Dante and the early astronomers . ^ Let PA be a greatrevolving circle upon which Mars is fixed. (In thehands of the Alexandrian mathematicians the spheresalmost disappear, and they deal practically only withcircles.) If the earth were at its centre, as Eudoxusdemanded. Mars must always be at the same distance,but if we make the circle eccentric to Earth, byputting its centre at C while Earth is at E, then the THE SCHOOL OF ALEXANDRIA. 119 distance and consequently the brightness will constantlyvary, and Mars will be brightest when at perigee P(point nearest Earth), and faintest when in apogeeA
Dante and the early astronomers . ^ Let PA be a greatrevolving circle upon which Mars is fixed. (In thehands of the Alexandrian mathematicians the spheresalmost disappear, and they deal practically only withcircles.) If the earth were at its centre, as Eudoxusdemanded. Mars must always be at the same distance,but if we make the circle eccentric to Earth, byputting its centre at C while Earth is at E, then the THE SCHOOL OF ALEXANDRIA. 119 distance and consequently the brightness will constantlyvary, and Mars will be brightest when at perigee P(point nearest Earth), and faintest when in apogeeA (point furthest from Earth).^ But, as the Greeks had discovered, Mars attains hisgreatest brilliance at different points of the zodiac, soP must be made moveable, and it always happenswhen he is opposite the sun, therefore P must keeppace with the suns apparent motion in the zodiac andPE always point towards him. This was accomplished. Fig. 23. The Moveable Eccentric. by making PC A turn round upon the fixed point E,so that for instance when the sun had moved througha quarter of his circle (in three months) P A had movedto P A, and the whole eccentric had moved into thenew position shown in the diagram, its centre C beingnow at C. In other words, the centre of the eccentricmoves round Earth in the same time and in the samedirection as the sun, that is in one j^ear, and withthe signs (from west to east). ^ Greek peri near, apo away from, ge Earth. 120 THE SCHOOL OF ALEXANDRIA. At the same time, Mars is moving in an oppositedirection on the eccentric, and without entering intoall the details of the problem, we may add that theGreek geometers found that by determining the properrelatives sizes of the large and the small circle theycould make the two motions neutralize one anotherwhen the planet reached its stationary points, and theretrograde motion prevail over the direct when itretrograded. A similar arrangement was
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