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 41_a_-42_b_ 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_ : E_b_ :: EB : BC. But E_b_ 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-p_ar_tyes þe hey[gh]t 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.