Page:First six books of the elements of Euclid 1847 Byrne.djvu/26

From Wikisource
Jump to navigation Jump to search
This page has been proofread, but needs to be validated.
xxii
BOOK I. POSTULATES.

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.

XXXIV.

All other quadrilateral figures are called trapeziums.

XXXV.

Parallel straight lines are such as are in the same plane, and which being produced continually in both directions, would never meet.

POSTULATES.

I.

Let it be granted that a straight line may be drawn from any one point to any other point.

II.

Let it be granted that a finite straight line may be produced to any length in a straight line.

III.

Let it be granted that a circle may be described with any centre at any distance from that centre.

AXIOMS.

I.

Magnitudes which are equal to the same are equal to each other.

II.

If equals be added to equals the sums will be equal.