The Science Absolute of Space Independent of the Truth Or Falsity of Euclids
The Science Absolute of Space Independent of the Truth Or Falsity of Euclids
Jnos Bolyai
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Call the ray AM the axis of L. Evidently also, in any plane containing the sect AM, there is for the axis ray AM a single L. Call any Lot this sort the L of this ray AM (in the plain- considered, being understood). Kyi- dent ly by revolving L around AM we describe the Fof which ray AM is called the axis, and in turn F tna y be ascribed to ///< axis ray AM. I?) 12. It" 1> i> anywhere on the L of ray AM, and UN II* AM (11); then the L of ray AM and the L of ray BN coincit/e. For suppose, in disti...nction, L the L of rav UN. . Let C be an v where in L . And CP H -BN (1D- &" BNH ^AM, so CPU *AM U ini, and so C also will fall on L. And if I is any where on L, and CPII^AM: thenCPH^BN (10); and C also falls on L (11). Thus L and L are the SCIENCE ABSOLUTE OF SPACE. 13 s o same; and every ray BN is also axis of L, and between all axes of this L, is . The same is evident in the same way of F. 13. If BN II AM, and CP II DQ, andZBAM + ZABN = st. Z; then also ZDCP+ZCDQ- st. Z. Q For let EA= EB, and EFM= DCP ( 4).
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