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Extra info for Category Theory, Applications to Algebra, Logic, and Topology: Proceedings, Gummersbach, FRG, 1981

Example text

LOR, which OF because the ; of the two adjacent equal to the angle is because these angles are opposite FOP at the vertex ; and : is the angle OIR, which is equal to the angle because the angle GIN, which, in the query, is supposed to be equal to AFN, is also equal to the angle the other OFP ; OIR, to which it is opposite at the vertex. Q. But of what use ORI gled in P, the triangle ORI OPF is right-an- must be right-angled the equal sides (remarks to quently the two lines same straight line Query 6, page 25) conseAB, CD, are both perpendicular to PR, and therefore parallel to each Supposing, now, Q.

VI. proved before (Query 3, an isosceles triangle, the been Sect. ), that in angles at the basis are equal prove the reverse; that must be when isosceles is, \ \ / / J angles? A. Yes. Because, AC, BC, were sides j that a triangle contains two equal it . can you noio : ^ of the two if either greater than the other, the angle opposite to that side would also be greater than the angle which at A is opposite to the other side B and ; but the two angles ar^ equal, therefore the sides AC, BC, are also equal.

EFC ; make the and, Wlien the sum of the two interior angles, made by of a third line, is equal to two right the intersection angles. GEOMETRY. 30 QUERY IX. ) ; or so as to have the alternate angles BHF, DBH and BHE or are cut by AM at unequal angles, ABC, BHE (Fig. sum of ner, that the unequal ; or in such a lines two straight Fig. ; CD, what is less will then he the case with the EF? JPig' II' I. JVC E cJsr M K. A. They man- CBH and the two interior angles BHE (Fig. L), or DBH and BHF (Fig. II), than two right angles 1.