Lenses and Waves

1653 - TRACTATUS 41
equation. 111 Despite his involvement in practical matters of telescopes Halley,
like Barrow, did not further apply his finding to the effect of lenses. His
principal goal seems to have been to supplement Molyneux’ theory of focal
distances by means of giving “An instance of the excellence of modern
algebra, …” 112 All in all, the telescope rarely directed the dioptrical studies
undertaken by mathematicians.
Kepler is rightly regarded as the founder of seventeenth-century
geometrical optics, yet it was Paralipomena rather than Dioptrice that
constituted the starting-point for later studies. Similarly, Descartes’ La
Géométrie was the starting-point for later studies of aplanatic surfaces rather
than La Dioptrique. I find it remarkable that an instrument that had
revolutionized astronomy was ignored by students of geometrical optics in
the same way as spectacles had been previously. Kepler alone had, right
upon its invention, insisted that a mathematical understanding of the
telescope was needed for its use in observation, and Huygens was the only
one to take the instruction to heart. His approach was that of a
mathematician, yet he applied his mathematical abilities to a practical
question: understanding the working of the telescope. In Tractatus, he used
the sine law to derive an exact and general theory of the properties of
spherical lenses and their configurations. It remains to be seen, however,
whether such a mathematical theory of the telescope was really of any use.
Tractatus remained unpublished, those interested had to do with Dioptrice.
2.2.3 THE NEED FOR THEORY
Dioptrice had arisen from Kepler’s conviction that, in order to make reliable
observations, and astronomical instrument should be understood precisely.
The mathematicians I have discussed in the preceding section did not follow
his lead. Even Descartes and Newton, who proposed innovations in
telescope design, did not bother to elaborate theories of the way telescopes
produce sharp, magnified images. Maybe this was so because they, like the
others mathematicians that have been discussed, did were not much involved
in telescopic observation. Could the case be different for the mathematicians
who were, the observers? We have seen that Galileo, the most renowned
telescopist, was not really interested in mathematical questions of dioptrics.
He applied himself rather to practical matters of the manufacture and
improvement of the telescope. It does not seem that Galileo had to invoke
dioptrical arguments to defend the reality of telescopic observations, at least
not arguments from the mathematical tradition of perspective and Kepler. 113
To be sure, as a pioneer in astronomical telescopy Galileo was confronted
with suspicions about the reality of heavenly things seen through the tube,
but these soon wore off. Likewise, telescopists like Scheiner and Hevelius in
111
Halley, “Instance”, 960.
112
See: Albury, “Halley, Huygens, and Newton”, 455-457.
113
Galileo, Sidereus nuncius, 112-113 and 92-93 (Van Helden’s conclusion). See Dupré, Galileo and the
telescope, 175-178.