Editor’s NoteEditor’s Note98To Samuel Bentham20–26 August 1773 (Aet 25)

Friday eveng. 9 o'clock

Dear Sam

I have just received your letter. Your queries in it I will do my endeavours to answer as soon as I have an opportunity, probably pg 159tomorrow; in the mean time I will execute a design which your letter has revived, and 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 circumstances of its situation—I drew these up immediately in a form which I will now transcribe, and which I reproach myself very much for not having transcribed and 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 three 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 the reader may find it convenient to view the figure from that figure in itself must ever be /(still)/ the same.

The purpose for which it is taken is, to distinguish some one of the three that one means to speak of, from the two others which, at the instant, one does not mean to speak of: which two others are still, by Euclid, continued under the common (or twin[?]) appellation of the sides.

Now then, for whatever purpose, by whatever reason, and 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, and in the same manner is he justifiable in distinguishing these 2 from one another—let them be so distinguished and call one of them the right, and 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; and 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).

Thursday eveng.

Extract from an advertisement in the Gazetteer of 28 July 1773.

Premiums given by the Society of Arts etc. dated April 14th 1773.

pg 160No 22 'Machine for preserving lives in case of Fire. For a Machine superior to any hitherto in use for preserving the lives of persons in case of fire; to be deliver'd the first Tuesday in Novr. 1773; the Gold Medal or £30.

N.B. Strength and cheapness in the Machine will be consider'd as part of its merit.

Compleat Books of Premiums may be seen at every Post Office in Great-Britain etc.' Thus far the Advertisement.

I have no notion of a man's being precluded from a Patent by the acceptance of one of these Premiums. It is possible this may be a condition annexed to the granting of the premiums in some cases, viz: not to apply for a Patent—I mean for aught I know to the contrary—though I never heard of any such thing. This I am certain of, that the bare acceptance of such a Premium, if no such condition be enter'd into, cannot by Law disable a man from obtaining any Patent he might otherwise.

Thursday evening 26th

I wrote word by Tuesday's Post to my Uncle that we should be with him on Monday if the weather permitt, and to Mr. Mulford that we shall be with him some day the latter end of the week.

I shall therefore expect to see you on Sunday.