made it the standard for pure mathematics as well. Descartes trumpeted the
news that mathematics has an infallible discovery-making method. Not sur-
prisingly, the network around him pushed rapidly into still further advances
in mathematics. Along with this spread the belief that science would follow
the same path.
The Scientific Revolution
If by scientific revolution we mean the invention of the techniques of rapid
discovery making, the scientific revolution came later than the mathematical
revolution. From the early to mid-1500s we can speak of a quickening pace
of innovation. In astronomy, Copernicus drafted his heliocentric system in
1514, finished it in 1530, and gradually publicized it over the next 13 years.
But it was another 50 years before Brahe’s intensive observations, and his
assistant Kepler formulated the laws of planetary motion only in 1609. There
was no consensus in astronomy in the 1500s, nor was there a rapid and
sustained movement of the research front. As an astronomer, Copernicus was
not unlike other medieval thinkers. Oresme in the 1350s, as well as other
medievals, had raised the possibility of the earth moving in space; so did
Cusanus. Regiomontanus foreshadowed Copernicus’s work in many respects,
elaborating trigonometry and proposing before his early death to reform
astronomy, possibly with a heliocentric model (Boyer, 1985: 304). As an
account of the observables, Copernicus’s model was not superior to Ptolemy’s
geocentric system; many professional astronomers were unconvinced on tech-
nical grounds. Without the takeoff of sustained developments in the next
century, Copernicus might well have been a forgotten late medieval figure in
the same category as Oresme or, in the Islamic world, al-Tusi.
Although we cannot speak of scientific revolution during the 1500s in the
strong sense, there were several parallel strands of activity building up. In
addition to astronomy, there were innovations in medical physiology. Servetus,
at the Paris medical faculty in the 1540s, put forward a new theory of the
circulation of the blood; his colleague Vesalius, moving on to the medical
faculty at Padua, published empirical support in 1543 and 1555. A network
of Padua professors carried on the doctrine, although empirical work was
broken off until around 1600, when Fabricus discovered valves in the veins;
his pupil William Harvey in turn performed dissections of many species of
animals and experiments with tourniquets, and between 1616 and 1628 for-
mulated a mechanical theory of circulation in which the heart acted as pump.
Again we have an intermittent buildup culminating in the early 1600s; in this
case the method was largely empirical rather than mathematical.
A third front comprises work in chemistry, including the “occult philoso-
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