[33.] Here 'senyth' is again used to mean azimuth, and the proposition is, to find the sun's azimuth by taking his altitude, and setting his degree at the right altitude on the almicanteras. Of course the two co-ordinates, altitude and azimuth, readily indicate the sun's exact position; and the same for any star or planet.
[34.] The moon's latitude is never more than 5¼° from the ecliptic, and this small distance is, 'in common treatises of Astrolabie,' altogether neglected; so that it is supposed to move in the ecliptic. First, then, take the moon's altitude, say 30°. Next take the altitude of some bright star 'on the moon's side,' i.e. nearly in the same azimuth as the moon, taking care to choose a star which is represented upon the Rete by a pointed tongue. Bring this tongue's point to the right altitude among the almicanteras, and then see which degree of the ecliptic lies on the almicantera which denotes an altitude of 30°. This will give the moon's place, 'if the stars in the Astrolabe be set after the truth,' i.e. if the point of the tongue is exactly where it should be.
[35.] The motion of a planet is called direct, when it moves in the direction of the succession of the zodiacal signs; retrograde, when in the contrary direction. When a planet is on the right or east side of the Meridional line, and is moving forward along the signs, without increase of declination, its altitude will be less on the second occasion than on the first at the moment when the altitude of the fixed star is the same as before. The same is true if the planet be retrograde, and on the western side. The contrary results occur when the second altitude is greater than the first. But the great defect of this method is that it may be rendered fallacious by a change in the planet's declination.
[36.] See fig. 14, [Plate VI]. If the equinoctial circle in this figure be supposed to be superposed upon that in fig. 5, [Plate III], and be further supposed to revolve backwards through an angle of about 60° till the point 1 (fig. 14) rests upon the point where the 8th hour-line crosses the equinoctial, the beginning of the 2nd house will then be found to be on the line of midnight. Similarly, all the other results mentioned follow. For it is easily seen that each 'house' occupies a space equal to 2 hours, so that the bringing of the 3rd house to the midnight line brings 1 to the 10th hour-line, and a similar placing of the 4th house brings 1 to the 12th hour-line, which is the horizon obliquus itself. Moving onward 2 more hours, the point 7 (the nadir of 1) comes to the end of the 2nd hour, whilst the 5th house comes to the north; and lastly, when 7 is at the end of the 4th hour, the 6th house is so placed. To find the nadir of a house, we have only to add 6; so that the 7th, 8th, 9th, 10th, 11th, and 12th houses are the nadirs of the 1st, 2nd, 3rd, 4th, 5th, and 6th houses respectively.
[37.] Again see fig. 14, [Plate VI]. Here the 10th house is at once seen to be on the meridional line. In the quadrant from 1 to 10, the even division of the quadrant into 3 parts shews the 12th and 11th houses. Working downwards from 1, we get the 2nd and 3rd houses, and the 4th house beginning with the north line. The rest are easily found from their nadirs.
[38.] This problem is discussed in arts. 144 and 145 of Hymes's Astronomy, 2nd ed. 1840, p. 84. The words 'for warping' mean 'to prevent the errors which may arise from the plate becoming warped.' The 'broader' of course means 'the larger.' See fig. 15, [Plate VI]. If the shadow of the sun be observed at a time before midday when its extremity just enters within the circle, and again at a time after midday when it is just passing beyond the circle, the altitude of the sun at these two observations must be the same, and the south line must lie half-way between the two shadows. In the figure, S and S′ are the 2 positions of the sun, OT the rod, Ot and Ot′ the shadows, and OR the direction of the south line. Ott′ is the metal disc.
[39.] This begins with an explanation of the terms 'meridian' and 'longitude.' 'They chaungen her Almikanteras' means that they differ in latitude. But, when Chaucer speaks of the longitude and latitude of a 'climate,' he means the length and breadth of it. A 'climate' (clima) is a belt of the earth included between two fixed parallels of latitude. The ancients reckoned seven climates; in the sixteenth century there were nine. The 'latitude of the climate' is the breadth of this belt; the 'longitude' of it he seems to consider as measured along lines lying equidistant between the parallels of latitude of the places from which the climates are named. See Stöffler, fol. 20 b; and Petri Apiani Cosmographia, per Gemmam Phrysium restituta, ed. 1574, fol. 7 b. The seven climates were as follows:—
1. That whose central line passes through Meroë (lat. 17°); from nearly 13° to nearly 20°.
2. Central line, through Syene (lat. 24°); from 20° to 27°, nearly.
3. Central line through Alexandria (lat. 31°); from 27° to 34°, nearly.