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" 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... "
Elements of Geometry: With Notes - Page 172
by John Radford Young - 1827 - 208 pages
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An introduction to geometry, consisting of Euclid's Elements, book ..., Volume 1

Euclides - 1884 - 182 pages
...much better, however, not to discuss it until we have made some further progress in the subject. 12. If a straight line meet two straight lines so as to...together less than two right angles, these straight lines,being continually produced, shall at length meet on that side on which are the angles which are...
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A Short History of Greek Mathematics

James Gow - Mathematics - 1884 - 350 pages
...the last three are 10. Two straight lines cannot enclose a space: 11. All right angles are equal: 12. If a straight line meet two straight lines, so as...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...
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The national encyclopędia. Libr. ed, Volume 2

National cyclopaedia - 1884 - 642 pages
...as stated by Euclid it is not a true axiom. It runs thus — 44 If a straight line meets two other straight lines, so as to make the two interior angles on the same side of it, taken j together, less than two right angles ; these straight lines, being continually produced, shall at...
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Mathematical Questions and Solutions, Volume 42

Mathematics - 1885 - 150 pages
...and thus is 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...together, less than two right angles, these straight linos being continually produced, shall at length meet upon that side on which are the angles which...
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Transactions and Proceedings of the New Zealand Institute, Volume 18

New Zealand Institute - Science - 1886 - 530 pages
...the 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...
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A Mathematical Solution Book Containing Systematic Solutions to Many of the ...

Benjamin Franklin Finkel - Mathematics - 1888 - 518 pages
...assumption is a substitute for Euclid's famous eleventh (also called the twelfth) axiom which reads, If a straight line meet two straight lines so as to make the two interior angles *For definitions of geometrical magnitudes, see Mensuration. on the same side of it taken together...
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The Teaching and History of Mathematics in the United States

Florian Cajori - Mathematics - 1890 - 574 pages
...His assumption consists in what is generally called the twelfth, by some the eleventh " axiom :" " If a straight line meet two straight lines so as to...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...
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Circular of Information of the Bureau of Education, for ..., Issues 1-3

United States. Office of Education - Digital images - 1890 - 958 pages
...His assumption consists in what is generally called the twelfth, by some the eleventh " axiom :" " If a straight line meet two straight lines so as to...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...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...— Prove 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...
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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....
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