1 The Birth of Science - MSRI

328 11. The Age-Long Recovery
that could account for the motion of planets and the more elongated
motion of comets. These were found in classical authors (Seneca, Pliny,
Vitruvius) but also, as we shall see, in writings stemming from the neo-
Pythagorean and Hermetic traditions of late antiquity.
– Some testimonia on an ancient theory of tides based on gravitational
interaction, whose memory had not been totally obliterated. 130
But all these prerequisites were not enough, since the technical tools
provided by the first set were insufficient for mathematizing the information
in the second. Two more elements were essential: a quantitative law page 403
of gravity and a mathematical theory that could derive from it the motion
of the planets. The first of these elements will occupy us later in this section;
the second was the theory of conic sections of Apollonius of Perga.
Since orbits under a central gravitational field are conic sections, one can
in large measure view the theory of gravitation mathematically speaking
as a set of “exercises in the theory of conics”. 131
The recovery of Apollonius’ theory had been one of the main goals of
seventeenth century mathematicians. We have already mentioned Bonaventura
Cavalieri’s The burning mirror (1632), which applied the theory’s
rudiments to burning mirrors, lighthouses, acoustics and motion under
gravity. In 1655 there appeared John Wallis’ Tractatus de sectionibus conicis;
but apparently the author had been able to study only the first four books
of Apollonius’ treatise, those that survived in Greek. 132 The next three
books of Apollonius’ Conics were first printed in Florence in 1661, in a
Latin translation (from an Arabic recension) prepared by Abraham Echellensis
and Giovanni Alfonso Borelli; the latter was reckoned by Newton
among his own forerunners concerning the universal law of gravitation.
This work of recovery continued after the publication of the Principia in
1687. A critical edition of the first seven books, containing the Greek text
of the first four and a Latin translation of the next three based on multi-
130 As we saw in Section 11.6, the sixteenth and seventeenth centuries saw the development of
two lines of thought concerning tides, in lively mutual antagonism: one attributed them to interactions
with the moon and sun, others to earthly motion. The second line did not die with Galileo’s
unfortunate arguments: instead, through intermediate steps due to G. B. Baliani and J. Wallis, it
led to the analysis of those forces that today we call inertial, due in particular to the earth’s motions
around the barycenter of the earth-moon system; see [Wallis]. Thus the two lines, which (as we
have seen) both appear to be inspired by reflection on fragmentary reports on Seleucus’ work, find
again common ground in modern mechanics.
131 For instance, Newton solves in the Principia the problem of finding a conic going through five
given points. According to Heath this problem had been solved by Apollonius, but its proof was
not included in his treatise, perhaps so as not to lengthen it too much. See [Apollonius/Heath],
Introduction, chapter VI, p. cli.
132 The first four books were a sort of introductory textbook; Apollonius’ original results appear
in the next four.
Revision: 1.11 Date: 2003/01/06 07:48:20