John Wallis

“[Mathematics were] scarce looked upon as Academical studies but rather Mechanical... And among more than two hundred students (at that time) in our college, I do not know of any two (perhaps not any) who had more of Mathematicks than I, (if so much) which was then but little; and but very few, in that whole university. For the study of Mathematicks was at that time more cultivated in London than in the universities.”

“Mathematicks were not, at the time, looked upon as Accademical Learning, but the business of Traders, Merchants, Seamen, Carpenters, land-measurers, or the like; or perhaps some Almanak-makers in London. And of more than 200 at that time in our College, I do not know of any two that had more of Mathematicks than myself, which was but very little; having never made it my serious studie (otherwise than as a pleasant diversion) till some little time before I was designed for a Professor in it.”

“You may find this work (if I judge rightly) quite new. For I see no reason why I should not proclaim it; nor do I believe that others will take it wrongly. ...it teaches all by a new method, introduced by me for the first time into geometry, and with such clarity that in these more abstruse problems no-one (as far as I know) has used...”

“This method of mine takes its beginnings where Cavalieri ends his Method of indivisibles. ...for as his was the Geometry of indivisibles, so I have chosen to call my method the Arithmetic of infinitesimals.”

“Around 1650 I came across the mathematical writings of Torricelli, where among other things, he expounds the geometry of indivisibles of Cavalieri. ...His method, as taught by Torricelli... was indeed all the more welcome to me because I do not know that anything of that kind was observed in the thinking of almost any mathematician I had previously met.”

“It was always my affectation even from a child, in all pieces of Learning or Knowledge, not merely to learn by rote, which is soon forgotten, but to know the grounds or reasons of what I learn; to inform my Judgement, as well as furnish my Memory; and thereby, make a better Impression on both.”

“I made no Scruple of diverting (from the common Road of Studies then in fashion) to any part of Useful Learning. Presuming, that Knowledge is no Burthen; and, if of any part thereof I should afterwards have no occasion to make use, it would at least do me no hurt; And what of it l might or might not have occasion for, I could not then foresee.”

“The Occasion of that Assembly was this; The Parliament which then was, (or the prevailing part of them,) were ingaged in a War with the King. ...The Issue of which War, proved very different from what was said to be at first intended. As is usual in such cases; the power of the sword frequently passing from hand to hand and those who begin a War, not being able to foresee where it wil end.”

“Thus in Compliance with your repeated desires, I have given you a short account of divers passages of my life, 'till I have now come to more than fourscore years of age. How well I have acquitted my self in each, is for others rather to say, than for Your friend and servant John Wallis. Oxford January 29. 1696, 7.”

“Upon this Occasion many Methods have been invented of secret Writing, or Writing in Cipher, a Thing heretofore scarce known to any but the Secretaries of Princes, or others of like Condition; but of late Years, during our Commotions and civill Wars in England, grown very common and familiar, so that now there is scarce a Person of Quality, but is more or lesse acquainted with it, and doth as there is Occasion, make use of it.”

“If any ask, with what Confidence I durst adventure upon a Task so unusuall, as interpreting of Letters committed to Cipher; I shall only give this plain Account thereof.”