strange degree in another signe is by-cause that the latitude of the 5 sterre fix is either north or south fro the equinoxial. But sothly, the latitudes of planetes ben comunly rekned fro the ecliptik, bi-cause that non of hem declineth but fewe degrees out fro the brede of the zodiak. And tak good keep of this chapitre of arysing of the celestial bodies; for truste wel, that neyther mone ne sterre 10 as in oure embelif orisonte aryseth with that same degree of his longitude, save in o cas; and that is, whan they have no latitude fro the ecliptik lyne. But natheles, som tyme is everiche of thise planetes under the same lyne. And for more declaracioun, lo here thy figure. 20. To knowe the declinacioun of any degree in the zodiak fro the equinoxial cercle, &c. [Ad cognoscendum declinacionem alicuius gradus in zodiaco a circulo equinoctiali.] 15 Set the degree of any signe up-on the lyne meridional, and rikne his altitude in almikanteras fro the est orizonte up to the same degree set in the forseide lyne, and set ther a prikke. Turne up thanne thy riet, and set the heved of Aries or Libra in the same meridional lyne, and set ther a-nother prikke. And whan that 5 this is don, considere the altitudes of hem bothe; for sothly the difference of thilke altitudes is the declinacion of thilke degree fro the equinoxial. And yif so be that thilke degree be northward south from the equinoctial, but rather because it is north or south of the ecliptic. For example, Regulus (a Leonis) is on the ecliptic, and of course rises with that very degree in which it is. Hence the reading equinoctial leaves the case in doubt, and we find a more correct statement just below, where we have 'whan they have no latitude fro the ecliptik lyne.' At all places, however, upon the earth's equator, the stars will rise with the degrees of the zodiac in which they stand. 20. Here the disc (fig. 5) is supposed to be placed beneath the Rete (fig. 2). The proposition merely tells us that the difference between the meridian altitudes of the given degree of the zodiac and of the Ist point of Aries is the declination of that degree, which follows from the very definition of the term. There is hardly any necessity for setting the second prick, as it is sufficiently marked by being the point where the equinoctial circle crosses the south line. If the given degree lie outside this circle, the declination is south; if inside, it is north. fro the equinoxial, than is his declinacion north; yif it be south10 ward, than is it south. And for the more declaracioun, lo here thy figure. 21 To knowe for what latitude in any regioun the almikanteras of any table ben compouned. [Ad cognoscendum pro qua latitudine in aliqua regione almicantre tabule mee sunt composite.] Rikne how manye degrees of almikanteras, in the meridional lyne, be fro the cercle equinoxial un-to the senith; or elles fro the pool artik un-to the north orisonte; and for so gret a latitude or for so smal a latitude is the table compouned. And for more 5 declaracion, lo here thy figure. 22. To knowe in special the latitude of oure countray, I mene after the latitude of Oxenford, and the heighte of oure pol. [Ad cognoscendum specialiter latitudinem nostri regionis, scilicet latitudinem Oxonie, et altitudinem poli nostri.] Understond wel, that as fer is the heved of Aries or Libra in the equinoxial from oure orisonte as is the senith from the pole artik; and as hey is the pol artik fro the orisonte, as the equinoxial is fer fro the senith. I prove it thus by the latitude of Oxenford. 5 Understond wel, that the heyghte of oure pool artik fro oure north orisonte is 51 degrees and 50 minutes; than is the senith from oure pool artik 38 degrees and 10 minutes; than is the equinoxial 21. In fig. 5, the almicanteras, if accurately drawn, ought to shew as many degrees between the south point of the equinoctial circle and the zenith as are equal to the latitude of the place for which they are described. The number of degrees from the pole to the northern point of the horizon obliquus is of course the same. The latitude of the place for which the disc is constructed is thus determined by inspection. 22. In the first place where 'orisonte' occurs, it means the South point of the horizon; in the second place, the North point. By referring to fig. 13, Plate V, it is clear that the arc YS, representing the distance between the equinoctial and the S. point, is equal to the arc ZP, which from oure senith 51 degrees and 50 minutes; than is oure south orisonte from oure equinoxial 38 degrees and 10 minutes. Understond wel this rekning. Also for-get nat that the senith is 90 10 degrees of heyghte fro the orisonte, and oure equinoxial is 90 degrees from oure pool artik. Also this shorte rewle is soth, that the latitude of any place in a regioun is the distance fro the senith unto the equinoxial. And for more declaracioun, lo here thy figure. 15 23. To prove evidently the latitude of any place in a regioun, by the preve of the heyghte of the pol artik in that same place. [Ad probandum evidenter latitudinem alicuius loci in aliqua regione, per probacionem altitudinis de polo artico in eodem loco.] In some winters night, whan the firmament is clere and thikkesterred, waite a tyme til that any sterre fix sit lyne-right perpendiculer over the pol artik, and clepe that sterre A. And wayte a-nother sterre that sit lyne-right under A, and under the pol, and clepe that sterre F. And understond wel, that F is nat 5 considered but only to declare that A sit evene overe the pool. Tak thanne a-non right the altitude of A from the orisonte, and forget it nat. Lat A and F go farwel til agayns the dawening a gret whyle; and come thanne agayn, and abyd til that A is evene underthe pol and under F; for sothly, than wol F sitte over the pool, 10 and A wol sitte under the pool. Tak than eft-sones the altitude of A from the orisonte, and note as wel his secounde altitude as his firste altitude; and whan that this is don, rikne how manye degrees measures the distance from the pole to the zenith; since PO Y and ZOS are both right angles. Hence also Chaucer's second statement, that the arcs PN and ʼnZ are equal. In his numerical example, PN is 51° 50'; and therefore ZP is the complement, or 38° 10′. So also TZ is 51° 50′; and TS is 38° 10'. Briefly, TZ measures the latitude. 