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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 Works of Dugald Stewart: Elements of the philosophy of the human mind - Page 134
by Dugald Stewart - 1829
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 546 pages
...enclose 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 same side of it taken together " less than two right angles, these straight lines being con" tinually produced,...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - 522 pages
...it will make the alternate angles equal, the' exterior angle equal to the interior opposite one, and the two interior angles on the same side together equal to two right angles. Let the straight line EFG fall upon the parallels AB and CD; the alternate angles AGF and DFG are equal,...
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Elements of the Philosophy of the Human Mind, Volume 2

Dugald Stewart - 1814 - 582 pages
...space are more nearly allied to geometrical theorems than we might be disposed at first to apprehend ; being involved or implied in the most simple and fundamental...angles, these two straight lines, though indefinitely pro" duced, will never meet ;"— is not the boundless immensity of space tacitly assumed as a thing...
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Elements of the Philosophy of the Human Mind, Volume 2

Dugald Stewart - 1814 - 560 pages
...space are more nearly allied to geometrical theorems than we might be disposed at first to apprehend ; being involved or implied in the most simple and fundamental...interior angles on the same side together equal to two righl angles, these two straight lines, though indefinitely produced, will never meet ;" — is not...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 350 pages
...the llth is accounted the 10th. rfhe 12th Axiom of Euclid is, that " 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, these straight " lines being continually produced,...
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Elements of the Philosophy of the Human Mind, Volume 2

Dugald Stewart - 1821 - 348 pages
...space are more nearly allied to geometrical theorems than we might be disposed at first to apprehend ; being involved or implied in the most simple and fundamental...interior angles on the same side together equal to tw.% * Philosophical Essays, pp. 94, ?5, 4to edit. " right angles, these two straight lines, though...
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Elements of the Philosophy of the Human Mind, Volumes 1-2

Dugald Stewart - 1821 - 706 pages
...space are more nearly allied to geometrical theorems than we might be disposed at first to apprehend ; being involved or implied in the most simple and fundamental...Euclid's Elements. When it is asserted, for example, that u if one straight line falls on two other straight lines, so as to make " the two interior angles on...
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Elements of the Philosophy of the Human Mind, Volumes 1-2

Dugald Stewart - 1822 - 572 pages
...space are more nearly allied to geometrical theorems than we might be disposed at first to apprehend ; being involved or implied in the most simple and fundamental...it is asserted, for example, that " if one straight Hue falls on two other straight "lines, so as to make the two interior angles on the same side together...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 1046 pages
...cannot inclose a space. 11. AH right angles are equal to one another. 12." 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, these straight lines being continually produced, shall...
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The Boston Journal of Philosophy and the Arts, Volume 3

1826 - 628 pages
...Consequently, all elementary treatises are defective in this point. Proposition. If a straight line meets two straight lines so as to make the two interior angles on the same side less than two right angles, these straight lines being continually produced, will at length meet upon...
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