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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 - 1837 - 318 Seiten
...interior and opposite. In order to demonstrate this proposition, Euclid assumed it as an Axiom, that " if a "straight line meet two straight lines, so as to make the interior angles on " the same side of it less than two right angles, these straight lines being " continually...
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The Elements of Euclid

Euclid - 1838 - 416 Seiten
...Two straight lines cannot enclose a space. XI. All right angles arc equal to one another. XII. •• If a straight line meet two straight lines, so as...right angles, these straight lines being continually pro" duced, shall at length meet upon that side on which are the angles " which are less than two right...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 Seiten
...X. Two straight linea cannot enclose a space, XI. All right angles are equal to one another. XII. " If a straight line meet two straight lines, so as...right angles, these straight lines being continually pro" duced, shall at length meet upon that side on which are the angles " which are less than two right...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...proceed with his 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...lines, being continually produced, shall at length meet upon that side on which are the angles which are less than two right angles. It is readily seen that...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 Seiten
...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...than two right angles, these straight lines being " produced, shall at length meet upon that side on " which are the angles which are less than two "...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...from any 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...lines, being continually produced, shall at length meet upon that side on which are the angles less than two right angles. AXIOMS. I. THINGS which are equal...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 Seiten
...interior and opposite. In order to demonstrate this proposition, Euclid assumed it as an Axiom, that " if a " straight line meet two straight lines, so as to make the interior angles on " the same side of it less than two right angles, these straight lines being " continually...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1844 - 317 Seiten
...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...being continually " produced, shall at length meet upon that side on which are the angles AMONG the Axioms there have been made only two alterations....
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - 1844 - 237 Seiten
...the 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...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...cannot inclose 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...lines being continually produced, shall at length meet upon that side on which are the angles which are less than two right angles. PROPOSITION I. PROBLEM....
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