Note 27 — PART II A COUPLE OF CENTURIES' PROGRESS. (continued 2)

A curve of the nth degree has ½n(n+3) arbitrary constants in its equation, hence this number of points specifically determine it. But special points, like focus or vertex, count as two ordinary ones. Hence three points plus the focus act as five points, and determine a conic or curve of the second degree. Three observations therefore fix an orbit round the sun.