Manning, Henry Parker, 1859- · Boston, U.S.A., Ginn & Company · leaf 99
de. 7T Produce OA and CB. They will meet at a distance, 77 > from the axis of z in a point, 0, on the other axis of the surface, andthere form an angle that is equal in measure to z. NON-EUCLIDEAN GEOMETRY From the right triangle OAB Butand Therefore, Similarly, tan OA cos« = -rr- tan OB tan OA… … For the length of the chord joining two points on the sur-face, we have cos 8 = cosp cos p (1 + tan x tan x + tan y tany + tan z tan «).Now, tan2 p = tan2 /c sec2s + tan2»; therefore, sec2 p = sec2 k sec2«, or cos p = cos k cos ». THE SURFACE OF DOUBLE REVOLUTION 89 That is, in terms of z, z, 6,…
Geometry, Non-Euclidean
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