Imatges de pàgina
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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

Io 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 more declaracioun, lo here thy figure.

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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 directavel retrograda.]

Tak the altitude of any sterre that is cleped a planete, and note it wel. And takeek 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 moeving of a planete, whether so he moeve forthward or bakward.

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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 A’ete 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

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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 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 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.

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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 Io 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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the degree that first assendeth, and set him on the ende of the 2

Io houre inequal; and thanne wol the by-ginning of the 5 hous sitte up-on the lyne of midnight; set thanne the nadir of the assendent on the ende of the 4 houre, than wol the byginning of the 6 house sitte on the midnight lyne. The byginning of the 7 hous is nadir of the assendent, and the byginning of the 8 hous is nadir of the

152; and the by-ginning of the 9 hous is nadir of the 3; and the by-ginning of the Io hous is the nadir of the 4; and the byginning of the 11 hous is nadir of the 5; and the byginning of the 12 hous is nadir of the 6. And for the more declaracion, lo here the figure.

37. A-nother manere of equaciouns of houses by the Astrolabie.

[De aliqua forma equacionis domorum secundum
astrolabium.]

Tak thyn assendent, and thanne hastow thy 4 angles; for wel thou wost that the opposit of thyn assendent, that is to seyn, thy by-ginning of the 7 hous, sit up-on the west orizonte; and the byginning of the Io hous sit up-on the lyne meridional; and his 5 opposit up-on the lyne of midnight. Thanne ley thy label over the degree that assendeth, and rekne fro the point of thy label alle the degrees in the bordure, til thou come to the meridional lyne; and departe alle thilke degrees in 3 evene parties, and take the evene equacion of 3; for ley thy label over everich of 3 parties, to and than maistow see by thy label in which degree of the zodiak is the by-ginning of everich of thise same houses fro the assendent: that is to seyn, the beginning of the 12 house next above thyn

to 2 hours, so that the bringing of the 3rd house to the midnight line brings I to the Ioth hour-line, and a similar placing of the 4th house brings I 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 Io, the even division of the quadrant into 3 parts shews the 12th and 11th assendent; and thanne the beginning of the 11 house; and thanne the Io, up-on the meridional lyne; as I first seide. The

same wyse wirke thou fro the assendent doun to the lyne of 15

midnight; and thanne thus hastow other 3 houses, that is to Seyn, the byginning of the 2, and the 3, and the 4 houses ; thanne is the nadir of thise 3 houses the by-ginning of the 3 houses that folwen. And for the more declaracioun, lo here thy figure.

38. To finde the lyne merydional to dwelle fix in any certein place.

[Ad inveniendum lineam meridionalem per subtiles
operaciones.]

Tak a rond plate of metal; for warping, the brodere the bettre; and make ther-upon a iust compas, a lite with-in the bordure; and ley this ronde plate up-on an evene grond, or on an evene ston, or on an evene stok fix in the gronde; and ley it even by a level. And in centre of the compas stike an evene pin or a wyr upright; 5 the smallere the betere. Set thy pin by a plom-rewle evene upright; and let this pin be no lengere than a quarter of the diametre of thy compas, fro the centre. And waite bisily, aboute 1o or 11 of the clokke and whan the sonne shyneth, whan the shadwe of the pin entreth any-thing with-in the cercle of thy plate 1 an heer-mele, and mark ther a prikke with inke. Abyde thanne stille waiting on the sonne after 1 of the clokke, til that the schadwe of the wyr or of the pin passe ony-thing out of the cercle of the compas, be it never so lyte; and set ther a-nother prikke of inke. Take than a compas, and mesure evene the middel 1 by-twixe bothe prikkes; and set ther a prikke. Take thanne a rewle, and draw a stryke, evene a-lyne fro the pin un-to the

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

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middel prikke ; and tak ther thy lyne meridional for evere-mo, as in that same place. And yif thow drawe a cros-lyne over-thwart the compas, iustly over the lyne meridional, than hastow est and west and south ; and, par consequence, than the nadir of the south lyne is the north lyne. And for more declaracioun, lo here thy figure.

39. Descripcion of the meridional lyne, of longitudes, and latitudes of citees and townes from on to a-nother of clymatz.

This lyne meridional is but a maner descripcion of lyne imagined, that passeth upon the poles of this world and by the senith of oure heved. And hit is y-cleped the lyne meridional; for in what place that any maner man is at any tyme of the yeer, whan that the sonne by moeving of the firmament cometh to his verrey meridian place, than is hit verrey midday, that we clepen oure noon, as to thilke man ; and therfore is it cleped the lyne of midday. And nota, for evermo, of 2 citees or of 2 tounes, of whiche that o toun aprocheth more toward the est than doth that other toun, truste wel that thilke tounes han diverse meridians. Mota also, that the arch of the equinoxial, that is conteyned or bounded by-twixe the 2 meridians, is cleped the longitude of the toun. And yif so be that two tounes have y-lyke meridian, or oon meridian, than is the distance of hem bothe y-lyke fer fro the est; and the contrarie. And in this manere they chaunge nat her meridian, but sothly they chaungen her almikanteras; for the enhausing of the pool and the distance of the

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 mine. 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

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