William Oughtred: A Great Seventeenth-Century Teacher of Mathematics — John Shaqi
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
Here we wish to give our reasons for our belief that Oughtred is the
author of an anonymous tract on the use of logarithms and on a method of
logarithmic interpolation which, as previously noted, appeared as an
“Appendix” to Edward Wright’s translation into English of John Napier’s
Descriptio, under the title, A Description of the Admirable Table of
Logarithmes, London, 1618. The “Appendix” bears the title, “An Appendix
to the Logarithmes, showing the practise of the Calculation of Triangles,
and also a new and ready way for the exact finding out of such lines and
Logarithmes as are not precisely to be found in the Canons.” It is an
able tract. A natural guess is that the editor of the book, Samuel
Wright, a son of Edward Wright, composed this “Appendix.” More probable
is the conjecture which (Dr. J. W. L. Glaisher informs me) was made by
Augustus De Morgan, attributing the authorship to Oughtred. Two reasons
in support of this are advanced by Dr. Glaisher, the use of x in the
“Appendix” as the sign of multiplication (to Oughtred is generally
attributed the introduction of the cross × for multiplication in 1631),
and the then unusual designation “cathetus” for the vertical leg of a
right triangle, a term appearing in Oughtred’s books. We are able to
advance a third argument, namely, the occurrence in the “Appendix” of
(S*) as the notation for sine complement (cosine), while Seth Ward, an
early pupil of Oughtred, in his Idea trigonometriae demonstratae, Oxford,
1654, used a similar notation (S’). It has been stated elsewhere that
Oughtred claimed Seth Ward’s exposition of trigonometry as virtually his
own. Attention should be called also to the fact that, in his
Trigonometria, p. 2, Oughtred uses (’) to designate 180°-angle.
Dr. J. W. L. Glaisher is the first to call attention to other points of
interest in this “Appendix.” The interpolations are effected with the aid
of a small table containing the logarithms of 72 sines. Except for the
omission of the decimal point, these logarithms are natural
logarithms—the first of their kind ever published. In this table we find
log 10=2302584; in modern notation, this is stated, log_e 10=2.302584.
The first more extended table of natural logarithms of numbers was
published by John Speidell in the 1622 impression of his New Logarithmes,
which contains, besides trigonometric tables, the logarithms of the
numbers 1-1000.
Public-domain text, read in full here on John Shaqi.
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