...less than two right angles, these straight lines, being continually produced, will at length meet on that side, on which are the angles which are less than two rig-fat angles.) Using the notation of your book, his assumption is, that C = $ : (A, B, c) : Now,...

...cannot enclose a space. XI. All right angles afe 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 continual" ly produced, shall at length meet upon that side on which " are the angles which are less...

...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...

...internal angles on the same side of it gee ff. taken together less than two right angles, these right lines being continually produced, shall at length...the angles, which are less than two right angles. u angles • 12 V' Elements of Euclid. Fig. 12. PROPOSITION 1. PROBLEM. To describe an equilateral...

...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...meet upon that side on which are the angles which are lest than two right angles." Proposition I. Problem. To describe an equilateral triangle upon a given...

...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...

...cannot 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...the angles " which are less than two right angles." See the notes on Prop. 29. of Book 1. PROPOSITION I. PROBLEM. To describe an equilateral triangle upon...

...subjoined the following corollary, viz., " It follows from this, that if two lines are cut by a third line, so as to make the two interior angles on the same side less than two right angles, these lines produced will meet, and form a triangle ;" from a slight examination,...

...greater than its part. 10. Two straight lines cannot inclose a space. 11. All right angles are equal. 12. If a straight line meets two straight lines so as...continually produced, shall at length meet upon that side upon which are the angles which are less than two right angles. The last of these has been added by...

...greater than its part. 10. Two straight lines cannot inclose a space. II. All right angles are equal. 12. .If a straight line meets two straight lines so as...angles on the same side of it taken together, less tkau two right angles, these straight lines being continually produced, shall at length meet upon that...