4. Central line through Rhodes (lat. 36°); from 34° to 39°, nearly.
5. Central line through Rome (lat. 41°); from 39° to 43°, nearly.
6. Central line through Borysthenes (lat. 45°); from 43° to 47°.
7. Through the Riphæan mountains (lat. 48°); from 47° to 50°. But Chaucer must have included an eighth climate (called ultra Mæotides paludes) from 50° to 56°; and a ninth, from 56° to the pole. The part of the earth to the north of the 7th climate was considered by the ancients to be uninhabitable. A rough drawing of these climates is given in MS. Camb. Univ. Lib. Ii. 3. 3, fol. 33 b.
[40.] The longitude and latitude of a planet being ascertained from an almanac, we can find with what degree it ascends. For example, given that the longitude of Venus is 6° of Capricorn, and her N. latitude 2°. Set the one leg of a compass upon the degree of longitude, and extend the other till the distance between the two legs is 2° of latitude, from that point inward, i.e. northward. The 6th degree of Capricorn is now to be set on the horizon, the label (slightly coated with wax) to be made to point to the same degree, and the north latitude is set off upon the wax by help of the compass. The spot thus marking the planet's position is, by a very slight movement of the Rete, to be brought upon the horizon, and it will be found that the planet (situated 2° N. of the 6th degree) ascends together with the head (or beginning of the sign) of Capricorn. This result, which is not quite exact, is easily tested by a globe. When the latitude of the planet is south, its place cannot well be found when in Capricorn for want of space at the edge of the Astrolabe.
As a second example, it will be found that, when Jupiter's longitude is at the end of 1° of Pisces, and his latitude 3° south, he ascends together with the 14th of Pisces, nearly. This is easily verified by a globe, which solves all such problems very readily.
It is a singular fact that most of the best MSS. leave off at the word 'houre,' leaving the last sentence incomplete. I quote the last five words—'þou shalt do wel y-now'—from the MS. in St. John's College, Cambridge; they also occur in the old editions.
[41.] Sections 41-43 and 41a-42b are from the MS. in St. John's College, Cambridge. For the scale of umbra recta, see fig. 1, [Plate I]. Observe that the umbra recta is used where the angle of elevation of an object is greater than 45°; the umbra versa, where it is less. See also fig. 16, [Plate VI]; where, if AC be the height of the tower, BC the same height minus the height of the observer's eye (supposed to be placed at E), and EB the distance of the observer from the tower, then bc : Eb :: EB : BC. But Eb is reckoned as 12, and if bc be 4, we find that BC is 3 EB, i.e. 60 feet, when EB is 20. Hence AC is 60 feet, plus the height of the observer's eye. The last sentence is to be read thus—'And if thy "rewle" fall upon 5, then are 5-12ths of the height equivalent to the space between thee and the tower (with addition of thine own height).' The MS. reads '5 12-partyes þe heyȝt of þe space,' &c.; but the word of must be transposed, in order to make sense. It is clear that, if bc = 5, then 5 : 12 :: EB : BC, which is the same as saying that EB = 5⁄12 BC. Conversely, BC is 12⁄5 EB = 48, if EB = 20.
[42.] See fig. 1, [Plate I]. See also fig. 17, [Plate VI]. Let Eb = 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 Eb = 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.