William Oughtred: A Great Seventeenth-Century Teacher of MathematicsCajori, Florian
History
William Oughtred: A Great Seventeenth-Century Teacher of Mathematics
Cajori, Florian
Mathematicians -- Biography; Mathematics -- Study and teaching -- History -- 17th century; Oughtred, William, 1575-1660
An idea of Oughtred’s influence upon mathematical thought and teaching
can be obtained from the spread of his symbolism. This study indicates
that the adoption was not immediate. The earliest use that we have been
able to find of Oughtred’s notation for proportion, A.B::C.D, occurs
nineteen years after the Clavis mathematicae of 1631. In 1650 John Kersey
brought out in London an edition of Edmund Wingates’ Arithmetique made
easie, in which this notation is used. After this date publications
employing it became frequent, some of them being the productions of
pupils of Oughtred. We have seen it in Vincent Wing (1651),[77] Seth Ward
(1653),[78] John Wallis (1655),[79] in “R. B.,” a schoolmaster in
Suffolk,[80] Samuel Foster (1659),[81] Jonas Moore (1660),[82] and Isaac
Barrow (1657).[83] In the latter part of the seventeenth century
Oughtred’s notation, A.B::C.D, became the prevalent, though not
universal, notation in Great Britain. A tremendous impetus to their
adoption was given by Seth Ward, Isaac Barrow, and particularly by John
Wallis, who was rising to international eminence as a mathematician.
In France we have noticed Oughtred’s notation for proportion in
Franciscus Dulaurens (1667),[84] J. Prestet (1675),[85] R. P. Bernard
Lamy (1684),[86] Ozanam (1691),[87] De l’Hospital (1696),[88] R. P. Petro
Nicolas (1697).[89]
In the Netherlands we have noticed it in R. P. Bernard Lamy (1680),[90]
and in an anonymous work of 1690.[91] In German and Italian works of the
seventeenth century we have not seen Oughtred’s notation for proportion.
In England a modified notation soon sprang up in which ratio was
indicated by two dots instead of a single dot, thus A:B::C:D. The reason
for the change lies probably in the inclination to use the single dot to
designate decimal fractions. W. W. Beman pointed out that this modified
symbolism (:) for ratio is found as early as 1657 in the end of the
trigonometric and logarithmic tables that were bound with Oughtred’s
Trigonometria.[92] It is not probable, however, that this notation was
used by Oughtred himself. The Trigonometria proper has Oughtred’s
A.B::C.D throughout. Moreover, in the English edition of this
trigonometry, which appeared the same year, 1657, but subsequent to the
Latin edition, the passages which contained the colon as the symbol for
ratio, when not omitted, are recast, and the regular Oughtredian notation
is introduced. In Oughtred’s posthumous work, Opuscula mathematica
hactenus inedita, 1677, the colon appears quite often but is most likely
due to the editor of the book.
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