42. See fig. 1, Plate I. See also fig. 17, Plate VI. Let E_b_ = 12, _bc_ = 1; also E'_b'_ = 12, _b'c'_ = 2; then EB = 12 BC, E'B = 6 BC; therefore EE' = 6 BC. If EE' = 60 feet, then BC = 1/6 EE'=10 feet. To get the whole height, add the height of the eye. The last part of the article, beginning 'For other poyntis,' is altogether corrupt in the MS. 43. Here _versa_ (in M.) is certainly miswritten for _recta_, as in L. See fig. 18, Plate VI. Here E_b_ = E'_b'_ = 12; _b'c'_ = 1, _bc_ = 2. Hence E'B = 1/12 BC, EB = 2/12 BC. whence EE' = 1/12 BC. Or again, if _bc_ become = 3, 4, 5, &c., successively, whilst _b'c'_ remains = 1, then EE' is successively = 2/12 or 1/6, 3/12 or 1/4, 5/12, &c. Afterwards, add in the height of E. 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. 45. Here the author enters a little more into particulars. If the mean motion be required for the year 1400, 3 years later than the starting-point, look for 3 in the table of expanse years, and add the result to the number already corresponding to the 'root,' which is calculated for the last day of December, 1397. Allow for months and days afterwards. For a date earlier than 1397 the process is just reversed, involving subtraction instead of addition.