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A plane rectilineal angle is the inclination of two straight lines to one
another, which meet together, but are not in the same straight line.
E4 N.B. “When several angles are at one point B, any one of them is expressed by three letters, of which the letter that is at the vertex of the angle, that is, at the point in which the straight lines that contain the angle meet one another, is put between the other two letters, and one of these two is somewhere upon one of these straight lines, and the other upon the other line. Thus the angle which is contained by the straight lines AB, CB, is named the angle ABC, or CBA; that which is contained by AB, BD, is named the angle ABD, or DBA; and that which is contained by DB, CB, is called the angle DBC, or CBD; but, if there be only one angle at a point, it may be expressed by a letter placed at that point, as the angle at E.”
When a straight line standing on another straight line makes the adjacent
angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
XIII. "A term or boundary is the extremity of any thing."
A circle is a plane figure contained by one line, which is called the cir
cumference, and is such that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
XVII. A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
XVIII. A semicircle is the figure contained by a diameter and the part of the
circumference cut off by the diameter.
“A segment of a circle is the figure contained by a straight line, and the
circumference it cuts off.”
Rectilineal figures are those which are contained by straight lines.
Trilateral figures, or triangles, by three straight lines.
XXX. Of four-sided figures, a square is that which has all its sides equal, and
all its angles right angles.
XXXI. An oblong is that which has all its angles right angles, but has not all its
XXXII. A rhombus is that which has all its sides equal, but its angles are not
' XXXIII. A rhomboid is that which has its opposite sides equal to one another, but
all its sides are not equal, nor its angles right angles.
XXXV. Parallel straight lines are such as are in the same plane, and which, being
produced ever so far both ways, do not meet.
Let it be granted that a straight line may be drawn from any one point to any other point.
II. That a terminated straight line may be produced to any length in a
And that a circle may be described from any centre, at any distance from
Things which are equal to the same are equal to one another.
If equals be taken from unequals, the remainders are unequal.
Things which are double of the same, are equal to one another.
Things which are halves of the same, are equal to one another.
VIII. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
IX. The whole is greater than its part.
Two straight lines cannot inclose a space.
All right angles are equal to one another.
“If a straight line meet two straight lines, so as to make the two interior
angles on the same side of it taken together less than two right angles, these straight lines being continually produced, shall at length meet upon that side on which are the angles which are less than two right angles."