By the use of the Umbra Recta on the back of the instrument, we can take the altitude of an accessible object by a single observation (ii. 41); or of an inaccessible object by two observations (ii. 43). Or, the height of an inaccessible object may likewise be taken by two observations, by the scale marked Umbra Versa (ii. 42).
The few Conclusions not here referred to are chiefly explanatory, or of minor interest.
§ 30. Stars marked on the Rete. Several of the Latin MSS. upon the Astrolabe give a list of the stars marked upon the Rete. There is a double list, for example, in MS. Ii. 3. 3, in the Cambridge University Library, fol. 70, back. It is given in the form of two tables; the first mentions forty-nine stars, with the degrees of the zodiac which south along with them, and their declinations from the equinoctial line. The second table mentions some only of the same stars, with their longitudes and latitudes, as referred to the ecliptic.
A list of the principal stars usually marked upon the Rete, as shewn in [Fig. 2], is given in the Note to Part i. § 21. 4 (p. [357]). [Fig. 9] shews another Rete, with many of the same stars, with the addition of Markep (ι Argous). Alchimech is the same as Azimech, i.e. α Virginis; Cor Leonis is α Leonis; and Alfart is α Hydræ.
§ 31. Astrological Notes. For a general sketch of Astrology, see the English Cyclopaedia, s.v. Worthless as the science is, it is useful to have a few 'facts' for handy reference. I therefore attempt a synopsis of the chief points of it, drawn from Johannis Hispalensis Isagoge in Astrologiam.
To save space, I give the information in a tabular form, wherein I denote the twelve Signs by A., T., G., C., L., V., Li., S., Sa., Cp., Aq., P.; and the seven Planets, Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon, by St., J., Ms., Sn., V., My., Mo. What the table exactly means shall be explained presently.
| Signs. | Man. | Ex. | Day. | Nt. | Com. | Face 1. | Face 2. | Face 3. |
| A. | Ms. | Sn. (19) | Sn. | J. | St. | Ms. | Sn. | V. |
| T. | V. | Mn. (3) | V. | Mn. | Ms. | My. | Mn. | St. |
| G. | My. | D. H. | St. | My. | J. | J. | Ms. | Sn. |
| C. | Mn. | J. (15) | V. | Ms. | Mn. | V. | My. | Mn. |
| L. | Sn. | Sn. | J. | St. | St. | J. | Ms. | |
| V. | My. | My. (15) | V. | Mn. | Ms. | Sa. | V. | My. |
| Li. | V. | St. (19) | St. | My. | J. | Mn. | St. | J. |
| S. | Ms. | V. | Ms. | Mn. | Ms. | Sn. | V. | |
| Sa. | J. | D. T. | Sn. | J. | St. | My. | Mn. | St. |
| Cp. | St. | Ms. (28) | V. | Mn. | Ms. | J. | Ms. | Sn. |
| Aq. | St. | St. | My. | J. | V. | My. | Mn. | |
| P. | J. | V. (21) | V. | Ms. | Mn. | St. | J. | Ms. |
The first line is to be read thus.
Aries is the mansion (or house) of Mars; the exaltation (or honour) of the Sun, in the 19th degree of the sign; the lord of the Triplicity of Aries with its attendant signs is the Sun by day, Jupiter by night, and Saturn in Common, both by day and night; the first Face of Aries (degrees 1 to 10) is that of Mars; the second Face (degrees 11 to 20) is that of the Sun; the third Face (degrees 21 to 30) is that of Venus. And so on for the rest; noting that Gemini is the Exaltation of the Dragon's Head (D. H.), and Sagittarius that of the Dragon's Tail (D. T.).
The meanings of the words are as follows:—