362
IV - Powers, Exponentials, Logarithms, Trigonometric Functions
Their diffusion to London occurred with the greatest of ease 21 • On his
death in 1579, a top-flight London merchant and financier, Sir Thomas Gresham, bequeathed the profits of his shops to the City and to the Mercers'
Company to provide an endowment for a college to be administered by the
merchants, and where the teaching, open to all, would be conducted on principles diametrically opposed to those of Oxford and of Cambridge. He certainly
did not forget a chair of Divinity, clearly the most prestigious, intended to
combat papist errors or heresies; Napier himself, author of a very popular
book on the Apocalypse, had proclaimed the Pope none other than the Antichrist and, when the Invincible Armada menaced England, suggested purely
theoretical tanks and submarines to the Queen; the North Sea was more efficacious. But apart from several courses in Latin intended for foreigners, most
of the rest were in English and oriented towards practical or useful themes:
navigation, geography, cartography, practical arithmetic and geometry, modern theories of medicine, juridical problems. The first professor of geometry
at Gresham, from 1594 to 1620, was the very Henry Briggs (1561-1631) who
popularised decimal numbers. Like Edward Wright, he had a close relationship with William Gilbert, the initiator of the first scientific, i.e. experimental,
studies on magnetism; Briggs calculated the first tables of magnetic declination while artisans of the same circle invented the instruments. For his part,
Wright explained the theory and use of the maps which the Flamand Gerard
Mercator published from 1538, and wrote a book entitled Certaine Errours
in Navigation detected; Briggs wrote a Treatise on the North- West Passage
and navigators paid homage to him (maybe ironically) by baptising Brigges
his M athematickes an isle of the "passage" which, they were sure, joined the
Atlantic to the Pacific by the North (correct, but a vast programme of exploration for the time). Briggs was the first to recognise the interest of Napier's
logarithms and immediately taught them at Gresham College. All this, as one
sees, is quite far from pure mathematics, but contributed no less strongly to
launch the scientific movement in England which led to the creation of the
Royal Society. Add that the calculation of log tables poses problems of interpolation very close to elementary differential calculus, and even, if one
believes some authors, to the binomial formula for exponent 1/2.
As to the mathematicians, they slowly discovered the interest of log22 for
analysis. The first almost to have seen - although he did not say it explicitly
- the relation between the area of the hyperbola and the log was the Belgian
Jesuit Gregoire de Saint-Vincent in an Opus geometricum quadraturae circuli
and sectionum coni of 1647 which claims above all to resolve the quadrature
of the circle. He shows essentially that if, in the hyperbola of figure 1, the
21 For what follows, see the superb book of Christopher Hill, Intellectual Origins
of the English Revolution (OUP, 1965 or Panther Books, 1972).
22 For what follows, see D. T. Whiteside, Patterns of Mathematical Thought in the
later Seventeenth Century (Archive for the History of Exact Sciences, Vol. 1,
1961, pp. 179-388); but read with care, for at this date the author still has some
problems with the mathematics ...
IV - Powers, Exponentials, Logarithms, Trigonometric Functions
Their diffusion to London occurred with the greatest of ease 21 • On his
death in 1579, a top-flight London merchant and financier, Sir Thomas Gresham, bequeathed the profits of his shops to the City and to the Mercers'
Company to provide an endowment for a college to be administered by the
merchants, and where the teaching, open to all, would be conducted on principles diametrically opposed to those of Oxford and of Cambridge. He certainly
did not forget a chair of Divinity, clearly the most prestigious, intended to
combat papist errors or heresies; Napier himself, author of a very popular
book on the Apocalypse, had proclaimed the Pope none other than the Antichrist and, when the Invincible Armada menaced England, suggested purely
theoretical tanks and submarines to the Queen; the North Sea was more efficacious. But apart from several courses in Latin intended for foreigners, most
of the rest were in English and oriented towards practical or useful themes:
navigation, geography, cartography, practical arithmetic and geometry, modern theories of medicine, juridical problems. The first professor of geometry
at Gresham, from 1594 to 1620, was the very Henry Briggs (1561-1631) who
popularised decimal numbers. Like Edward Wright, he had a close relationship with William Gilbert, the initiator of the first scientific, i.e. experimental,
studies on magnetism; Briggs calculated the first tables of magnetic declination while artisans of the same circle invented the instruments. For his part,
Wright explained the theory and use of the maps which the Flamand Gerard
Mercator published from 1538, and wrote a book entitled Certaine Errours
in Navigation detected; Briggs wrote a Treatise on the North- West Passage
and navigators paid homage to him (maybe ironically) by baptising Brigges
his M athematickes an isle of the "passage" which, they were sure, joined the
Atlantic to the Pacific by the North (correct, but a vast programme of exploration for the time). Briggs was the first to recognise the interest of Napier's
logarithms and immediately taught them at Gresham College. All this, as one
sees, is quite far from pure mathematics, but contributed no less strongly to
launch the scientific movement in England which led to the creation of the
Royal Society. Add that the calculation of log tables poses problems of interpolation very close to elementary differential calculus, and even, if one
believes some authors, to the binomial formula for exponent 1/2.
As to the mathematicians, they slowly discovered the interest of log22 for
analysis. The first almost to have seen - although he did not say it explicitly
- the relation between the area of the hyperbola and the log was the Belgian
Jesuit Gregoire de Saint-Vincent in an Opus geometricum quadraturae circuli
and sectionum coni of 1647 which claims above all to resolve the quadrature
of the circle. He shows essentially that if, in the hyperbola of figure 1, the
21 For what follows, see the superb book of Christopher Hill, Intellectual Origins
of the English Revolution (OUP, 1965 or Panther Books, 1972).
22 For what follows, see D. T. Whiteside, Patterns of Mathematical Thought in the
later Seventeenth Century (Archive for the History of Exact Sciences, Vol. 1,
1961, pp. 179-388); but read with care, for at this date the author still has some
problems with the mathematics ...