...straight line EF, which is contrary to Proposition XVI. PROPOSITION XXIII.—THEOREM. 42. Through a given point one line, and only one, can be drawn parallel to a given line. Let A be the given point and ~4 E BC the given line. I From A draw AD perpendicular * jc to BC, and...

...straight line EF, which ia contrary to Proposition XVI. PROPOSITION XXIII.— THEOREM. 42. Through a given point one line, and only one, can be drawn parallel to a given line. Let A be the given point and BC the given line. From A draw AD perpendicular to BC, and through A draw...

...straight lines perpendicular to the same straight line are parallel. PROPOSITION XXIII. Through a given point one line, and only one, can be drawn parallel to a given line. PROPOSITION XXIV. When two straight lines are cut by a third, if the alternateinterior angles are equal,...

...determination of a straight line by two conditions. Thus two points determine a line, and through a given point one line, and only one, can be drawn parallel to a given line. Sometimes, however, there will be two or more lines satisfying the two conditions ; thus through a...

...determination of a straight line by two conditions. Thus two points determine a line, and through a given point one line, and only one, can be drawn parallel to a given line. Sometimes, however, there will be two or more lines satisfying the two conditions ; thus through a...

...straight lines perpendicular to the same straight line are parallel. PROPOSITION XXIII. Through a given point one line, and only one, can be drawn parallel to a given line. PROPOSITION XXIV. When two straight lines are cut by a third, if the alternateinterior angles are equal,...

...determination of a straight line by two conditions. Thus two points determine a line, and through a given point one line, and only one, can be drawn parallel to a given line. Sometimes, however, there will be two or more lines satisfying the two conditions; thus through a given...

...drawn to the line. 6. At a point in a line but one perpendicular can be drawn to the line. 8. Through a point one line and only one can be drawn parallel to a given line. 9. Any figure may be transferred from one position in space THREE PRELIMINARY THEOREMS ON INEQUALITY...

...postulate of parallels being introduced when needed, as follows: Postulate of Parallels. Thru a given point one line and only one can be drawn parallel...point, line, and angle, nor to assume that a line drawn thru a point in a triangle must cut the perimeter twice, nor to add a postulate of continuity. It is...

...postulate of parallels being introduced when needed, as follows: Postulate of Parallels. Thru a given point one line and only one can be drawn parallel...is considered later. It is not deemed desirable to i, postulate explicitly the existence of such concepts as point, line, and angle, nor to assume that...