...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,...

...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,...

...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...

...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...

...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,...

...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...

...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...

...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...

...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...

...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...