Point
Defined by Euclid as “that which hath no parts.” Playfair
defines it as “that which has position but not magnitude,” and Legendre
says it “is a limit terminating a line;” but none of these definitions
can be called either philosophical or exact. A point is not necessarily
a “limit terminating a line,” for if so a point could not exist, even
in imagination, without a line. Besides, Legendre's definition
presupposes that we know what a line is; but assuredly a “point”
precedes a “line,” as a line precedes a “superficies.” To arrive at
Legendre's idea we must begin with a solid, and say a superficies is
the “limit terminating each face of a solid,” lines are the “limits
terminating a superficies,” and points are the “limits terminating a
line.” In regard to Euclid's definition, we say: Ex nihilo nihil
fit.
In good point
(French, embonpoint, plump.) (See Stretch a point.)
To carry one's point.
To gain the object sought for. The allusion is to archery. To
dine on potatoes and point. To have potatoes without salt, a very
meagre dinner indeed. When salt was very dear, and the cellar was
empty, parents used to tell their children to point their potato to the
salt cellar, and eat it. This was potato and point. In the tale of Ralph Richards the Miser, we are told that he gave his boy dry
bread, and
whipped him for pointing it towards the cupboard where a bit of
cheese was kept in a bottle.
To make a point of [doing something].
To consider the matter as a point of duty. The reference is to the
old Roman way of voting by ballot. The ballot tablets were thrown by
the voters into a chest, and were afterwards counted by points
marked on a tablet, and to obtain every vote was to “carry every
point” (“Omne talit punctum” [Horace]). Hence a point of duty or
point of conscience is a plank on the platform of duty or conscience.
To stretch a point.
To exceed what is strictly right. Points were the tagged laces used
in ancient dress: hence, to “truss a point,” to truss or tie the laces
which held the breeches; to “stretch a point” is to stretch these
laces, so as to adjust the dress to extra growth, or the temporary
fulness of good feeding. At Whitsuntide these points or tags were given
away by the churchwardens.
“Their points being broken, down fell their hose.” —Shakespeare:
1 Henry IV., ii. 4.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894 More on Point from Infoplease:

