- Of the six instruments so far known, two have been recorded in the International Checklist (hereafter IC) by Gibbs S.L. Henderson J.A. de Solla Price D. A Computerized Checklist of Astrolabes New Haven 1973 (This listing includes numbers up to 4000.) This checklist is in the course of revision and extension by Professor David A. King (numbers up to 9999), and I am indebted to him for bringing a number of less well-known astrolabe quadrants to my attention. The outline of the new catalogue is described in D. A. King, ‘Medieval Astronomical Instruments: A Catalogue in Preparation’, Bulletin of the Scientific Instrument Society, 31 (1991), 3–7. For future reference all the instruments, including the newly recorded one described here, are listed with their IC number. IC 2110: Merton College, Oxford; IC 5507: Washington, National Museum of American History, inv. no. 326975; IC 5508: private collection (hereafter PC II); IC 5509: private collection (hereafter PC I), the newly recorded instrument described here; IC 5511: Rouen, Musée des Antiquités de la Seine Maritime, inv. no. 919; IC 2111: Angers, Musée de Saint-Jean, inv. no. MA GF39; IC 5514: Lüneburg, Museum für das Fürstentum Lüneburg, inv. no. 122, briefly described in G. Körner, Leitfaden durch das Museum (Lüneburg, 1975), 167. Another instrument in the collection of the National Museum of American History in Washington, inv. no. 318198 (IC 2006) is a zoomorphic astrolabe with the basic curves of the astrolabe quadrant engraved on the back and no stars. For that reason it has not been included in this study.
- Anthiaume , A. and Sottas , J. 1910 . L'Astrolabe-quadrant du Musée des antiquités de Rouen, recherches sur les connaissances mathématiques, astronomiques et nautiques au moyen âge Paris R. T. Gunther, Early Science in Oxford (Oxford, 1923), II, 165–9; and E. Poulle, ‘Le quadrant nouveau médiéval’, Journal des Savants (1964), 148–67, 182–214.
- Vernet , J. 1976 . “ Jacob ben Machir ibn Tibbon ” . In Dictionary of Scientific Biography Edited by: Gillispie , C.C. Vol. XIII , 400 – 400 . New York See also Encyclopaedia Judaica (Jerusalem, 1971), XV, 1129–30.
- For the manuscripts, see Steinschneider M. Die hebräischen Übersetzungen des Mittelalters Berlin 1893 reprinted Graz, 1956), and J. M. M. Vallicrosa, Tractat de l'assafea d'Azarquiel (Barcelona, 1933).
- Poulle . 1964 . Le quadrant nouveau médiéval . Journal des Savants , : 183 – 183 .
- Private communication with D. A. King; see also King D.A. Islamic Astronomical Instruments Variorum London 1987 8 10 Reprints chapter I
- Poulle . 1964 . Le quadrant nouveau médiéval . Journal des Savants , : 203 – 203 . lists 28 such problems
- Fine , O. 1524 . Quadrans novus Paris A number of astrolabe quadrants of the sixteenth century are known. Poulle (footnote 2), 150, reports on two sixteenth-century astrolabe quadrants in the Museo di Storia della Scienza in Florence, Catalogo degli strumenti del Museo di Storia della Scienza (Florence, 1954), inv. nos 2509 and 2523. No. 2509 is by Thomas Gemini, London, c. 1550, depicted in G. L'E. Turner, Gli Strumenti (Milan, 1991), 122–3; the other is by Joannis Giamin, Rome, sixteenth century. The Museum of the History of Science, Oxford, owns an astrolabe quadrant bearing the name of Giovanni Antonio Magini (1555–1617) (inv. no. LE.I 11). An astrolabe quadrant of 1571 by Johannis Praetorius is shown in Focus Behaim Globus, edited by G. Bott (Nuremberg, 1992), II, 643, no. 1.127. One made by Christophorus Schissler, dated 1576, was offered for sale by Christie's, South Kensington, on 28 September 1989. Another astrolabe quadrant of the sixteenth century is described by Tullio Tomba and Giuseppe Brusa in Museo d'Arti Applicate: Strumenti Scientifici-Orologi (Milan, 1983), 21, no. 18 (inv. no. 262). The pendent dial of 1537 described by Gunther (footnote 2), 135–9, also includes a projection of the zodiac after Profatius. For medieval and later astrolabe quadrants from the Islamic world, see D. A. King, ‘Strumentazione astronomica nel mondo medievale islamico’, in G. L'E. Turner, Gli Strumenti (Milan, 1991), 154–89, in particular 148, 174, and 182–3, and King (footnote 6), IAI, chapter XIV, 376.
