The Mathematical Practitioners of Tudor and Stewart England, 1486-1714", Oughtred is given author credit while Forster is listed as translator.

Here is the relevant quote from Forster's dedication, which places Oughtred's inventions back into the middle or late 1620s. Let me first point out that the Horizontal Instrument mentioned in the title IS NOT the linear slide rule. I have added a discussion after the quote to clarify that.

Start of quote:

"For being in the time of the long vacation 1630, in the country, at the house of the reverend, and my most worthy friend, and teacher, Mr. William Oughtred (to whose instruction I owe both my initiation, and whole progress in these sciences).

I upon occasion of speech told him of a ruler of numbers, sines and tangents, which one had bespoken to be made (such as is usually called Mr. Gunter’s Ruler) six feet long, to be used with a pair of beam-compasses.

He answered that was a poor invention, and the performance very troublesome: ‘But’, said he, ‘seeing you are taken with such mechanical ways of instruments, I will show you what devices I have had by me THESE MANY YEARS [my emphasis].’

AND FIRST, HE BROUGHT TO ME TWO RULERS OF THAT SORT, TO BE USED BY APPLYING ONE TO THE OTHER, WITHOUT ANY COMPASSES [my emphasis--this is in my opinion the origin story of the linear slide rule]; and after that he showed me those lines cast into a circle or ring, with another, moveable circle upon it.

I seeing the great expedience of both those ways, but especially of the latter, wherein it far excels any other instrument which has been known; told him, I wondered that he could so many years conceal such useful inventions, not only from the world, but from myself, to whom in other parts and mysteries of art, he had been so liberal.

He answered that the true way of art is not by instruments, but by demonstration; and that it is a preposterous course of vulgar teachers, to begin with instruments, and not with the sciences, and so instead of artists, to make their scholars only doers of tricks, and as it were jugglers; to the despite of art, loss of precious time, and betraying of willing and industrious wits, unto ignorance and idleness. That the use of instruments 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 have me well instructed in the sciences.

He also showed me many notes, and rules for the use of those circles, and of his horizontal instrument (which he had projected about 30 years before), the most part written in Latin. All which I obtained of him leave to translate into English, and make public, for the use, and benefit of such as were studious, and lovers of these excellent sciences."

End of quote.


The horizontal instrument mentioned in the book's title, and in the last part of the dedication, is NOT the "two rulers of that sort" mentioned earlier in the dedication. That is, the horizontal instrument is not a linear slide rule. However, the two rulers mentioned were a linear slide rule. The rulers were Gunter's rulers with the log scales of numbers, sines and tangents etched on them. I assume they had square cross-sections with a different scale on each face/edge. The horizontal instrument was an entirely different device that Oughtred had invented many years earlier that had nothing to do with logarithms. It was a tool with astronomical, navigational, and time keeping scales.

The dedication implies to me that at this early stage the circular slide rule was the dominant form. Much of the Oughtred/Delamain debate is based on differing designs for circular slide rules, and on which design is best, and who developed theirs first. When Oughtred showed Forster the "two rulers of that sort", he showed how calculation could be done by sliding two logarithmic rulers against one another without compasses, but he soon put those away and brought out his circular side rule, which is the form stressed thereafter.

I conclude that Oughtred did not think that the linear slide rule made from two Gunter's rulers was all that important. This might be hard for us sliderule fanatics to come to grips with, but I'm afraid it was true. Circular slide rules was where it was at for a long time.

It could be that Oughtred showing Forster how to slide two Gunter's rulers against one another was a very early demonstrations of how the future of linear sliderules would unfold. (I still contend that Gunter himself must have known his rulers could be used in this way.)

There exist examples of circular slide rules made by Oughtred (designed by him, fabricated by Elias Allen), but there are no linear slide rules I know of. I have pictures I can supply to those interested.

I believe this evidence points to Oughtred inventing the circular slide rule around 1627, and knowing at the same time that two Gunter's rulers could be used together without compasses.

Tom Wetmore

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