Leonid Zhmud The Origin of the History of Science in Classical Antiquity

Data and On Division (of Figures). His
authorship of
Catoptrics is debatable. Aristoxenus’ Elements of Harmonics is not re-
lated to the exact sciences.
8
Astronomy and geometry appeared in the sixth century, arithmetic and harmonics in
the late sixth to early fifth century, optics and mechanics in the early fourth century.
Descriptive geography stems from the sixth century; the application of mathematical

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Chapter 4: The historiographical project of the Lyceum
120
foundations laid down by the end of the classical period remained unchanged
on the whole.
This conclusion applies not only to the disciplines that later underwent little
changes, such as Aristotle’s zoology or his theory of motion,
9
but also to those
that were far from stagnating. Euclid’s mathematics, though developed by
Archimedes, Apollonius, and a dozen other less eminent scientists, remained
until the end of Antiquity, with very few exceptions, the same Euclidean mathe-
matics. Mathematical harmonics and optics, improved to a certain extent by
Ptolemy, still do not reveal any remarkable progress. The greatest changes
seemed to occur in astronomy, in the first place due to the Babylonian observa-
tional and numerical data on planetary motions, which became accessible to the
Greeks from the second century BC. This gave astronomy a new impetus and
permitted it to achieve a hitherto unattainable accuracy by passing from quali-
tative to quantitative models.
10
All the same, there is no reason to speak of a
radical transformation of Greek astronomy under the influence of Babylonian
data: its conceptual basis remained mostly unchanged, even in Ptolemy’s
epoch. The main aim of astronomy, as formulated by Eudoxus, was to create a
kinematic theory of the motion of heavenly bodies, which would explain their
visibly irregular motion in the firmament through the postulation of uniform
circular motion. Developed by Autolycus and Euclid, the method of exposing
an astronomical theory as a system of deductive arguments from initial prin-
ciples eventually became a standard for any serious astronomical treatise.
Among the basic axioms and definitions figuring in the preface to Euclid’s
Phaenomena, we find practically the same fundamental notions as in the pref-
ace to Ptolemy’s
Almagest.
11
Conventional as analogies ever remain, there is no doubt that, after the
fourth century BC, nothing happening in Greek science could be compared to
the 16
th
- to 18
th
-century transformation of astronomy connected, in particular,
with the transition to the heliocentric model, the invention of the telescope, and
methods to it is connected with Dicaearchus (fr. 104–115; Keyser, P. The geographi-
cal work of Dikaiarchos,
Dicaearchus of Messana, 353–372).
9
Though some aspects of Aristotle’s dynamics were modified by Strato of Lampsa-
cus, a decisive step away from it was made only by Ioannes Philoponus (sixth cen-
tury AD).
10
Also important in this respect was Apollonius’ and Hipparchus’ research on spheri-
cal trigonometry, completed later by Menelaus (ca. 100 AD). See Björnbo, A.A.
Stu-
dien über Menelaos’ Sphärik, Leipzig 1902, 124ff., 133f. Sidoli, N. Hipparchus and
the ancient metrical methods on the sphere,
JHA 35 (2004) 71–84, makes Hippar-
chus’ crucial contribution to spherical trigonometry more feasible.
11
Ptolemy proceeds from the general assumptions that were formulated by the end of
the fourth century BC: 1) the skies have a spherical shape and rotate as a sphere;
2) the earth has a spherical shape; 3) it is situated in the center of cosmos; 4) in terms
of its dimensions and its distance from the stellar sphere, the earth relates to the latter
as a point to a sphere; 5) the earth does not take part in any motion (I, 2).

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1. Greek science in the late fourth century BC
121
the creation of Newtonian dynamics. Nor was there anything comparable to the
development of algebra and analytic geometry, or later to the revolution in bi-
ology, starting with the discovery of the cell and the emergence of evolutionary
theory. Accordingly, we have every reason to assert that, on the whole, by the
end of the fourth century, the