- Anthiaume and Sottas . 1910 . L'Astrolabe-quadrant du Musée des antiquités de Rouen, recherches sur les connaissances mathématiques, astronomiques et nautiques au moyen âge Vol. II , 120 – 125 . Paris R. T. Gunther, Early Science in Oxford (Oxford, 1923) describe in detail the relation between the scale and the sine and cosine.
- Kunitzsch , P. 1966 . Typen von Sternverzeichnissen in astronomischen Handschriften des zehnten bis vierzehnten Jahrhunderts Wiesbaden
- For collum corvi, see Kunitzsch Typen von Sternverzeichnissen in astronomischen Handschriften des zehnten bis vierzehnten Jahrhunderts Wiesbaden 1966 91 91 and note 23, p. 93. I most gratefully acknowledge the help and advice offered by Paul Kunitzsch in identifying the stars.
- For these two cycles, see Ginzel F.K. Handbuch der mathematischen und technischen Chronologie Leipzig 1914 III 134 143 3 vols
- van Wijk , W.E. 1936 . Le Nombre d'Or: Étude de chronologie technique suivie du texte de la Massa Compoti d'Alexandre de Villedieu avec traduction et commentaire 115 – 115 . The Hague
- van Wijk , W.E. 1936 . Le Nombre d'Or: Étude de chronologie technique suivie du texte de la Massa Compoti d'Alexandre de Villedieu avec traduction et commentaire 116 – 116 . The Hague Two tables for both definitions, named ‘Antiquus’ and ‘Campani’ respectively are presented for the period 1100–1500.
- The 19-year cycle has also been described in Dekker Elly Epacts on Instruments: Their Definition and Use Annals of Science 1993 50 303 324 (p. 304)
- van Wijk . 1936 . Le Nombre d'Or: Étude de chronologie technique suivie du texte de la Massa Compoti d'Alexandre de Villedieu avec traduction et commentaire 90 – 90 . The Hague
- Tables such as those shown in van Wijk Le Nombre d'Or: Étude de chronologie technique suivie du texte de la Massa Compoti d'Alexandre de Villedieu avec traduction et commentaire The Hague 1936 90 90 cover several centuries
- Poulle . 1964 . Le quadrant nouveau médiéval . Journal des Savants , : 185 – 186 .
- van Wijk . 1936 . Le Nombre d'Or: Étude de chronologie technique suivie du texte de la Massa Compoti d'Alexandre de Villedieu avec traduction et commentaire 116 – 116 . The Hague The years for the solar cycle cited here cannot be compared with those encountered on our instruments because the ordinal number is defined differently as the remainder of {year + 9}/28. Poulle (footnote 2), 186, recognizes the two sequences of years as the beginnings (points de départ) of the respective cycles. This is confusing. A simple calculation shows that they present the last years of their cycles. For example, the remainder of {1307 + 9}/28 is 0 (equivalent to ordinal number 28), and also the remainder of {1310 + 1}/19 is 0 (equivalent to golden number 19).
- Poulle . 1964 . Le quadrant nouveau médiéval . Journal des Savants , : 186 – 186 .
- For the dates of the instruments in Rouen, Oxford, and Angers, see the references in Anthiaume A. Sottas J. L'Astrolabe-quadrant du Musée des antiquités de Rouen, recherches sur les connaissances mathématiques, astronomiques et nautiques au moyen âge Paris 1910 Anthiaume and Sottas, 160–1; Gunther, 165; Poulle, 162.
- Oxford, Bodleian Library, MS Ashmole 1522 Tractatus Quadrantis Novi compositi a magistro Profatio Hebreo, anno domini 1288 et correctus ab eodem A.D. 1301 fol. 122–32, in particular fol. 132r.
