Friday evening 9 o'clock August 17th 1773

Dear Sam,

I have just received your letter yr queries

in it I will do my endeavours to answer as soon as I

have an opportunity, probably tomorrow; in the mean time

I will execute a design which your letter has revived, &

which I formed soon after your departure: it is that of

communicating to you a few considerations which I believe

will perfectly obviate your scruples about taking the description of the parts of a mathematical

figure from the accidental circumstance of its situation – I drew them up immediately

in a form which I will now transcribe, & which I reproach

myself much for not having transcribed&sent to you before,

as it would have put you in possession as it were, of

a very useful, perhaps even necessary expedient which perhaps you may have been losing a good deal of time in

endeavouring to steer clear of.

“It is to be observed that, of the 3 sides (better called

bounds or boundary lines

, for a reason that will appear presently) of a triangle, as such, there is no one

in particular to which the name of base more properly belongs than to another: the source

from whence that name is taken,

is never any other than the accidental circumstance of the situation of the figure with respect to the reader. And from

this source the name may well be taken: since it is easy

to conceive, that whatever station a reader may find it convenient

to view the figure from, that figure in itself must ever be [still] the name.

The purpose for which it is taken is, to distinguish

some one of the three that one means to speak of, from the two when which, at the instant, one does

not mean to speak of: which two others are still,

by Euclid, combined under the common [or twin] appellation of the sides.

Now then, for whatever purpose, by whatever reason, &

in whatever manner a man is justified in distinguishing any one of the bounds from the 2 remaining

ones, for the same purpose, by the same reason, & in the same manner is he justifiable in distinguishing

those 2 from one another. let them be so distinguished & call one of them the right & the other of them the left.

So of the Angles call one the angle to the right:

(not the right angle for an obvious reason) the other, the

angle to the left; & the remaining angle which is opposite

to the base [boundary-line] the angle at the top. [not the

vertical angle, that being to be reserved for a twin name,

ex. gr. the vertical angles.