Footnote 70
Supp. Prop., §44. Sections 44 and 45 are from MS. Digby 72.  This long explanation of the method of finding a planet's place depends upon the tables which were constructed for that purpose from observation.  The general idea is this.  The figures shewing a planet's position for the last day of December, 1397, give what is called the root, and afford us, in fact, a starting-point from which to measure.  An `argument' is the angle upon which the tabulated quantity depends; for example, a very important `argument' is the planet's longitude, upon which its declination may be made to depend, so as to admit of tabulation.  The planet's longitude for the given above-mentioned date being taken as the root, the planet's longitude at a second date can be found from the tables.  If this second date be less than 20 years afterwards, the increase of motion is set down separately for each year, viz. so much in 1 year, so much in 2 years, and so on.  These separate years are called anni expansi.  But when the increase during a large round number of years (such as 20, 40, or 60 years at once) is allowed for, such years are called anni collecti.  For example, a period of 27 years includes 20 years taken together, and 7 separate or expanse years.  The mean motion during smaller periods of time, such as months, days, and hours, is added in afterwards.