Books Books If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles... The Elements of Euclid [book 1] for beginners, by J. Lowres - Page 10
by Euclides - 1852 ## A Short History of Greek Mathematics

James Gow - Mathematics - 1884 - 350 pages
...lines cannot enclose a space: 11. All right angles are equal: 12. If a straight line meet two straight lines, so as to make the two interior angles on the same side of it together less than two right angles, these straight lines will meet if produced on that side. Of these... ## Mathematical Questions and Solutions, Volume 42

Mathematics - 1885 - 150 pages
...it proved that all right angles are equal.* Axiom XII.: — " If a straight line meets two straight lines, so as to make the two interior angles on the...taken together, less than two right angles, these straight linos being continually produced, shall at length meet upon that side on which are the angles... ## Transactions and Proceedings of the New Zealand Institute, Volume 18

New Zealand Institute - Science - 1886 - 530 pages
...parallel-axiom mentioned in my paper. Form (a), (Euclid's) is : — " If a straight line meets two straight lines, so as to make the two interior angles on the same I side of it taken together less than two right angles, these straight lines being continually produced... ## A Mathematical Solution Book Containing Systematic Solutions to Many of the ...

Benjamin Franklin Finkel - Mathematics - 1888 - 518 pages
...so as to make the two interior angles *For definitions of geometrical magnitudes, see Mensuration. on the same side of it taken together less than two right angles, these straight lines being continually produced shall at length meet on that side< on which are the angles... ## Circular of Information of the Bureau of Education, for ..., Issues 1-3

United States. Office of Education - Digital images - 1890 - 958 pages
...generally called the twelfth, by some the eleventh " axiom :" " If a straight line meet two straight lines so as to make the two interior angles on the same side of it taken together less than two right-angles, these straight lines, being continually produced, shall at length meet on that side on... ## The Teaching and History of Mathematics in the United States

Florian Cajori - Mathematics - 1890 - 422 pages
...generally called the twelfth, by some the eleventh "axiom :"* " If a straight line meet two straight lines so as to make the two interior angles on the same side of it taken together less than two right-angles, these straight lines, being continually produced, shall at length meet on that side on... ## The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...this proposition independently of Prop. 27. Ax. 12. — If a straight line meet two other straight lines so as to make the two interior angles on the same side of it together less than two right angles, these two straight lines being continually produced shall at length... ## The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 418 pages
...straight line cut two other straight lines, (1) so as to make the exterior-interior angles equal, or (2) so as to make the two interior angles on the same side together equal to two right angles, then the two straight lines are parallel. xE (1) Hyp. Let the st.... ## Geometrical Researches on the Theory of Parallels

Nikolaĭ Ivanovich Lobachevskiĭ - Geometry, Non-Euclidean - 1891 - 142 pages
...alternate angles, he brings in the un wieldly postulate or axiom: " If a straight line meet two straight lines, so as to make the two interior angles on the...it taken together less than two right angles, these straight lines, being continually produced, shall at length meet on that side on which are the angles... 