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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... "
The Elements of Euclid [book 1] for beginners, by J. Lowres - Page 10
by Euclides - 1852
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...space. XI. All right angles are equal to one another. XII. " If a straight line meets two straight lines, so as to make the " two interior angles on...taken together " less than two right angles, these straight lines being con" tinually produced, shall at length meet upon that side on " which are the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 320 pages
...Euclid is, that ' If a straight line ' meet two straight lines so as to make the two interior an' gles on the same side of it taken together less than two right ' angles, these straight lines being continually produced will, ' at length meet upon that side on which are the angles...
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Elements of the Philosophy of the Human Mind, Volume 2

Dugald Stewart - Psychology - 1814 - 564 pages
...Elements. When it is asserted, for example, that " if one straight line falls on two 'other straight lines, so as to make the two interior angles on the same side together equal to two righl angles, these two straight lines, though indefinitely produced, will never...
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Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - Geometry - 1817 - 454 pages
...equation,) a principle which is equivalent to Euclid's 12th axiom, (If a straight line meets 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, will at length meet on that side on which are the angles...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...is accounted the 10th. The 12th Axiom of Euclid is, that " if a straight line meets 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 upon that " side on which are the...
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Elements of the Philosophy of the Human Mind, Volume 2

Dugald Stewart - Psychology - 1821 - 350 pages
...Elements. When it is asserted, for example, that " if one straight line falls on two other straight lines, so as to make :' the two interior angles on the same side together equal to tw.% * Philosophical Essays, pp. 94, ?5, 4to edit. " right angles, these two straight...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...inclose a space. 11. AH right angles are equal to one another. 12." If a straight line meets 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 upon that side on which are the angles...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 246 pages
...Legendre is enabled to demonstrate Euclid's twelfth axiom, viz. : If a straight line meet two straight lines so as to make the two interior angles on the...taken together, less than two right angles, these straight lines being continually produced shall at length meet upon that side on which are the angles...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...a space. XI. All right angles are equal to one another. XII. " If a straight line meet two straight lines, so as to " make the two interior angles on...it taken together less than two right angles, these " straight lines being continually produced, shall at " length meet upon that side on which are the...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 208 pages
...subjoined the following corollary, viz., " It follows from this, that if two lines are cut by a third line, so as to make the two interior angles on the same side less than two right angles, these lines produced will meet, and form a triangle ;" from a slight examination,...
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