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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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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 333 Seiten
...Axioms, and that which was before the llth is accounted the 10th. The 12th Axiom of Euclid is, that " if a straight line meet two " straight lines, so as..."lines being continually produced, shall at length meet upon that " side on which are the angles which are less than two right angles." Instead of this proposition,...
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Elements of Geometry: With Notes

John Radford Young - 1833 - 216 Seiten
...proportional. From this general proposition 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 same side \T> HAUM T> of it, taken together, less than two right angles, these straight lines being continually...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - 1833 - 183 Seiten
...equal to one another. 12. If a right line meet two right lines, so as to make See N. .the two internal angles on the same side of it taken together less than two right angles ; these right lines, being continually produced, shall at length meet upon that side on which are the angles,...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - 1835 - 513 Seiten
...cannot enclose a 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..." being continually produced, shall at length meet upon that " side on which are the angles which are less than two right " angles. See the notes on Prop....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 Seiten
...cannot enclose a 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..." being continually produced, shall at length meet upon that " side on which are the angles which are less than two right " angles. See the notes on Prop....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1835 - 316 Seiten
...therefore removed from among the Axioms. 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•same side of it taken " together less than two right angles, these straight lines being continually...
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The Element of Geometry

John Playfair - 1836 - 114 Seiten
...may be produced until the perpendicular is greater than any given straight line. PROP. XIII. THEOR. If a straight line meet two straight lines, so as...being continually produced, shall at- length meet upon that side on which are the angles, which are less than two right angles. Let the straight line...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1836 - 471 Seiten
...of Euclid is, that " if a straight line " meets two straight lines, so as to make the two inte" rior angles on the same side of it taken together less " than two right angles, these straight lines oeing con" tinually produced, shall at length meet upon that side " on which are the angles which are...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 Seiten
...this proposition has been demonstrated by some writers in the following manner •. the same plane, so as to make the two interior angles on the same...together, less than two right angles, these straight lines shall at length meet upon that side, if they be continually produced.* PROPOSITION I. PROBLEM.f To...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 Seiten
...by showing that the alternate Zs AGK, GKD are equal. PROPOSITION. " If a right line meet two right lines, so as to make the two interior angles on the...it taken together less than two right angles, these right lines being continually produced, shall at length meet on that side on which are the angles which...
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