- B.N. lat. 7437, which contains a treatise on the construction of the astrolabe. See Poulle Le quadrant nouveau médiéval Journal des Savants 1964 206 206 and passim
- From a letter dated 14 July 1987, written by John Clark, Senior Assistant Keeper, Department of Medieval Antiquities of The Museum of London, to Professor Gerard L'E. Turner. For the case of the Rouen instrument, see Anthiaume Sottas L'Astrolabe-quadrant du Musée des antiquités de Rouen, recherches sur les connaissances mathématiques, astronomiques et nautiques au moyen âge Paris 1910 157 160
- This principle was used by Anthiaume Sottas L'Astrolabe-quadrant du Musée des antiquités de Rouen, recherches sur les connaissances mathématiques, astronomiques et nautiques au moyen âge Paris 1910 110 111 and by R. K. E. Torode, ‘A Mathematical System for Identifying the Stars of an Astrolabe and Finding its Age’, in Astrolabica, 5 (Paris, 1990), 53–76. The principle is criticized by Elly Dekker, ‘Of Astrolabes and Dates and Dead Ends’ (Essay Review) Annals of Science, 49 (1992), 175–84.
- Poulle , E. 1956 . Peut-on dater les astrolabes médievaux? . Revue d'histoire des sciences et de leurs applications , 9 : 301 – 322 . P. Kunitzsch, ‘Zur Problematik der Astrolabsterne-eine weitere unbrauchbare Sterntafel’, Archives Internationales d'Histoire des Sciences, 43 (1993), 197–208.
- Kunitzsch . 1966 . Typen von Sternverzeichnissen in astronomischen Handschriften des zehnten bis vierzehnten Jahrhunderts 73 – 73 . Wiesbaden For the universal astrolabe, see A. J. Turner, ‘Astrolabes, Astrolabe Related Instruments’, Vol. 1, Part 1, ‘Time Measuring Instruments’, in The Time Museum, edited by B. Chandler (Rockford, 1985), 151–66.
- Kunitzsch , P. 1989 . The Arabs and the Stars , 197 – 201 . Northampton : Variorium . Reprints chapter IV
- Kunitzsch . 1966 . Typen von Sternverzeichnissen in astronomischen Handschriften des zehnten bis vierzehnten Jahrhunderts Wiesbaden
- Poulle . 1964 . Le quadrant nouveau médiéval . Journal des Savants , published three star tables on pp. 188, 189, and 192. The first (p. 188) is an extract of Type XIII (see Kunitzsch, footnote 12, 89); the second listing, for the epoch 1466, is an extract from a list added by John of Gmunden to his treatment on the astrolabe quadrant; the third listing, for the epoch 1316, stems from an anonymous treatise on the astrolabe quadrant. The latter list is also mentioned in Kunitzsch (footnote 12), 77.
- See Tractatus Quadrantis Novi compositi a magistro Profatio Hebreo, anno domini 1288 et correctus ab eodem A.D. 1301 and Figure 1
- For the Rouen instrument, see Anthiaume Sottas L'Astrolabe-quadrant du Musée des antiquités de Rouen, recherches sur les connaissances mathématiques, astronomiques et nautiques au moyen âge Paris 1910 110 110 the stars on the Oxford instrument are listed in Gunther (footnote 2), 167. Gunther mentions only ten stars. However, close to the North Pole, at a declination of 71°, another unnamed star is indicated. This star has not been identified.
- For the instrument in Angers, see Poulle Le quadrant nouveau médiéval Journal des Savants 1964 156 156 There is β Ori instead of γ Gem for pes geminorum, ι Cet instead of β Cet for cauda caytoz, δ Cap instead of γ Cap for cauda capricorni. The names of Orion and Gemini were often confused in Latin translations from the Arabic; see P. Kunitzsch, Arabische Sternnamen in Europa (Wiesbaden, 1959), 195. The difference in the identification of cauda caytoz results from a positional error. The mediation of this star on the instrument is Pisces 26°, not 18·5° (Table 9).
- All stars concerned also figure in the more extensive list of MS Erfurt, Amplon.4° 351, fol. 55, edited by Poulle Le quadrant nouveau médiéval Journal des Savants 1964 192 192 All but one of the names of the stars in this list are similar to those on the instruments in Oxford and Rouen. The exception is ‘alfart’, for which the list in Poulle has ‘Humerus equi’. Since the analysis of the positional data shows that this list was not involved in making the astrolabe quadrants of Rouen and Oxford, it has been excluded from this discussion.
