>1570 Billingsley Euclid xi. xxxi. 342 Parallelipipedons consisting vpon
>equall bases, and being vnder one and the selfe same altitude, are equall
>the one to the other.
But I find interesting the way Euclid introduced it, earlier than
XI.31 cited above, and also a bit earlier than Sam Kutler's reference:
>2. On page 326 of volume III of Heath's Euclid, we find
>
>The proper translation of stereon parallElepipedon is parallelepipedal
>solid, >not solid parallelepiped, as it is usually translated. Still less
>is the
>solid a parallelopiped, as the word is not uncommonly written.
I point out to students that the word has the familiar prefix
"epi-" in the middle, to help them with the pronunciation and spelling. It
occurs in a course on geometrical vectors, first in expressing a vector as
a linear combination of vectors in three chosen directions (not necessarily
perpendicular), and later in showing that its volume is a scalar triple
product.
But the most interesting aspect may be the origin of the word
within Euclid. It's not listed among his Book XI definitions, but sidles
in later, just as "parallelogram" does in Book I. This is quite
well-known, but may be new to some people.
Euclid I.33 sets up a figure without naming it. In I.34 he refers
to such figures by a descriptive phrase "parallelogrammic areas"
(presumably meaning "parallel-drawn areas" in the Greek?), and thereafter
just settles into using "parallelogram" as a technical term.
This is one of the places where Book XI resembles Book I. Euclid
XI.24 sets up a figure without naming it. In XI.25 he refers to it by a
descriptive phrase "parallelepipedal solid" ("parallel-planed solid"), and
thereafter just settles into using that as a technical term.
These cases illustrate that the Greeks didn't share our attitude to
definitions, as John Conway has pointed out in the past. Also, Euclid's
brief and rather rough descriptions of both figures, criticised in Heath's
notes, may illustrate the lecture by Reviel Netz recently posted by Julio
(The Shaping of Deduction in Greek Mathematics); which stressed that the
meaning is conveyed by the text and diagram jointly.
Ken Pledger.