The Surveyor in Foure Bookes (1616) - Page 15

DEFINITION II.

A line is length, without breadth or thickness.

Euclid, Book 1, Def. 2.

Two line diagrams labeled A and B. Diagram A is a straight horizontal line. Diagram B is a curved arc bowing upwards.
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 of these lines are there two sorts, namely: right (straight), as the line A, and crooked or spherical, as the line B.

DEFINITION III.

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

Euclid, Book 1, Def. 5.

A rectangular plane labeled A in its center. The four vertices are labeled with letters: B at the top-left, C at the top-right, D at the bottom-left, and E at the bottom-right.
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.

DEFINITION IV.

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

Four diagrams of angles labeled A, B, C, and D. Diagram A shows a rectilineal angle formed by two straight lines. Diagram B shows an angle formed by two curved lines (concave). Diagram C shows an angle formed by two curved lines (convex). Diagram D shows a mixed angle formed by one straight line and one curved line.

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.