1 The Birth of Science - MSRI

262 10. Lost Science
The meaning of the figure is clear. It shows how a planet’s orbit (supposed
circular) can be constructed as a succession of small strokes, each
of which is obtained by composing two simultaneous displacements: one
along the tangent to the circle (this would be the actual movement of the
planet if, in the absence of the sun, it could continue on a straight line, as
Pliny says) and another, directed toward the sun. The figure is an illustration
of the notion transmitted in qualitative form by Plutarch: indeed, the page 327
motion of the planet arises as the result of a series of “thrusts toward the
center”. We have already seen that the technical tool of vector addition
for displacements is present in Heron and in the pseudo-Aristotelian Mechanics,
and indeed it is used in this latter work to explain how a uniform
circular motion can be regarded as a continuous superposition of a displacement
“according to nature”, along the tangent, with one “contrary to
nature”, directed toward the center. 108
The figure we have drawn explains the origin of the otherwise inexplicable
statement by Pliny and Vitruvius that the planets are prevented from
moving on a straight line by “sun rays shaped like triangles”.
The way in which Vitruvius tries to explain what’s special about the fifth
signum (“id autem nec plus nec minus est ad quintum ab eo signo”) seems
to confirm that a signum meant a point in the source: the exact equality
of distance implied by the words “neither more nor less” seems more appropriate
to describing the position of a point than that of a zodiacal sign.
Moreover Vitruvius’ sentence matches the procedure throught which one
obtains point E in the proposed construction: namely, as the point on the
half-line H∆ that makes the side HE exactly equal (“nec plus nec minus”)
to the other side, HΓ, of the triangle.
Of course, Vitruvius’ statement that the second and third signa are closer
to the sun than the fifth is false when applied to points B, Γ and E of Figure
10.2. Within our proposed reconstruction, this can be seen as a natural
consequence of Vitruvius’ error. If he interpreted the points of the geometric
construction as signs of the zodiac and the letters used to denote them
as ordinal numerals, he might have thought that the zodiacal signs were
ordered starting from the one where the sun is. page 328
10.7 The Idea of Gravity from Aristotle to Hipparchus
In Aristotle, geocentrism is closely connected to his notion of gravity. The
center of the earth, which is also the stationary center of the cosmos, is
the “natural place” for which all “heavy objects” yearn. “Light” objects,
108 See pages 244–244 including notes 49 and 50.
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