Wherefore, that I might more clearly behold the things themselves, I uncasing the Propositions and Demonstrations out of their covert of words, designed them in notes and species appearing to the very eye. After that by comparing the divers affections of Theorems, inequality, proportion, affinity, and dependence, I tryed to educe new out of them. It was this motive which led him to introduce the many abbreviations in algebra and trigonometry to which reference has been made in previous pages. The pedagogical experience of recent centuries has indorsed Oughtred’s view, provided of course that the pupil is carefully taught the exact meaning of the symbols. There have been and there still are those who oppose the intensive use of symbolism. In our day the new symbolism for all mathematics, suggested by the school of Peano in Italy, can hardly be said to be received with enthusiasm. In Oughtred’s day symbolism was not yet the fashion. To be convinced of this fact one need only open a book of Edmund Gunter, with whom Oughtred came in contact in his youth, or consult the Principia of Sir Isaac Newton, who flourished after Oughtred. The mathematical works of Gunter and Newton, particularly the former, are surprisingly destitute of mathematical symbols. The philosopher Hobbes, in a controversy with John Wallis, criticized the latter for that “Scab of Symbols,” whereupon Wallis replied: I wonder how you durst touch M. Oughtred for fear of catching the Scab. For, doubtlesse, his book is as much covered over with the Scab of Symbols, as any of mine. . . . . As for my Treatise of Conick Sections, you say, it is covered over with the Scab of Symbols, that you had not the patience to examine whether it is well or ill demonstrated.[142] Oughtred maintained his view of the importance of symbols on many different occasions. Thus, in his Circles of Proportion, 1632, p. 20: This manner of setting downe Theoremes, whether they be Proportions, or Equations, by Symboles or notes of words, is most excellent, artificiall, and doctrinall. Wherefore I earnestly exhort every one, that desireth though but to looke into these noble Sciences Mathematicall, to accustome themselves unto it: and indeede it is easie, being most agreeable to reason, yea even to sence. And out of this working may many singular consectaries be drawne: which without this would, it may be, for ever lye hid. RIGOROUS THINKING AND THE USE OF INSTRUMENTS The author’s elevated concept of mathematical study as conducive to rigorous thinking shines through the following extract from his preface to the 1647 Clavis: