"A piece of a straight is called a sect."
"If two equal coplanar sects are erected perpendicular to a straight, if they do not meet, then the sect joining their extremities makes equal angles with them and is bisected by a perpendicular erected midway between their feet."
"The sum of the angles of a rectilineal triangle is a straight angle, in the hypothesis of the right (angle); is greater than a straight angle in the hypothesis of the obtuse (angle); is less than a straight angle in the hypothesis of the acute (angle)."
"The hypothesis of right is Euclidean; the hypothesis of the acute is Bolyai-Lobachevskian; the hypothesis of obtuse is Riemannian."
"If one straight is parallel to a second the second is parallel to the first."
"Parallels continually approach each other."
"The perpendiculars erected at the middle point of the sides of a triangle are all parallel, if two are parallel."
"If the foot of a perpendicular slides on a straight its extremity describes a curve called an equidistant curve, or an equidistantial."
"An equidistantial will slide on its trace."
"In the hypothesis of the obtuse a straight is of finite size and returns into itself."