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ELEMENTS OF EUCLID.
point is that which hath no parts, or which hath no mag- Book I. nitude.
II. A line is length without breadth.
III. The extremities of a line are points.
IV. A straight line is that which lies evenly between its extreme points.
V. A superficies is that which hath only length and breadth.
VI. The extremities of a superficies are lines.
VII. A plain superficies is that in which any two points being See N. taken, the straight line between them lies wholly in that su
VIII. "A plane angle is the inclination of two lines to one See N. "another in a plane, which meet together, but are not in "the same direction."
IX. 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.
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 those 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 BD, 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.'
X. When a straight line standing on
XI. An obtuse angle is that which is greater than a right angle.
XII. An acute angle is that which is less than a right angle.
XV. A circle is a plane figure contained by one line, which Book I. is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
XVI. And this point is called the centre of the circle.
XIX. "A segment of a circle is the figure contained by a
XX. Rectilineal figures are those which are contained by
XXI. Trilateral figures, or triangles, by three straight lines.
XXIII. Multilateral figures, or polygons, by more than four
XXIV. Of three sided figures, an equilateral triangle is that which has three equal sides.
XXV. An isosceles triangle is that which has (only) two sides equal.
Book I. XXVI. A scalene triangle is that which has three unequal sides.
XXIX. An acute angled triangle is that which has three acute
XXX. Of four sided figures, a square is that which has all its
XXXI. An oblong is that which has all its angles right angles,
XXXII. A rhombus is that which has all its sides equal,
XXXIII. A rhomboid is that which has its opposite sides
XXXIV. All other four sided figures besides these are call-
XXXV. Parallel straight lines are such as are in the same
I. 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 straight line.
III. And that a circle may be described from any centre, at any distance from that centre.
I. THINGS which are equal to the same are equal to one
II. If equals be added to equals, the wholes are equal.
III. If equals be taken from equals, the remainders are equal.
VI. Things which are double of the same, are equal to one
VII. 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.
X. Two straight lines cannot enclose a space.
XI. All right angles are equal to one another.