III.
If equals be taken away from equals the remainders will be equal.
IV.
If equals be added to unequals the sums will be unequal.
V.
If equals be taken away from unequals the remainders will be unequal.
VI.
The doubles of the same or equal magnitudes are equal.
VII.
The halves of the same or equal magnitudes are equal.
VIII.
Magnitudes which coincide with one another, or exactly fill the same space, are equal.
IX.
The whole is greater than its part.
X.
Two straight lines cannot include a space.
XI.
All right angles are equal.
XII.
If two straight lines (
) meet a third straight line (
) so as to make the two interior angles (
and 
) on the same side less than two right angles, these two straight lines will meet if they be produced on that side on which the angles are less than two right angles.
