"Two straights always intersect."
"Two straights perpendicular to a third straight intersect at a point half a straight from the third either way."
"A pole is half a straight from its polar."
"A polar is the locus of coplanar points half a straight from its pole. Therefore, if the pole of one straight lies on another straight the pole of this second straight is on the first straight."
"The cross of two straights is the pole of the join of their poles."
"Any two straights inclose a plane figure, a digon."
"Two digons are congruent if their angles are equal."
"The equidistantial is a circle with center at the poles of its basal straight."
A typical postulate based upon the Bolyai hypothesis of the acute angle is the following: