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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... "
Orr's Circle of the Sciences: The mathematical sciences - Page 60
edited by - 1854
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The Monthly review. New and improved ser, Volume 26

1798
...they meet a third line, make the alternate angles with it equal, Eu~; cljj assumée this axiom : " If a straight line meets two straight ' lines, so as to make the two interior angle's on the same side ' of it .less than two right angles, these straight lines, being CQniinfwtly...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...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,...than two right angles, these straight lines being con" tinually produced, shall at length meet upon that side on " which are the angles Which are less...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...Euclid is, that ' If a straight line ' meet two straight lines so as to make the two interior an' gles on the same side of it taken together less than two right ' angles, these straight lines being continually produced will, ' at length meet upon that side on which are the angles which ' are less...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1810 - 518 pages
...cannot enclose a space. XI. All right angles are equal to one another. XII. " If a straight line meet two straight lines, so as to make the " two interior...than two right angles, these straight lines being continually " produced, shall at length meet upon that side on which are " the angles which are less...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 558 pages
...X. Tvio strzLJ?ht lilies canncrt inclose a spare. XI. All riirfct angles are equal to one another. XII. " If a straight line meets two straight lines, so as to make " the two Lriterior angles on the same ade of it taken to" gether less than two right angles, these straight...
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Elements of the Philosophy of the Human Mind, Volume 2

Dugald Stewart - Psychology - 1814
...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 righl angles, these two straight lines, though indefinitely produced, will never...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...Axioms, und that which was before the llth is accounted the 10th. The 12th Axiom of Euclid is, that " if a straight line meets two " straight lines, so...than two right angles, these straight " lines being continually produced, shall at length meet upon that " side on which are the angles which are less...
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Elements of the Philosophy of the Human Mind, Volume 2

Dugald Stewart - Psychology - 1821 - 350 pages
...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 tw.% * Philosophical Essays, pp. 94, ?5, 4to edit. " right angles, these two straight...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...part. 10. Twfc«».^^^ lines cannot inclose a space. 11. AH right angles are equal to one another. 12." If a straight line meets two straight lines so as...than two right angles, these straight lines being continually produced, shall at length meet upon that side on which are the angles which are lest than...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1826 - 320 pages
...before the 1 tth is aeeounted the lOthr The 12th Axiom of Euelid is, that " if a straight line meet two "straight lines, so as to make the two interior...than two right angles, these straight " lines being eontinually produeed, shall at length meet upon that *' side on whieh are the angles whieh are less...
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