The Surveyor in Foure Bookes (1616) - Page 13

Definition II.

A line is length, without breadth or thickness.

Euclid, Book 1, Def. 2.

This is the first quantity in geometry, and may be divided into parts in respect of its length, but admits no other division or dimension; and has for its terms and limits that geometrical point formerly spoken of. And these lines are of two sorts, namely: right (straight), as line A, and crooked or spherical, as line B.

A horizontal straight line labeled A and a curved arc labeled B.

Definition III.

A superficies (surface) is that which has only length and breadth.

Euclid, Book 1, Def. 5.

This is the second quantity in geometry, having two several dimensions, namely, length and breadth, without depth or thickness (for that belongs to a solid or body, being the third quantity in geometry, and impertinent to this place, where all three dimensions are attributed, such as length, breadth, and thickness). And as a line is limited with points, so is a superficies with lines, and a solid or body with superficies. As the figure A, being a superficies, has for its length B-C or D-E, and for its breadth B-D or C-E; which four lines are the bounds, limits, and terms of the same superficies.

A rectangle labeled A with corners labeled B, C, D, and E.

Definition IV.

An angle is the meeting of two lines in any sort, so that they do not form a single straight line.

Four angles labeled A, B, C, and D. A is two straight lines meeting at a point. B, C, and D are various combinations of straight and curved lines meeting at a point.

Euclid, Book 1, Def. 8. Generally, there are three sorts of angles (in respect of their lines): namely, right-lined, spherical, and mixed. As the angle A is called a right-lined angle, being composed of two straight lines; the angles B and C are spherical, or crooked angles; and the angle D is a mixed angle, being caused by both.