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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 - Σελίδα 12
των Euclides - 1852
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...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...taken together, less than two right angles, these straight lines shall at length meet upon that side, if they be continually produced.* PROPOSITION I....

Euclid's Elements [book 1-6] with corrections, by J.R. Young

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...subject, and which he calls an Axiom, is as follows. AXIOM XII. If a straight line meets 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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...equal to one another. XII. " If a straight line meet two straight lines, which are " in the same plane, so as to make the two interior " angles on the same...taken together, less " than two right angles, these straight lines being " produced, shall at length meet upon that side on " which are the angles which...

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...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...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...

Elements of geometry: consisting of the first four,and the sixth, books of ...

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...centre, at any distance from that centre. IV. [Ax. XI.] V. And that if a straight line meets 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...

Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

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...necessity of a new axiom. Euclid's axiom alluded to is this : " If a straight line meet two other 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 produced, will at length meet on the side on which...

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

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...Euclid is, that " if a straight line meets two straight " lines, so as to make the two interior anples on the same side of 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...

Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

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...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 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...

Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

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...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 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...

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...to one another. |j 12. If a straight line meet two other straight lines which are in the same plane, so as to make the two interior angles on the same...taken together, less than two right angles, these straight lines shall at length meet upon that side, if they be continually produced.^ * ln this axiom...




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