 | 1894 - 834 pages
...points in common, they will coincide throughout their whole length, and form but one straight line; through a given point only one straight line can be drawn parallel to a given line; two straight lines cannot inclose a space. Axioms of this class apply to geometrical... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...points in common, they will coincide throughout their whole length, and form but one straight line. 12. Through a given point only one straight line can be drawn parallel to a given straight line. SYMBOLS AND ABBREVIATIONS. 47. The following are some of the principal symbols... | |
 | Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...the side CD, and the angle ABC to the angle BCD. Prove by superposition that AD is parallel to BC. 4. Through a given point only one straight line can be drawn parallel to a given straight line. 5. Construct a right-angled triangle, having one side equal to a given finite... | |
 | Seth Thayer Stewart - Geometry - 1891 - 428 pages
...directions of a will cause one end to incline toward s.nA the other end from b. 59. Postulate III. Through a given point only one straight line can be drawn parallel to a given line. For other postulates, see p. 6. RULE AND COMPASS. 6O. To draw one line perpendicular... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...line can be drawn. 108. Axiom. A straight line is the shortest line between two points. 109. Axiom. Through a given point only one straight line can be drawn parallel to a given straight line. 110. Axiom. For any quantity its equal can be substituted. 111. Axiom. If equals... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...two straight lines are parallel.] But AB is parallel to CD. Hyp. Hence AB coincides with XY. Ax. b [Through a given point only one straight line can be drawn parallel to a given straight line.] And POB-POY. Coinciding Hence b-\-POB=b + POY. Ax. 2 But b + PO Y= 2 right... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...two straight lines are parallel.] But AB is parallel to CD. Hyp. Hence AB coincides with XY. Ax. b [Through a given point only one straight line can be drawn parallel to a given straight line.] And POB=POY. Coinciding Hence b + POB=b + POY. Ax. 2 But b + POY= 2 right angles.... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...be drawn to a given line from a given external point). .'. AB and CD are parallel. QED 105. Axiom. Through a given point only one straight line can be drawn parallel to a given straight line. 106. COR. Two straight lines in the same plane parallel to a third straight... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...straight lines in the same plane perpendicular to the same straight line are parallel. 105. AXIOM. Through a given point only one straight line can be drawn parallel to a given straight line. 107. If a straight line is perpendicular to one of two parallel lines, it is... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...be drawn to a given line from a given external point). .'. AB and CD are parallel. QED 105. Axiom. Through a given point only one straight line can be drawn parallel to a given straight line. 106. COR. Two straight lines in the same plane parallel to a third straight... | |
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Axiom. Through a given point only one straight line can be drawn parallel to a given straight line. 