- Stars absent in the lists published by Poulle Le quadrant nouveau médiéval Journal des Savants 1964 188 188 189, and 192, are: γ Ori, the ghost star mocadani or aldiraan, α Cet, ϑ UMa, the ghost star coruus, γ Crv, ι and ζ Cet, α Cep, and ϵ Del.
- An instrument will be said to have a ‘composite’ star table when the list involved is a combination of two of Kunitzsch's Types. Such lists do not necessarily derive from existing manuscript lists. They may have come into being through the initiative of the maker, when using more than one star list. For composite lists in manuscripts, see Type VIII in Kunitzsch Typen von Sternverzeichnissen in astronomischen Handschriften des zehnten bis vierzehnten Jahrhunderts Wiesbaden 1966 52 52 Kunitzsch (footnote 37), and Kunitzsch (footnote 39). Chapter X, ‘On the authenticity of the treatise on the composition and use of the astrolabe ascribed to Messahalla’.
- Kunitzsch . 1966 . Typen von Sternverzeichnissen in astronomischen Handschriften des zehnten bis vierzehnten Jahrhunderts 32 – 32 . Wiesbaden Type IV, no. 6
- Kunitzsch . 1966 . Typen von Sternverzeichnissen in astronomischen Handschriften des zehnten bis vierzehnten Jahrhunderts 67 – 71 . Wiesbaden The Ptolemaic values were taken from P. Kunitzsch, editor, Der Sternkatalog des Almagest. III. Gesamtkonkordanz der Sternkoordinaten (Wiesbaden, 1991). Ptolemy + 14°7′ is chosen because the epoch for this excess in longitude is clearly defined by Type XII, and therefore can serve as a reliable standard for comparison.
- Type XI may derive from Type III, but see Kunitzsch Typen von Sternverzeichnissen in astronomischen Handschriften des zehnten bis vierzehnten Jahrhunderts Wiesbaden 1966 67 67
- Kunitzsch . 1966 . Typen von Sternverzeichnissen in astronomischen Handschriften des zehnten bis vierzehnten Jahrhunderts 15 – 15 . Wiesbaden 23, and 87. The epoch of Type XIII mentioned on p. 87 has to be corrected to 527 AH ( = AD 1132–3). Private communication from Paul Kunitzsch.
- A comparison made in Kunitzsch P. Dekker E. The Stars on the Rete of the Carolingian Astrolabe to be published, Table 1, shows that the mediations of Ptolemy + 12°40′ and those of Type III differ systematically by > 1° if all stars are included.
- Too little is known about the precession theories used in the middle of the thirteenth century. The so-called trepidation theory of Thābit ibn Qurra predicts, according to Poulle, 16·1° for the epoch 1252. The star catalogue appended to the Alphonsine Tables is based on 17·1° (17°8′). See Poulle E. The Alphonsine Tables and Alfonso X of Castille Journal for the History of Astronomy 1988 19 97 113 Note that Anthiaume and Sottas (footnote 2), 151–2, using modern data, arrived at the early epoch of 1180 for the Rouen instrument.
- 1984 . Ptolemy's Almagest 153 – 157 . London translated and annotated by G. J. Toomer The interval from the spring equinox to the summer solstice is longer (according to Hipparchus it lasts 94·5 days) than that from the summer solstice to the autumnal equinox (92·5 days)
- 1984 . Ptolemy's Almagest 153 – 153 . London translated and annotated by G. J. Toomer
- Hartner , W. 1970 . “ Al-Battānī ” . In Dictionary of Scientific Biography Edited by: Gillispie , C.C. Vol. I , 510 – 510 . New York reports that in AD 883/4, Al-Battānī measured 82°17′
- Poulle . 1964 . Le quadrant nouveau médiéval . Journal des Savants , : 194 – 194 . According to a calculation by Anthiaume and Sottas (footnote 2), 147, again using modern data, another misleading epoch of 1188 is derived for the apogee of Gemini 29°.
