Before the Sun in the Church

Heibron J. L. , The Sun in the Church: Cathedrals as solar observatories (Cambridge, Mass., and London, 1999).

Danti E. , La prospettiva di Euclide (Florence, 1573), 84, cited in Settle T. , “Dating Toscanelli's meridian in Santa Maria del Fiore”, Annali dell'lstituto e Museo di Storia della Scienza di Firenze , iii (1978), 69–70; and in Saalman H. , Filippo Brunelleschi: The cupola of Santa Maria del Fiore (London, 1980), 146. As Heilbron, op. cit. (ref. 1), 70f, indicates, Danti wished to make measurements at equinoxes and solstices, whereas Toscanelli's gnomon could have been used only for a few weeks before and after summer solstice.

Heilbron , op. cit. (ref. 1), 333, n. 42, cites Settle , op. cit. (ref. 2), but Settle gives credit to Saalman (not cited by Heilbron) and indicates that Saalman gave him permission to publish a slightly adapted version of the note that had not yet appeared: See Saalman, op. cit. (ref. 2), 146–7, 294.

See now Jervis J. , Cometary theory in fiteenth-century Europe (Wroclaw, 1985).

Goldstein B. R. , The astronomy of Levi ben Gerson (1288–1344) (New York and Berlin, 1985), 14; see also Mancha J. L. , “The Latin translation of Levi ben Gerson's Astronomy”, in Studies on Gersonides: A fourteenth-century Jewish philosopher-scientist , ed. by Freudenthal G. (Leiden, 1992), 21–46. Note that there were two versions of Levi's Astronomy in Latin, a short version (extant in six manuscripts) with chaps. 4–11 only, and a long version (extant in four manuscripts) with chaps. 1–103, 106, 109, and 110. The table of contents in Hebrew and in the long Latin version indicates that there were 136 chapters, but a few of them are missing in all the extant manuscripts.

Goldstein , op. cit. (ref. 5), 86–92, 170–8.

Goldstein , op. cit. (ref. 5), 95–101, 146. Note that chaps. 13–15 are included in the long Latin version, but not in the short Latin version, of Levi's Astronomy.

For an estimate of the size of the synagogue in fourteenth-century Orange where Levi lived, see Goldstein, op. cit. (ref. 5), 178. There is no information about the synagogue in Orange, but in nearby Cavaillon the old synagogue has the right orientation with windows on the south and east walls, and the appropriate dimensions, approximately. Concerning the old synagogues in Comtat Venaissin, including the one in Cavaillon, we are told, “si leur aspect actuel date essentiellement du XVIII^e siècle, leur emplacement et leurs fondations remontent au moyen âge, XIV^e ou XV^e siècle”: Molinas R. , “Les vieilles synagogues d'Avignon et du Comtat Venaissin”, Archives juives , xvi (1980), 14–26, esp. p. 14.

ben Gerson Levi , Astronomy , chap. 55 (Paris, Bibliothèque Nationale de France, MS Heb. 724, f. 104a; and MS Heb. 725, f. 79b). See also Goldstein B. R. , “Medieval observations of solar and lunar eclipses”, Archives internationales d'histoire des sciences , xxix (1979), 101–56; idem, “A new set of fourteenth century planetary observations”, Proceedings of the American Philosophical Society , cxxxii (1988), 371–99; and Mancha J. L. , “Levi ben Gerson's astronomical work: Chronology and Christian context”, Science in context , x (1997), 471–93, esp. pp. 490–2.

Goldstein , op. cit. (ref. 5), 48–50, 69–73, 140–4; see also Goldstein B. R. , “Levi ben Gerson: On astronomy and physical experiments”, in Physics, cosmology and astronomy, 1300–1700 , ed. by Unguru S. (Dordrecht, 1991), 75–82. Levi indicates it is best for the aperture to be very small. Although Kepler is usually given credit for the proper understanding of the camera obscura, the same explanation (in an abbreviated form) is given by Levi.

Goldstein , op. cit. (ref. 5), 11. On the dispute between Regiomontanus and George of Trebizond, see Shank M. H. , “Regiomontanus and homocentric astronomy”, Journal for the history of astronomy , xxix (1998), 157–66, esp. pp. 161f. As far as I know, Regiomontanus only refers to Levi ben Gerson one time: See Regiomontanus , “Defensio Theonis contra Trapezuntium”, in de Murr C. T. , Notitia trium codium autographorum Iohannis Regiontani in Bibliotheca Christophori Theophili de Murr (Nuremberg, 1801), 11–12.

