The Science Absolute of Space Microform Independent of the Truth Or Falsity
The Science Absolute of Space Microform Independent of the Truth Or Falsity
Jnos Bolyai
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34. =*, ( 28), X=l : sin # rt. Z=2, and x will be constructed geometrically. And NBQ may be so computed, that IA dif- fers from i less than by anything given, which happens for sin NBQ=V0. 39. If (in a plane) PQ and ST are I! to the straight MN (27), and AB, CD are equal perpendiculars to MN; manifestly ADEC= c A BE A; and so the angles Q (perhaps mixtilinear) ECP, EAT will fit, and EOEA. If, moreover, CF= AG, then AACF^ACAG, and each is half of the quadrilateral FAGC. If FAGC, HAGK are two qua...drilaterals of this sort on AG, between PQ and ST; their equivalence (as in Euclid) is evident, as also 42 SCIENCE ABSOLUTE OF SPACE. the equivalence of the triangles AGC, AGH, standing on the same AG, and having their vertices on the line PQ. Moreover, ACF = CAG, GCQ=CGA, and ACF+ACG+GCQ= st. Z (32); and so also CAG+ACG+CGA= [23] st. Z ; therefore, in any triangle ACG of this sort, the sum of the three angles =st. ^. But whether the straight AG may have fallen upon AG (which III MN), or not; the equivalence of the rectilineal triangles AGC, AGH, as well of themselves, as of the sums of their angles, is evident.
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