Imatges de pàgina
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30. To knowe the altitude of planetes fro the wey of the sonne, whether so they be north or south fro the forseide wey.

[Ad cognoscendum altitudinem planetarum a cursu solis, utrum sint in parte australi vel boreali a cursu supra dicto.]

Lok whan that a planete is in the lyne meridional, yif that hir altitude be of the same heyghte that is the degree of the sonne for that day, and than is the planete in the verrey wey of the sonne, and hath no latitude. And yif the altitude of the planete be heyere than the degree of the sonne, than is the planete north fro 5 the wey of the sonne swich a quantite of latitude as sheweth by thyn almikanteras. And yif the altitude of the planete be lasse than the degree of the sonne, thanne is the planete south fro the wey of the sonne swich a quantite of latitude as sheweth by thyn almikanteras. This is to seyn, fro the wey wher-as the sonne 10 wente thilke day, but nat from the wey of the sonne in every place of the zodiak. And for the more declaracioun, lo here the figure.

31. To knowe the senith of the arysing of the sonne, this is to seyn, the partie of the orisonte in which that the sonne aryseth.

[Ad cognoscendum signum de ortu solis, scilicet, illam partem orientis in qua oritur sol.]

Thou most first considere that the sonne aryseth nat al-wey verrey est, but some tyme by north the est, and som tyme by southe the est. Sothly, the sonne aryseth never-mo verrey est in oure

30. This turns upon the definition of the phrase 'the wey of the sonne.' It does not mean the zodiacal circle, but the sun's apparent path on a given day of the year. The sun's altitude changes but little in one day, and is supposed here to remain the same throughout the time that he is, on that day, visible. Thus, if the sun's altitude be 61, the way of the sun is a small circle, viz. the tropic of Cancer. If the planet be then on the zodiac, in the 1st degree of Capricorn, it is 47° S. from the way of the sun, and so on.

31. The word 'senith' is here used in a peculiar sense; it does not mean, as it should, the zenith point, or point directly overhead, but is made to imply the point on the horizon, (either falling upon an

orisonte, but he be in the heved of Aries or Libra. Now is thyn 5 orisonte departed in 24 parties by thy azimutz, in significacion of 24 partiez of the world; al-be-it so that shipmen rikne thilke partiez in 32. Thanne is ther no more but waite in which azimut that thy sonne entreth at his arysing; and take ther the senith of the arysing of the sonne. The manere of the devisioun of thyn 10 Astrolabie is this; I mene, as in this cas. First is it devided in 4 plages principalx with the lyne that goth from est to west, and than with a-nother lyne that goth fro south to north. Than is it devided in smale partiez of azimutz, as est, and est by southe, whereas is the firste azimut above the est lyne; and so forth, fro 15 partie to partie, til that thou come agayn un-to the est lyne. Thus maistow understond also the senith of any sterre, in which partie he ryseth, &c. And for the more declaracion, lo here the figure.

32. To knowe in which partie of the firmament is the
coniunccioun.

[Ad cognoscendum in qua parte firmamenti sunt
coniuncciones solis et lune.]

Considere the tyme of the coniunccion by thy kalender, as thus ; lok how many houres thilke coniunccion is fro the midday of the day precedent, as sheweth by the canoun of thy kalender. Rikne thanne thilke nombre of houres in the bordure of thyn Astrolabie,

azimuthal line, or lying between two azimuths), which denotes the point of sunrise. In the Latin rubric, it is called signum. This point is found by actual observation of the sun at the time of rising. Chaucer's azimuths divide the horizon into 24 parts; but it is interesting to observe his remark, that'shipmen' divide the horizon into 32 parts, exactly as a compass is divided now-a-days. The reason for the division into 32 parts is obviously because this is the easiest way of reckoning the direction of the wind. For this purpose, the horizon is first divided into 4 parts; each of these is halved, and each half-part is halved again. It is easy to observe if the wind lies halfway between S. and E., or half-way between S. and S.E., or again half-way between S. and S.S.E.; but the division into 24 parts would be unsuitable, because third-parts are much more difficult to estimate. 32. The Latin rubric interprets the conjunction to mean that of the sun and moon. The time of this conjunction is to be ascertained from a calendar. If, e. g. the calendar indicates 9 A.M. as the time of conjunction on the 12th day of March, when the sun is in the first point of

as thou art wont to do in knowing of the houres of the day or of 5 the night; and ley thy label over the degree of the sonne; and thanne wol the point of thy label sitte up-on the hour of the coniunccion. Loke thanne in which azimut the degree of thy sonne sitteth, and in that partie of the firmament is the coniunccioun. And for the more declaracioun, lo here thy figure.

