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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, containing the first six books, with a selection of ... - Side 6
av Euclides - 1874
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1849 - 317 sider
...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...shall at length meet upon that side on which are the angle* " which are less than two right angles." Instead of this proposition, which, though true, is...
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Prolegomena Logica: An Inquiry Into the Psychological Character of Logical ...

Henry Longueville Mansel - 1851 - 320 sider
...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 first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852
...across the other two so as to inclose a space.] XI. All right angles are equal to one another. XII. " If a straight line meets two straight lines, so as...the angles which are less than two right angles." [These are truths which no person can possibly doubt, who are others besides these, but these are sufficient...
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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 geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...part. 10. Two straight lines cannot enclose a space. 11. All right angles are equal to one another, 12. If a straight line meets two straight lines, so as...are the angles which are less than two right angles. PROPOSITIONS. PROPOSITION I. PROBLEM. To describe an equilateral triangle upon a given finite straight...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 sider
...part. X. Two straight lines cannot enclose a space. XI. All right angles are equal to one another. XII. If a straight line meets two straight lines, so as...are the angles which are less than two right angles. PROPOSITION I. — PROBLEM. To describe an equilateral triangle upon a given finiie straight line....
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...lines cannot inclose a space. All right angles are equal to one another. XII. " If a straight line meet two straight lines, so as to make the two interior...the angles which are less than two right angles." PROPOSITION I. — PROBLEM. To describe an equilateral triangle upon a given finite straight line....
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Bok 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 ..., Del 1

Euclid - 1853 - 136 sider
...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
...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, so as...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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