I wonder if the convention of labeling points in geometric
diagrams with uppercase symbols ultimately derives from
Greek mathematics, which was originally written in
"majuscule" (uppercase) Greek script (in contrast to the "minuscule"
script that was introduced much later (9th century?)).
Certainly Euclid and Archimedes used only uppercase,
and all of Descartes diagrams in La Geometrie (1637)
follow the same convention.
It seems that middle- and high-school textbooks continue
to use uppercase labels (is this only in the U.S.?),
but college texts do not follow
this as rigidly. This was brought home to me when I wrote
a chapter for high-school teachers and the editors changed
all my lowercase vertex labels to uppercase.
I much prefer lowercase for point labels, although
I do not quite know why I have this preference.
(Maybe because uppercase seems like SHOUTING?)
But when writing for an audience accustomed to
a particular convention, it seems prudent to follow that convention.
My questions are:
(1) Is the Greek majuscule script the origin of the uppercase
diagram-labeling convention?
(2) In so far as I am correct that the uppercase convention
is followed up to high school but dissolves at more advanced
levels, why does it persist to one level but dissolve beyond?
Best Answer
On the one hand:
Ratdolt's 1482 editio princeps (albeit of a Latin translation of an Arabic translation) labels points with lower case letters.
Herwegen's 1533 editio princeps of the original Greek text also labels points with lower case letters.
Moreover, for instance, as late as 1565, a corrected edition of Commandino's Latin translation of Archimedes still labels points with lower case letters. One might well argue that this continues the manuscript tradition, as exemplified by the Codex Vaticanus.
On the other hand, just a few years later:
Billingsley's 1570 English translation labels points rather with upper case letters.
Commandino's 1572 Latin translation labels points with upper case letters.
Clavius's 1574 Latin translation labels points with upper case letters.
So, writing admittedly as a complete layman with regards to the textual transmission of Greek Mathematics, I would suggest that the custom of labelling points with upper case letters might well be an innovation of mid-late 16th century publishing, and that it in any event demonstrably has nothing to do with the earliest printed editions and the manuscript traditions they would have derived from.