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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, based on Euclid, books i-iii - Side 9
av Edward Atkins - 1876 - 119 sider
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Mathematical Questions and Solutions, Volum 42

1885
...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, Volum 18

New Zealand Institute - 1886
...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 - 1888 - 481 sider
...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 - 1890 - 400 sider
...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[s] of Information, Utgaver 1-3

1890
...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 - 515 sider
...— 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 - 1890 - 393 sider
...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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Geometrical Researches on the Theory of Parallels

Nikolaĭ Ivanovich Lobachevskiĭ - 1891 - 50 sider
...cut by a transversal make equal alternate angles, he brings in the un wieldly postulate or axiom: " If a straight line meet two straight lines, so as...continually produced, shall at length meet on that side on which are the angles which are less than two right angles." Do you wonder that succeeding geometers...
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Educational Review

Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - 1892
...to one another," is not required for use before proposition 14 of his first book. Also the axiom, " If a straight line meet two straight lines, so as...continually produced, shall at length meet on that side on which are the angles which are less than two right angles," is not required till proposition...
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Science, Volum 20

1892
...at least one which is not axiomatic.1 This is the axiom of parallel?, which reads as follows : — " 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 oh that side on...
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