33. To knowe the senith of the altitude of the sonne, &c. [Ad cognoscendum signa de altitudine solis.]

This is no more to seyn but any tyme of the day tak the altitude of the sonne; and by the azimut in which he stondeth, maystou seen in which partie of the firmament he is. And in the same wyse maystou seen, by the night, of any sterre, whether the sterre sitte est or west or north, or any partie by-twene, after the 5 name of the azimut in which is the sterre. And for the more declaracioun, lo here the figure.

34. To knowe sothly the degree of the longitude of the mone, or of any planete that hath no latitude for the tyme fro the ecliptik lyne.

[Ad cognoscendum veraciter gradum de longitudine lune, vel alicuius planete qui non habet longitudinem pro tempore causante linea ecliptica.]

Tak the altitude of the mone, and rikne thyn altitude up among

Aries, as in § 3, the number of hours after the preceding midday is 21, which answers to the letter X in the border (fig. 2). Turn the rete till the first point of Aries lies under the label, which is made to point to X, and the label shews at the same moment that the degree of the sun is very nearly at the point where the equinoctial circle crosses the azimuthal circle which lies 50° to the E. of the meridian. Hence the conjunction takes place at a point of which the azimuth is 50° to the E. of the S. point, or 5° to the eastward of the S.E. point. The proposition merely amounts to finding the sun's azimuth at a given time. Fig. 11 shews the position of the rete in this case.

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 5° from the ecliptic,

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thyne almikanteras on which syde that the mone stande; and set there a prikke. Tak thenne anon-right, up-on the mones syde, the altitude of any sterre fix which that thou knowest, and set his 5 centre up-on his altitude among thyn almikanteras ther the sterre is founde. Waite thanne which degree of the zodiak toucheth the prikke of the altitude of the mone, and tak ther the degree in which the mone standeth. This conclusioun is verrey soth, yif the sterres in thyn Astrolabie stonden after the trowthe; of 10 comune, tretis of Astrolabie ne make non excepcioun whether the mone have latitude, or non; ne on whether syde of the mone the altitude of the sterre fix be taken. And nota, that yif the mone shewe himself by light of day, than maystow wyrke this same conclusioun by the sonne, as wel as by the fix sterre. And for the 15 more declaracioun, lo here thy figure.

35. This is the workinge of the conclusioun, to knowe yif that any planete be directe or retrograde.

[Hec conclusio operatur ad cognoscendum si aliqua planeta sit directa vel retrograda.]

Tak the altitude of any sterre that is cleped a planete, and note it wel. And tak eek anon the altitude of any sterre fix that thou knowest, and note it wel also. Come thanne agayn the thridde or the ferthe night next folwing; for thanne shaltow aperceyve wel the 5 moeving of a planete, whether so he moeve forthward or bakward.

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

Awaite wel thanne whan that thy sterre fix is in the same altitude that she was whan thou toke hir firste altitude; and tak than eftsones the altitude of the forseide planete, and note it wel. For trust wel, yif so be that the planete be on the right syde of the meridional lyne, so that his seconde altitude be lasse than his firste altitude 10 was, thanne is the planete directe. And yif he be on the west syde in that condicion, thanne is he retrograd. And yif so be that this planete be up-on the est syde whan his altitude is taken, so that his secounde altitude be more than his firste altitude, thanne is he retrograde, and yif he be on the west syde, than is he 15 directe. But the contrarie of thise parties is of the cours of the mone; for sothly, the mone moeveth the contrarie from othere planetes as in hir episicle, but in non other manere. And for the more declaracioun, lo here thy figure.

36. The conclusiouns of equaciouns of houses, after the Astrolabie, &c.

[Conclusio de equacione domorum.]

Set the by-ginning of the degree that assendeth up-on the ende of the 8 houre inequal; thanne wol the by-ginning of the 2 hous sitte up-on the lyne of midnight. Remeve thanne the degree that assendeth, and set him on the ende of the 10 hour inequal; and thanne wol the byginning of the 3 hous sitte up-on the midnight 5 lyne. Bring up agayn the same degree that assendeth first, and set him up-on the orisonte; and thanne wol the be-ginning of the 4 hous sitte up-on the lyne of midnight. Tak thanne the nadir of

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 I (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

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