Stevin: 1548-1620

Decimal Fractions

Although he did not invent decimals (they had been used
by the Arabs and the Chinese long before Stevin's time) he did introduce
their use in European mathematics. His notation was to be taken up by __Clavius__
and __Napier__. Stevin states that the
universal introduction of decimal coinage, measures and weights would only
be a matter of time.

Stevin's notion of a real number was accepted by essentially all later scientists. Particularly important was Stevin's acceptance of negative numbers but he did not accept the 'new' imaginary numbers and this was to hold back their acceptance.

Napier: 1550-1617

Uses decimals to compute first tables of logarithms,
based on ratios, not exponents.

Briggs:1561-1630

At their meeting __Napier__
suggested to Briggs the new tables should be constructed with base 10 and
with log 1 = 0. Briggs wrote that __Napier__
proposed (see for example [1]):-

Briggs's first work on logarithms *Logarithmorum Chilias
Prima* was published in London in 1617. The recent death of __Napier__
is referred to in the preface as is Briggs reason to publish that work,
namely:-

The completed tables were printed at Gouda, in the Netherlands,
in 1628 in an edition by __Vlacq__ in which
__Vlacq__ had added the logarithms of the
natural numbers from 20,000 to 90,000. The tables were also published in
London in 1633 under the title of *Trigonometria Britannica.* The
printing of the London edition took place after Briggs had died but he
had asked his friend Henry __Gellibrand__
to look after the project on his behalf. __Gellibrand__
was professor of astronomy at Gresham College and was particularly interested
in applications of logarithms to trigonometry. He therefore added a preface
of his own on applications of logarithms to both plane trigonometry and
to spherical trigonometry.

Descartes: 1596-1650

Creates an algebra for measuring and analyzing lengths... analytic geometry.

** x, x^{2 }, and x^{3}
and higher powers of x can all represent (measure) lengths**
[as well as areas and volumes].

Newton1643-1727/ Mercator 1620-1687:

Computation of Hyperbolic logarithms using decimals.

Newton and Leibniz 1646-1716:

use "limits and functions and numbers" with level of
rigor typical of that period.