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