a concatenation of points (971a6–972a13); a point cannot be added to or subtracted from a
line (972a13–30); a point is not a minimum component of a line (972a30–b24). The treatise
concludes (972b25–33) by arguing that a point is not an indivisible connector (arthron).
Unfortunately our knowledge of the ideas refuted here comes only from such refutations,
making it difficult to understand why such ideas were propounded.
Ed.: H.H. Joachim, De Lineis Insecabilibus, in W.D. Ross, ed., The Works of Aristotle v. 6 (Loeb 1913);
M. Timpanaro Cardini (with Italian trans.), Pseudo-Aristotele, De Lineis Insecabilibus (1970).
O. Apelt, Beiträge zur Geschichte der Griechischen Philosophie (1891) 255–286; RE S.7 (1940) 1542–1543,
O. Regenbogen.
Ian Mueller
A C O M, X, G ⇒ M, ...
Aristotelian Corpus Me ̄khanika (Proble ̄mata me ̄khanika) (320 – 200 BCE)
This collection of problems (or a similar one) apparently has been part of the Aristotelian
corpus from early on: a work with the title Me ̄khanikon features in D L’ list
of A’s works. Internal characteristics also place the work quite early: its math-
ematical terminology is close to E’s, and it is not acquainted with A’
contributions to the study of mechanics. This, however, does not necessarily exclude that
the work was written after Archime ̄de ̄s.
The key concepts in the Me ̄khanika are the force (iskhus or dunamis) and the load (baros): a
force has to be equal to hold a load, or it has to exceed the load to be able to lift it or move
it. These fundamental relations are apparently not observed when a mechanical device is
operative: little forces are able to hold or move a much bigger load. The Me ̄khanika uses a
balance-lever model to explain how such mechanical devices work. The aspect of the bal-
ance addresses cases of equilibria, whereas the aspect of the lever accounts for cases when
the device described is in motion. The Me ̄khanika opens with a general explanation why
lesser forces are able to move greater loads with the help of a lever. This is possible because
of the amazing features of the circle, which combines in itself the opposites of motion and
rest, and of two component motions – one centripetal, another tangential – which for no
extended period of time remain in the same relation to each other. On account of these, the
author argues (§8), circles have an intrinsic tendency to move. This is also why the circular
motion of the balance and the lever is able to make the small force produce a greater effect.
It is important to note that the author does not formulate this enhancing capacity of the
lever, or of circles in general, in terms of explicit proportionalities. Nevertheless the idea of
the proportionality among the distances of the force and the load from the fulcrum, and of
the magnitude of the force and the load themselves is expressed repeatedly (for the most
unequivocal formulation see §3).
The authorship of the Me ̄khanika is still being debated. Among other indications, the most
compelling one against an Aristotelian authorship is the way §§ 32 – 33 give a rather unskillful
recapitulation of Aristotle’s account of projectile motion (Physics 8.10). As the title Me ̄khan-
ikon also occurs in Diogene ̄s Laërtios’ list of S’s works (5.59), it has been repeatedly
suggested that the work is by Strato ̄n. The fact, however, that Strato ̄n is credited with a work
on mechanics does not require that he should be identified with the author (or indeed,
any of the authors) of these mechanical problems.
Ed.: O. Apelt, Aristotelis quae feruntur De plantis, De mirabilibus auscultationibus,... (1888); M.E. Bottecchia,
ARISTOTELIAN CORPUS ME ̄KHANIKA (PROBLE ̄MATA ME ̄KHANIKA)