The arte of nauigation conteyning a compendious description of the sphere, with the making of certayne instruments and rules for nauigations, and exemplifyed by many demonstrations. Written by Martin Cortes Spanyarde. Englished out of Spanishe by Richard Eden, and now newly corrected and amended in diuers places.

¶ The viii. Chapter, of the d••finition of the altitude. And howe the altitude of the Pole may well be knowen by the Meridian altitude and eleuation of the Sunne.

IT is conuenient to d••fine the altitude, b••fore we geue rules of the vse there∣of. The Altitude of the Sunne, or the Moone, or of any other Starres,* 1.1 is the distaunce that is betweéne it and the Horizon. And this ought to beé ac∣compted by the degreés of the great Circle, which passeth by the Zenith, & by the center of the Sunne, or of the Moone, or of the Star, vn∣to the Horizon. And the degreés that are from the H••rizon to the Star, or to the Sunne, that is the altitude:* 1.2 And the degreés that are from the Center of the S••arre, or of the Sunne, vnto the Zenith, is called the complement, or supplement of the alti∣tude. The altitude of the Equinoctiall, is euer co••nted by the Meridian. And the degreés of the Meridian, that are betweéne the Equinoctiall and the Horizon, is the altitude of the Equi∣noctiall: and other so many are they, that are from the Zenith to the Pole.* 1.3 For the altitude of the Equinoctial, is equall to the complement of the altitude of the Pole. The degreés of the Me∣ridian that are be••w••••ne the Equinoctiall, and the Zenith, is cal∣led the complement of the altitude of the Equinoctiall, and is equal to the altitude of the Pole. And al••hough we haue defined the altitude in generall, ye•• shall we only profit our selues by the Meridional altitude of the Sunne. The Meridian altitude, is the greatest altitude that the Sunne hath euery day:* 1.4 and this shall be, when the Center of the Sunne is in the Meridian. And the Arke of the Meridian, that is betweene the Horizon and the Sunne,* 1.5 is the Meridian altitude. So that when we say the altitude of the Sunne is taken, it is vnderstoode at mydday. The shadowes that the Sunne then maketh, are in threé sorts.

for either to vs it casteth the shadow toward the North part, or toward the South, or pendiculer by a right vp line, so that at midday, or noone, nothyng that standeth vpryght, geueth any shadow at all. But forasmuch as there is such variation in decli∣nations, altitudes, shadowes, an•• paralelles, i•• shalbe necessarie to geue rules for all varia••ions. And these shalbe reduced into foure briefe and compe••dious rules the which I haue here des∣cribed,* 1.6 that the wyttie may haue profite by them, and the rude learne them: not caryng for the rules of the Mariners, because they are so long and tedious. For (as the Philosopher saith) it is vainely done by many, that may well be done by few.

When the shadowe shalbe perpendiculer,* 1.7 it is because the Sunne is in the Zenith, and 90 degreés aboue the Horizon. And then how many degreés of declination the Sunne hath•• so much shal we be distant from the Equi••octiall, toward the part where the Sunne declineth. And if it haue no declination, it and we shalbe vnder the Equinoctiall.

But when the Sunne and the shadowes shalbe to vs from the Equinoctiall,* 1.8 towarde one of the Poles, we shall take away the declination from the Meridian altitude, and then shall remayne the complement of the eleuation, which complement being ta∣ken from 90. degreés, then shall remayne that which we be di∣staunt from the Equinoctiall, toward the same Pole.

When the Sunne declineth from the Equinoctiall, toward the one Pole, and the shadowes shalbe towarde the other, we shal ioyne the declination with the meridian altitude: and if all come not to 90. then substract them from 90. degrées, a••d we shall haue the complement, and so much shal we be distan•• from the Equinoctiall, toward that Pole to the whi••h the shadowe falleth. And yf they be more in number then 90. then the ouer∣plus of 90. shall we be distaunt from the Equinoctiall, towarde the Pole where the Sunne declineth•• And if they be iust 90•• we shalbe vnder the Equinoc••iall.

