Abstract
The most substantial reaction to Ramus’s histories of mathematics came from an unexpected quarter. In September 1570, a young Oxford master, Henry Savile, began to deliver a series of ordinary lectures on astronomy – “ordinary” because they were structured around the orderly reading of a text, but in every other respect quite out of the ordinary. They brought the 20-year-old lecturer local fame, and were to be remembered as one of the notable academic events in Elizabethan Oxford.
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Notes
- 1.
Wood (1813–1820, p. 310).
- 2.
MS Oxford, Bodleian Library, Savile 29, fol. 2v: “Sed O me somnio nescio quo felicem, qui hoc seculo, his hominum moribus scholis mathemata mathematicis dignitatem restituere sperarem.”
- 3.
For Savile’s biography, see Goulding (2004a); Wood (1813–1820, vol 2, pp. 310–317); Feingold (1984, pp. 124–131); Highfield (1997).
- 4.
Savile’s heavily annotated copy of Euclid is in the Bodleian Library with shelfmark Savile W.9(1) (Euclid, Stoicheia, ed. Simon Grynaeus, Basel, 1533; this, the editio princeps of Euclid’s Greek text, also contains the first edition of Proclus’s Commentary on the Elements; Savile has also annotated this). The style of the hand shows that the annotations are certainly from Savile’s early career. His copy of Archimedes is so copiously annotated that it was once classified as a manuscript (MS Savile 51); this Greek printed book (Opera quae quidem extant omnia, Basel, 1543) is now Savile X.9(1); it may have been annotated in part later in his career. I have not found Savile’s copy of Copernicus.
- 5.
The translation occupies MSS Savile 26–28, and is dated to the first term of the 1568–1569 university year.
- 6.
One of the most copiously annotated volumes in the whole of Savile’s library is his copy of Reinhold’s translation and commentary of the first book of the Almagest (Savile Aa.13(1): Ptolemaei Mathematicae constructionis liber primus, additae explanationes aliquot locorum ab Erasmo Rheinhold, Paris, 1556. Savile clearly annotated the book while writing his own translation. Peucer’s Elementa doctrinae de circulis coelestibus, et primo motu (Savile Aa.14; annotated by his younger brother Thomas, but not by Savile himself) served not only as a good elementary introduction to astronomy, but more importantly as a source for Savile’s history of mathematics,
- 7.
See discussion below of Savile’s lectures.
- 8.
Many of Savile’s books and manuscripts eventually made their way into the library he established for the two mathematical professorships he founded at Oxford – a library that was eventually absorbed into Bodleian Library. Unfortunately it seems that he did not bequeath his copy of Ramus’s Prooemium mathematicum to the library.
- 9.
MS Savile 29, fol. 2r. The title most probably covers the introductory section of the lectures, the description of the individual sciences and the history of mathematics (Sects. 1–3 of the division given below), thereby taking in all the material corresponding to Ramus’s own Prooemium mathematicum.
- 10.
To give but one example, MS Savile 29, fol. 6v, starting at the phrase “Physica illa quae dicitur…,” is closely based on Scholae mathematicae, p. 46 (see discussion of this passage at p. 72 above). It is ironic that Savile, asserting here that physics was essentially mathematical, apologized for the boldness of his claims; everything he said about the physics had in fact been said before by Ramus. A similar, but far more significant, example of Savile’s pretended boldness while copying from Ramus (the redating of Euclid) will be examined in the next chapter.
- 11.
Compare text at n. 2 above with Ramus (1569, p. 110): “Sed o me somnio nescio quo tota cohortatione felicem et fortunatam! Sum P. Ramus regius Lutetiae professor …”
- 12.
For a detailed account of Savile’s diagnosis of the shortcomings of Oxford’s system of mathematical instruction, see Goulding (2002) and Goulding (1999). The passage in which Savile considers the problems besetting mathematics at Oxford is considered below, at p. 90.
- 13.
Fletcher (1986).
- 14.
Gibson (1931, p. 235).
- 15.
Harvey (1992, pp. 750–751). A document from 1300 records 54 such “schools” scattered throughout the city of Oxford; see Pantin (1972, p. 235).
- 16.
On these so-called “wall lectures,” see Mallet (1924, vol. 1, p. 199).
- 17.
Fletcher (1986, p. 186); Clark (1887–1889, vol. 1, pp. 96–99).
- 18.
A decree condemning masters and students who missed lectures was issued in 1556–1557 (Gibson 1931, p. 369). Another decree, of 1566–1567, laid down a fine of a shilling for each lecture omitted by an ordinary lecturer (ibid., p. 398).
- 19.
Fletcher (1986, p. 187).
- 20.
Curtis (1959, chapters 3 and 4).
- 21.
Feingold (1984, p. 30).
- 22.
The 1584 Cena de le ceneri was Bruno’s bitter lampoon of Oxford pedantry and philistinism; and in his De la causa, principio e l’uno written later the same year he laid out his side of the complaint against Oxford: see Bruno (1996, p. 81).
