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" 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... "
Euclid's Elements of geometry, books i. ii. iii. iv - Seite 4
von Euclides - 1862
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A Mathematical Solution Book Containing Systematic Solutions to Many of the ...

Benjamin Franklin Finkel - 1888 - 481 Seiten
...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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Circular[s] of Information, Ausgaben 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 Teaching and History of Mathematics in the United States

Florian Cajori - 1890 - 400 Seiten
...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 Seiten
...— 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 Seiten
...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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Science, Band 20

John Michels (Journalist) - 1892
...at least one which is not axiomatic.1 This id the axiom of parallels, 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 on that side on...
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Science, Band 20

John Michels (Journalist) - 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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1892 - 518 Seiten
...that all right angles are equal, admits of proof, and is therefore perhaps out of place as an Axiom.] 12. If a straight line meet two straight lines so as to make the interior angles on one side of it together less than two right angles, these straight lines will meet...
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Journal of the Michigan Schoolmasters' Club, Band 22;Bände 31-40

Michigan Schoolmasters' Club - 1894
...any center with any radius. 4. That all right angles are equal. 6. 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 rig~ht angles, these two straight lines being continually produced shall at...
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Studies in Deductive Logic: A Manual for Students, by W. Stanley Jevons

William Stanley Jevons - 1896 - 304 Seiten
...Give the logical opposites, converse and contrapositive, of Euclid's (so-called) twelfth axiom — If a straight line meet two straight lines, so as to make the interior angles on the same side of it taken together less than two right angles, those straight lines...
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