When the Sunne hath no declination••* 1.9 we shalbe distaunt frō the Equinoctial the complement of the Meridian altitude, toward the Pole where the shadowes are. By these rules (be∣side the vse whereof we haue spoken) may be knowen how much

is the greatest declination of the Sunne, th•• altitude of the E∣quinoctial, the day, houre, and minute, when the Equinox was: the which is knowen as foloweth.

Hauing taken the greater Meridian altitude of the Sommet (which is in the beginning of Cancer) and the lesse of Winter,* 1.10 (which is in the beginning of Capricorne) taking away the lesse from the more, the ••est is that, that is from Tropike to Tropike, & consequently par••ed by the middest, is the greatest declination. As for example.* 1.11 I suppose, that being in the Ci∣tie of Cadi••, to finde the great Meridian altitude of the Sunne (being in the beginning of Cancer) to be 77. degrées, and the lesser Meridian altitude (which is, when the Sunne is in the beginning of Capricorne) to be 30. degreés: then taking 30. from 77. remayne 28. degrées: and so much is frō Tropike to Tropike. And the halfe (which is 23. and a halfe) is the greatest declination.

Consequently the greatest declination added to the lesse Me∣ridian altitude, taking it away from the greater Meridian alti∣tude, that riseth thereof, is the altitude of the Equinoctiall. Ex∣ample 23. and a half of the greatest declination,* 1.12 ioined with 30. of the least Meridian altitude, or taken away from the 77. of the greatest Meridian altitude, remayne 53. degreés and a halfe, which is the altitude of the Equinoctiall, in the Citie of Cadiz. Hereof it foloweth,* 1.13 that w••ē we shal ••ake the meridian altitude in 53. degreés and a halfe, that day is the true Equinoctial. But if it had one day lesse, and the other day folowing it had more, we must take the lesse from the more, & fourme the rule of threé vppon the rest, saying, If 24. minutes (which is that that the Sunne declineth in one day) doth yeéld 24. houres, how much shall those minutes that lacketh of 53. degreés and a halfe of the altitude of the Equinoctial, yeéld me? Multiplying & deuiding according to the foresayd rule, then that which commeth there∣of, shall be the houres after the midday, when it is Equinox.

* 1.14Example of the experience that I made in the Citie of Cadiz the tenth day of March at midday or high noone, I toke the altitude of the Sunne, in 53•• degreés, and 26. minutes, they lacke to be the Equinoctial 4. minutes. An other day, the xi. of

Marche, at noone, I tooke the Sunne, in 53. degrées, and fiftie minutes: which are more then the Equinoctiall by twenty mi∣nutes. Then to knowe at what houre the Sunne was in the 53. degreés, and thirtie minutes of the Equinoctiall, I tooke away the Meridian altitude that I tooke at the tenth of March, from that that I tooke at the eleuenth, which is the difference 24. mi∣nutes, and I formed the rule, saying: if 24. minutes the Sunne did rise to me, in 24. houres, then in how much time shall ryse vnto me the four minutes that failed me at the tenth of March? I multiplyed, deuided, & found, that in four houres: and so shall you say, that the Equinoctiall was in the citie of Cadiz the tenth day of March, at foure of the clocke at after noone, which is vn∣derstoode (according to the Astronomers) at foure houres run at the eleuenth day of March, at this present yeére 1545.

Notes

• * 1.1

  VVhat is the altitude of the Planets or Starres.
• * 1.2

  The comple∣ment of the altitude.
• * 1.3

  ••rom the Ze∣nith to the Pole.
• * 1.4

  The Meridian altitude of the Sunne.
• * 1.5

  The shadows that the Sun maketh at mydday.
• * 1.6

  Rules for all variations.
• * 1.7

  The pe••pendi∣culer shadow.
• * 1.8

  The declinin•• shadowes.
• * 1.9

  VVhen the Su••ne hath no declina∣tion.
• * 1.10

  To know the greatest decli∣nation of th•• ••••nne.
• * 1.11

  Exampl••.
• * 1.12

  Example.
• * 1.13

  The true Equinoctial.
• * 1.14

  Example.