General acceptance has been accorded to Oughtred’s symbol ×. The first printed appearance of this symbol for multiplication in 1618 in the form of the letter x hardly explains its real origin. The author of the “Appendix” (be he Oughtred or someone else) may not have used the letter x at all, but may have written the cross ×, called the St. Andrew’s cross, while the printer, in the absence of any type accurately representing that cross, may have substituted the letter x in its place. The hypothesis that the symbol × of multiplication owes its origin to the old habit of using directed bars to indicate that two numbers are to be combined, as for instance in the multiplication of 23 and 34, thus,
| 2 | 3 | × | 3 | 4 |
| 7 | 8 | 2 |
has been advanced by two writers, C. Le Paige[138] and Gravelaar.[139] Bosmans is more inclined to the belief that Oughtred adopted the symbol somewhat arbitrarily, much as he did the numerous symbols in his Elementi decimi Euclidis declaratio.[140]
Le Paige’s and Gravelaar’s theory finds some support in the fact that the cross ×, without the two additional vertical lines shown above, occurs in a commentary published by Oswald Schreshensuchs[141] in 1551, where the sign is written between two factors placed one above the other.
CHAPTER V
OUGHTRED’S IDEAS ON THE TEACHING OF MATHEMATICS
GENERAL STATEMENT
Nowhere has Oughtred given a full and systematic exposition of his views on mathematical teaching. Nevertheless, he had very pronounced and clear-cut ideas on the subject. That a man who was not a teacher by profession should have mature views on teaching is most interesting. We gather his ideas from the quality of the books he published, from his prefaces, and from passages in his controversial writing against Delamain. As we proceed to give quotations unfolding Oughtred’s views, we shall observe that three points receive special emphasis: (1) an appeal to the eye through suitable symbolism; (2) emphasis upon rigorous thinking; (3) the postponement of the use of mathematical instruments until after the logical foundations of a subject have been thoroughly mastered.