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Mars is in each case in the same position. Now for any date when Mars is at M and the earth at E3 the date of the year gives the angle E3SM. And the observation of Tycho gives the direction of Mars compared with the sun, SE3M. So all the angles of the triangle SEM in any of these positions of E are known, and also the ratios of SE1, SE2, SE3, SE4 to SM and to each other.
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