- Michel , Henri . 1947 . Traité de l'astrolabe 135 – 141 . Paris Poulle (footnote 37), 304–9
- Again, using modern data Anthiaume Sottas L'Astrolabe-quadrant du Musée des antiquités de Rouen, recherches sur les connaissances mathématiques, astronomiques et nautiques au moyen âge Paris 1910 149 149 calculated that in 1212 the vernal equinox was at 13 March. The same value is obtained using Michel (footnote 64). All known dated instruments with 13 March for the vernal equinox were made in the fourteenth century or later.
- Poulle . 1964 . Le quadrant nouveau médiéval . Journal des Savants , : 161 – 161 .
- Gunther . 1923 . Early Science in Oxford 168 – 168 . Oxford In principle, the division in 28 equal parts could also be intended for the ordinal number in the solar cycle. The very fact that the empty circle with a division into 28 parts coincides with Aries 10°, like the lunar mansions on the Rouen instrument and on the drawing in MS Ashmole 1522, excludes this possibility.
- Oxford, Bodleian Library Ashmole 1522, fol. 131v
- Poulle . 1964 . Le quadrant nouveau médiéval . Journal des Savants , : 185 – 185 . with footnote 27, and 194. He suggests that the starting point of the mansions was fixed by the amount of accession and recession of the movement of the ninth sphere after the so-called trepidation theory of Thābit ibn Qurra (836–901). It is not clear when this coupling between the series of lunar mansions and the ninth sphere was made. Anthiaume and Sottas (footnote 2), 144, use Aries 10° to derive an epoch of 788, again using modern data for the precession. D. A. King has described a later European astrolabe (1457) on which the lunar mansions start at c. Aries 20°; see Bott (footnote 8), 175, no. 1.75.
- I am greatly indebted to Paul Kunitzsch for the correct readings of the lunar mansions collected in Table 11. See also Anthiaume Sottas L'Astrolabe-quadrant du Musée des antiquités de Rouen, recherches sur les connaissances mathématiques, astronomiques et nautiques au moyen âge Paris 1910 40 40 for the names on the Rouen instrument, and Poulle (footnote 2), 160–1, for those on the instrument of Angers. The manuscript source is the drawing from the Oxford, Bodleian Library, Ashmole 1522, fol. 131v. The names of the lunar mansions were published by Gunther (footnote 2), 169. The Arabic names and the star configurations were obtained from Kunitzsch (footnote 39), Chapter XX, ‘Al-Manāzil’.
- Kunitzsch , P. private communication
- Astrolabe quadrants are, in fact, the first European instruments to incorporate both the lunar mansions and the lunar volvelle. I do not know a single example of a medieval European astrolabe with lunar mansions, whereas a lunar volvelle is only rarely seen on the back of astrolabes. The London astrolabe in Merton College is an exception, see Gunther Robert T. Astrolabes of the World London 1932 482 482 reprinted 1976 IC 303
- Poulle . 1964 . Le quadrant nouveau médiéval . Journal des Savants , : 161 – 162 .
- For the perpetual calendar, see Pedersen O. The Ecclesiastical Calendar and the Life of the Church Gregorian Reform of the Calendar: Proceedings of the Vatican Conference to Commemorate its 400th Anniversary, 1582–1982 Coyne G.V. Hoskin M.A. Pedersen O. Città di Vaticano 1983 17 74
- For dominical letters, see Ginzel Handbuch der mathematischen und technischen Chronologie Leipzig 1914 III 143 143 3 vols
- van Wijk . 1936 . Le Nombre d'Or: Étude de chronologie technique suivie du texte de la Massa Compoti d'Alexandre de Villedieu avec traduction et commentaire 115 – 115 . The Hague
- For the Sloane astrolabe (IC 290), see Gunther Astrolabes of the World London 1932 463 465 F. A. B. Ward, A Catalogue of European Scientific Instruments in the Department of Medieval and Later Antiquities of the British Museum (London, 1981), 112, no. 324.
- van Wijk . 1936 . Le Nombre d'Or: Étude de chronologie technique suivie du texte de la Massa Compoti d'Alexandre de Villedieu avec traduction et commentaire 116 – 116 . The Hague ‘Celui de Sacrobosco—Campanus a disparu; je n'ai trouvé nulle part une date avec le nombre du cycle solaire, qui convienne à FEDBA’.
Annals of Science
Volume 52, 1995 - Issue 1
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