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
This much is certain, the Trigonometry bears the impress characteristic
of Oughtred. Like all his mathematical writings, the book was very
condensed. Aside from the tables, the text covered only 36 pages. Plane
and spherical triangles were taken up together. The treatise is known in
the history of trigonometry as among the very earliest works to adopt a
condensed symbolism so that equations involving trigonometric functions
could be easily taken in by the eye. In the work of 1657, contractions
are given as follows: s=sine, t=tangent, se=secant, s co=cosine (sine
complement), t co=cotangent, se co=cosecant, log=logarithm, Z cru=sum of
the sides of a rectangle or right angle, X cru=difference of these sides.
It has been generally overlooked by historians that Oughtred used the
abbreviations of trigonometric functions, named above, a quarter of a
century earlier, in his Circles of Proportion, 1632, 1633. Moreover, he
used sometimes also the abbreviations which are current at the present
time, namely sin=sine, tan=tangent, sec=secant. We know that the Circles
of Proportion existed in manuscript many years before they were
published. The symbol sv for sinus versus occurs in the Clavis of 1631.
The great importance of well-chosen symbols needs no emphasis to readers
of the present day. With reference to Oughtred’s trigonometric symbols.
Augustus De Morgan said:
This is so very important a step, simple as it is, that Euler is justly
held to have greatly advanced trigonometry by its introduction. Nobody
that we know of has noticed that Oughtred was master of the
improvement, and willing to have taught it, if people would have
learnt.[41]
We find, however, that even Oughtred cannot be given the whole credit in
this matter. By or before 1631 several other writers used abbreviations
of the trigonometric functions. As early as 1624 the contractions sin for
sine and tan for tangent appear on the drawing representing Gunter’s
scale, but Gunter did not use them in his books, except in the drawing of
his scale.[42] A closer competitor for the honor of first using these
trigonometric abbreviations is Richard Norwood in his Trigonometrie,
London, 1631, where s stands for sine, t for tangent, sc for sine
complement (cosine), tc for tangent complement (cotangent), and sec for
secant. Norwood was a teacher of mathematics in London and a well-known
writer of books on navigation. Aside from the abbreviations just cited
Norwood did not use nearly as much symbolism in his mathematics as did
Oughtred.
Public-domain text, read in full here on John Shaqi.
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