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G135

is like a hyperbola so placed that the straight line lies half way between its two branches. The hyperbola is all in one piece because in the projective plane there is but one point at an infinite distance along any straight line. So that if the straight line is a vertical line and the hyperbola cuts the celestial sphere at any distance, say 1°, to the north of the zenith, this is the same point as the point of the celestial-sphere 1° south of the nadir. The result is that the hyperbola passes along the whole length of the vertical line twice before returning into itself, and will cut the north and south vertical plane into two parts, just as your second line on the ribbon separates its middle part from the edges, though your

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