...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,...

...for any tiling we are able to discover to the contrary, be only contingent, local, and temporary 1 It must indeed be owned, with respect to the conclusions...angles, these two straight lines, though indefinitely pro" duced, will never meet ;"— is not the boundless immensity of space tacitly assumed as a thing...

...conclusions hitherto mentioned on the subject of space, that they are rather of a metaphysical lhan of a mathematical nature; but they are not, on that...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,...

...at least, all that part of the former which is employed about space, or extension, — a faTourite object of metaphysical as well as of mathematical...interior angles on the same side together equal to tw.% * Philosophical Essays, pp. 94, ?5, 4to edit. " right angles, these two straight lines, though...

...fundamental propositions which occur in Euclid's Elements. When it is asserted, for example, that u if one straight line falls on two other straight lines,...interior angles on the same side together equal to two ' Philoiophical Emyi, pp. 94, 95, 4to edit. " right angles, these two straight lines, though indefinitely...

...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...

...inclose 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 angles on the same side of. " it taken together less than two right angles, these " straight lines being continually produced,...