23. Here the altitude of a star (A) is to be taken twice; firstly, when it is on the meridian in the most southern point of its course, and secondly, when on the meridian in the most northern point, which would be the case twelve hours later. The mean of these altitudes is the altitude of the pole, or the latitude of the place. In the example given, the star A is only 4° from the pole, which shews that it is the that the firste altitude of A excedeth his seconde altitude, and tak 15 half thilke porcioun that is exceded, and adde it to his seconde altitude; and tak ther the elevacioun of thy pool, and eke the latitude of thy regioun. For thise two ben of a nombre; this is to seyn, as many degrees as thy pool is elevat, so michel is the latitude of the regioun. Ensample as thus: par aventure, the 20 altitude of A in the evening is 56 degrees of heyghte. Than wol his seconde altitude or the dawing be 48; that is 8 lasse than 56, that was his firste altitude at even. Take thanne the half of 8, and adde it to 48, that was his seconde altitude, and than hastow 52. Now hastow the heyghte of thy pol, and the latitude 25 of the regioun. But understond wel, that to prove this conclusioun and many another fair conclusioun, thou most have a plomet hanging on a lyne heyer than thin heved on a perche; and thilke. lyne mot hange evene perpendiculer by-twixe the pool and thyn eye; and thanne shaltow seen yif A sitte evene over the pool and 30 over F at evene; and also yif F sitte evene over the pool and over A or day. And for more declaracion, lo here thy figure. 24. Another conclusioun to prove the heyghte of the pool artik fro the orisonte. [Alia conclusio ad probandum altitudinem de polo artico ab orizonte.] Tak any sterre fixe that nevere dissendeth under the orisonte in thilke regioun, and considere his heyest altitude and his lowest altitude fro the orisonte; and make a nombre of bothe thise altitudes. Tak thanne and abate half that nombre, and tak ther 5 the elevacioun of the pol artik in that same regioun. And for more declaracioun, lo here thy figure. The star F is, Pole-star, then farther from the Pole than it is now. according to Chaucer, any convenient star having a right ascension differing from that of the Pole-star by 180°; though one having the same right ascension would serve as well. If then, at the first observation, the altitude of A be 56, and at the second be 48, the altitude of the pole must be 52. See fig. 13, Plate V. 24. This comes to much the same thing. The lowest or northern altitude of Dubhe (a Ursa Majoris) may be supposed to be observed to be 25°, and his highest or southern altitude to be 79°. Add these; the sum is 104; 'abate' or subtract half of that number, and the result is 52°; the latitude. 25. A-nother conclusioun to prove the latitude of the regioun, &c. [Alia conclusio ad probandum latitudinem regionis.] Understond wel that the latitude of any place in a regioun is verreyly the space by-twixe the senith of hem that dwellen there. and the equinoxial cerkle, north or southe, taking the mesure in the meridional lyne, as sheweth in the almikanteras of thyn Astrolabie. And thilke space is as moche as the pool artik is hey 5 in the same place fro the orisonte. And than is the depressioun of the pol antartik, that is to seyn, than is the pol antartik by-nethe the orisonte, the same quantite of space, neither more ne lasse. Thanne, yif thow desire to knowe this latitude of the regioun, tak the altitude of the sonne in the middel of the day, whan the sonne 10 is in the hevedes of Aries or of Libra; (for thanne moeveth the sonne in the lyne equinoxial); and abate the nombre of that same sonnes altitude out of 90, and thanne is the remenaunt of the noumbre that leveth the latitude of the regioun. As thus: I suppose that the sonne is thilke day at noon 38 degrees and 10 15 minutes of heyghte. Abate thanne thise degrees and minutes out of 90; so leveth there 51 degrees and 50 minutes, the latitude. I sey nat this but for ensample; for wel I wot the latitude of Oxenforde is certein minutes lasse, as I mighte prove. Now yif so be that thee semeth to long a taryinge, to abyde til that the 20 sonne be in the hevedes of Aries or of Libra, thanne waite whan the sonne is in any other degree of the zodiak, and considere the degree of his declinacion fro the equinoxial lyne; and yif it so be that the sonnes declinacion be northward fro the equinoxial, abate thanne fro the sonnes altitude at noon the nombre of his de- 25 clinacion, and thanne hastow the heyghte of the hevedes of Aries and Libra. As thus: my sonne is, par aventure, in the firste 25. Here, as in § 22, Chaucer says that the latitude can be measured by the arc Z or PN; he adds that the depression of the Antarctic pole, viz. the arc SP' (where P' is the S. pole), is another measure of the latitude. He explains that an obvious way of finding the latitude is by finding the altitude of the sun at noon at the time of an equinox. If this altitude be 38° 10', then the latitude is the complement, or 51° 50'. But this observation can only be made on two days in the year. If then this seems to be too long a tarrying, observe his midday |