Rose P. L. , The Italian renaissance of mathematics (Geneva, 1975), 30.

Petz H. , “Urkundliche Nachrichten über den literarischen Nachlass Regiomontans und B. Walters 1478–1522”, Mitteilungen des Vereins für Geschichte der Stadt Nürnberg , vii (1888), 237–62, esp. p. 260; and Rose , op. cit. (ref. 12), 107. This text is presumably identical with the short Latin version of Levi's Astronomy, concerning trigonometry, the cross staff, and the camera obscura, called in the fourteenth century Tractatus instrumenti astronomie (Paris, Bibliothèque Nationale de France, MS lat. 7293). In the secondary literature this text is usually cited with the title, De sinibus, cordis et arcubus, item instrumento reuelatore secretorum : See Mancha J. L. , “The Provençal version of Levi ben Gerson's tables for eclipses”, Archives internationales d'histoire des sciences , xlviii (1998), 269–352, esp. p. 270 n. 2.

Schöner J. , Scripta clarissimi mathematici (Nuremberg, 1544), 34v–60v; see Roche J. J. , “The radius astronomicus in England”, Annals of science , xxxviii (1981), 1–32, esp. p. 11. Roche, following Celoria G. ( Sulle osservazioni di comete fatte da Paolo dal Pozzo Toscanelli e sui lavori astronomici suoi in generate (Milan, 1921)), assumed that Toscanelli also used a cross staff for his observations of the comet of 1433, but Jervis, op. cit. (ref. 4), 67f, does not accept that claim.

Goldstein , op. cit. (ref. 5), 51–56, 146–7.

Rose , op. cit. (ref. 12), 189; Roche , op. cit. (ref. 14), 8. I am informed by J. L. Mancha that Vat. lat. 3380 dates from the fifteenth century.

Naples, Biblioteca Nazionale, MS Heb. III.F.9. On Finzi, see Langermann Y. T. , “The scientific writings of Mordekhai Finzi”, Italia , vii (1988), 7–44; repr. in idem, The Jews and the sciences in the Middle Ages (Aldershot, 1999), Essay IX. See also Goldstein , op. cit. (ref. 5), 10, 136; and S. Simonsohn, History of the Jews in the Duchy of Mantua (New York, 1977), 601, 640–1, 709.

della Mirandola Pico G. , Disputationes adversus astrologiam , ed. by Garin E. (Florence, 1952), viii.1, ix.9, and ix.11.

T. Settle has informed me, on the basis of a discussion by Ximenes L. ( Del vecchio e nuovo gnomone fiorentino (Florence, 1757)), that there is some indirect evidence that already about the time of the turn of the millennium the Florentine Baptistry was being used as an “internal gnomon”. The internal dimensions are such that a gnomon using the opening of the lantern would function much in the same way as Toscanelli's in Santa Maria del Fiore, that is, for a few weeks on either side of the summer solstice. No meridian line remains but, since the pavement of the Baptistry has been “renewed” so many times, this is inconclusive. In other words, Toscanelli may have depended on a local tradition, rather than on (or in addition to) a text by Levi. Bear in mind, however, that there are very few examples of dated astronomical observations made in Europe in the Middle Ages, and that Levi was exceptional in making over eighty dated (or datable) astronomical observations: For a list, see Mancha , op. cit. (ref. 9). Another medieval astronomer, William of Saint-Cloud, made an observation of a solar eclipse on 4 June 1285 with a camera obscura. He suggests making “an aperture in the roof or in a window of a house…. Let the size of the aperture be like that through which wine is drawn in barrels. Once the light of the Sun passes through the aperture, let there be placed at a distance of 20 or 30 feet from the aperture something flat … in such a way that the light of the Sun falls perpendicularly on the surface of that flat object”: See Mancha J. L. , “Pinhole images in William of Saint-Cloud's Almanach planetarum (1292)”, Archive for history of exact sciences , xliii (1992), 275–98, esp. p. 282. Mancha reports that the procedure for casting images of the eclipsed Sun through a small aperture was already described in a twelfth-century Latin text. William of Saint-Cloud also made observations of the solar altitude at summer and winter solstices (presumably in 1290), but no instrument is mentioned ( ibid. , 283).