1 The Birth of Science - MSRI

10.6 Rays of Darkness and Triangular Rays 259
over in this passage the words “lines” and “triangle” 103 clearly indicate
a geometric construction. Thus we may suppose that Vitruvius is trying,
with difficulty, to convey a geometrical argument from a Greek scientific
source. 104 If this is the case, one hint to the meaning of Vitruvius’ source
may be gained by literally translating the more obscure terms into Greek.
If we do this to the expression “second signum”, the Latin term signum page 323
becomes semeion (¨), while the ordinal is indicated in Greek by the
letter ; likewise “third” and “fifth” become the letters and . The Greek
term semeion, as we know, meant not only a sign but also (from Euclid on)
a point, 105 and the letters of the alphabet were used not only for ordinals,
but to indicate the points of a geometric construction. In a context marked
by the presence of triangles and lines, the literal translation into Greek of
the Latin expressions “secundum signum”, “tertium signum”, “quintum
signum” has a clear meaning: “point ”, “point ”, “point ” in a geometric
construction. Could this have been the meaning, misunderstood
by Vitruvius, of the expressions in the Greek original?
When he talks about diagrams that he does understand, Vitruvius uses
expressions such as “where the letter A will be”, or “let’s draw a line from
the letter S”. 106 Thus he uses the letter not as a label for a point, but to
indicate the actual place in the drawing where the letter is written. In one
passage where signum is used in a sense that seems to correspond approximately
to the meaning “point”, he writes: “from this signum and letter C,
let’s draw a line to the center, where the letter A is”. 107 “Signum and letter”:
it is clear that here too, Vitruvius does not use signum to mean a point, but
simply a sign next to which is a letter. The absence of the abstract geometric
notion of a point in Vitruvius’ work should neither surprise us nor be
held against him. Never until his time had a geometrical work been written
in Latin, so it was not easy to express in that language the notion of a
point.
103 Trigonum is the Latin transliteration of the Greek word for triangle. In Vitruvius the word is
generally assumed to mean the astrological trine or trigon, a configuration where the sun and a
planet appear separated by 120 ◦ in the sky. Under this interpretation the passage is rendered essentially
meaningless; there is no explanation for the trigonal rays of the sun, which according
to Pliny prevent the planet from moving on a straight line, nor for Vitruvius’ words “with equal
sides”. This astrological interpretation of trigonum, like that of signum, may even reflect Vitruvius’
own thinking, but not that of his source.
104 One example of the scientific reliability of this source is the value Vitruvius gives for the period
of revolution of Saturn: 29 years and 160 days. This is closer to the true value (29 years and 167)
than the value Ptolemy would later adopt in the Almagest (29 years and 182 days).
105 See page 157.
106 “Ubi erit littera A” (Vitruvius, De architectura, IX, vii, 2); “ab littera S ducatur linea” (Vitruvius,
De architectura, IX, vii, 6).
107 “Ab eo signo et littera C per centrum, ubi est littera A, linea perducatur” (Vitruvius, De archi-
tectura, IX, vii, 3).
Revision: 1.11 Date: 2003/01/06 02:20:46