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" If a straight line meet 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 first six books of the Elements of Euclid, with numerous exercises - Seite 4
von Euclides - 1853 - 147 Seiten
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Prolegomena Logica: An Inquiry Into the Psychological Character of Logical ...

Henry Longueville Mansel - 1851 - 320 Seiten
...character, analogous to the geometrical principles, " two straight lines cannot enclose a space," or, " if a straight line meets two straight lines, so as to make the two interior angles on the same side together less than two right angles, the two straight lines will meet if produced." As a matter of...
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The Elements of Euclid [book 1] for beginners, by J. Lowres

Euclides - 1852
...inclose a space. 11. All right angles are equal to one another. 12. If a right line meet two other right lines, so as to make the two interior angles on the...it taken together less than two right angles, these two right lines being continually induced, shall at length meet on that side on which are the angles,...
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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New ..., Bücher 1

Euclides - 1853
...parallel to FG; but both cannot. »^^F/ — 1 5- jf" * 3. — To BK. I. PEOP. A. If a straight line cut two straight lines, so as to make the two interior angles on the same side of it together less than two right angles : then these two straight lines, being continually produced, shall...
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The Elements of Euclid: With Many Additional Propositions ..., Teil 1

Euclid - 1853 - 136 Seiten
...internal an£;^' '\ the same side, fS6g..£ ''• ' ^uol to two right I. 29, theor. . . I. 29, cor. . . If a straight line meets two straight lines so as to make the two internal angles on the same side together less than two right angles. {These '' stralgnt lines being...
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Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - 1854
...crossed shall be meeting-lines. This is the twelfth axiom, and is thus expressed in Euclid : — AXIOM XII. — If a straight line meets two straight lines,...than two right angles, these straight lines, being prolonged, shall at length meet upon that side on which are the angles that are less than two right...
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The Collected Works of Dugald Stewart, Band 3

Dugald Stewart - 1854
...Euclid's 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 right angles, these two straight lines, though indefinitely produced, will never...
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The Collected Works of Dugald Stewart, Esq. F.R.SS.: Elements of the ...

Dugald Stewart - 1854
...Euclid's 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 right angles, these two straight lines, though indefinitely produced, will never...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...axiom, another, viz. , th " the whole is equal to all its parts taken together." at X. Two straight Unes cannot enclose a space. XI. All right angles are equal...being \ continually produced, shall at length meet ' V ' 'L upon that side on which are the angles -which \ are less than two right angles. It H admitted...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 Seiten
...self-evident propositions. It is therefore removed from among the Axioms. The 12th Axiom of Euclid is, that " if a straight line meets two straight lines, so as...the two interior angles on the same side of it taken " which are less than two right angles." Instead of this proposition, which, though true, is by no...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1856 - 318 Seiten
...self-evident propositions. It is therefore removed from among the Axioms. The 12th Axiom of Euclid is, that " if a straight line meets two straight lines, so as...' produced, shall at length meet upon that side on w^^^ <»•« the angle* " which are less than two right angles." Instead of this proposition, which,...
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