- 23.
Yates (1938–1939, especially pp. 230–231). It should be noted that evidence discovered after Yates’s article showed that the stated reason for the cancellation of Bruno’s lectures was not his Copernicanism, but his apparent plagiarism of a work of Marsilio Ficino’s. See McNulty (1960), Aquilecchia (1963) and Aquilecchia (1995). It is still possible, of course, that Bruno was correct in his assessment of Oxford, even if he was not entirely candid about the circumstances of his dismissal – but this circumstance demonstrates at least that the Oxford dons were quite well-read in Renaissance Neoplatonism, as well as Aristotelian traditions.
- 24.
McConica (1979, especially pp. 298, 314–315).
- 25.
Ibid., p. 310.
- 26.
Rose (1977, especially pp. 46, 58–59).
- 27.
Feingold (1984).
- 28.
Curtis (1959, p. 93).
- 29.
On Savile’s tour, see Feingold (1984, 124–129); and for more detail of his astronomical work with fellow mathematicians, see Goulding (1995).
- 30.
See Goulding (2002), passim, for more details of Savile’s complaints against the university, and the remarkably similar observations made by Henry Briggs in Cambridge 18 years later.
- 31.
MS Savile 29, fol. 3r: “…eloquentiae, graecae linguae, philosophiae civilis studia vigent apud nos tanta, ut ne ipsas quidem Athenas magis umquam Atticas extitisse putem.”
- 32.
Ibid.
- 33.
Ibid.: “…eandem mendam diem noctemque tundentes…”
- 34.
Ibid.: “Nae permultos habebimus, non Orontios quales Gallia, non Munsteros quales Germania, sed Archimedes, Ptolemaeos, vel quales illud Oxonium huic nostro dissimillimum, Swinsetos, Bacones, Wallingfordos et Academiam per se ipsam tot iam disciplinarum professione claram, clarorum mathematicorum accessione longe clarissimam reddemus.”
- 35.
On this theme in Savile’s lectures, see Goulding (1999), passim.
- 36.
For details of Savile’s humanistic scholarship, and bibliography, see Goulding (2004a,b).
- 37.
MS Savile 29, fol. 64r: “Et credo si Ciceroni dedissem Archimedem convertendum, non potuit non saepissime decipi.”
- 38.
Earlier, he had referred to Roger Bacon, Walter Burley, Duns Scotus, William of Ockham and John Wycliffe.
- 39.
Plummer (1887, p. 265): “…quos, cum ab omnibus cum ingenii tum doctrinae subsidiis fuerint instructissimi, isto orationis flore, quo nunc fere solum, certe nimium, gloriamur.”
- 40.
MS Savile 29, fol. 9r: “Nam neque conamur eum docere Ptolemaeum, qui numerare nesciat, nec speramus qui addere, subducere, multiplicare, dividere numeris huiusmodi non possit, eum aliquando planetarum epochous, eccentrotates, apogea perite numeraturum.”
- 41.
Ibid.: “Quae tamen omnia, ne quis desit ad artis integritatem, una lectione comprehendi audietis. Perridiculum autem est, integrum annum in definitionibus et divisionibus circulorum, id est terminorum sola cognitione consumere.”
- 42.
Ibid.: “Nec tamen, quamvis Sacroboscus vel Orontius forte non peraeque requirant, summam ideo rationem auditorum meorum non habeo, cum ii sint, aut esse debeant, et extitisse sperem, qui tres terminos Arithmeticae, duos geometricae, cum publicis in scholis, tum privatis meditationibus fructuose impenederint.”
- 43.
MS Savile 29, fol. 13v: “Sed homines eam solam opinantur astronomiam, quam ipsi didicerunt, et quia nihil tale videant in Sacrobosco vel Orontio, nec esse quidem arbitrantur non ex rei natura, sed ex propria ignavia iudicantes.”
- 44.
See passage cited below, at n. 77.
- 45.
Fletcher (1986, p. 186).
- 46.
Clark (1887–1889, vol. 1, pp. 145–146): “Praxis eius scientiae si non inutilis at inusitata reputatur.”
- 47.
Ibid.. Music students were often transferred to the “more useful” arithmetic lectures (Feingold 1984, p. 28, n. 14).
- 48.
Gibson (1931, p. 390).
- 49.
Clark (1887–1889, vol. 1, p. 99): “Supplicatur ut baccalaurei qui teneantur interesse lectioni geometriae promoveantur ad audiendam astronomiam pro tempore intermissae praedictae lectionis. Causa est quod Mr Wignall, publicus geometriae praelector, necessariis avocatus negotiis profectus est.”
- 50.
MS Savile 29, fol. 3v: “praelector ordinarius, id est paene minus quam nihil.”
- 51.
Ibid., fol. 2v: “Suscepto professionis istius onere, sponte an secus nihil ad hoc tempus…” (“Having taken on the burden of this teaching – willingly or otherwise, at the moment it matters not…”).
- 52.
Statues of 1431, in Gibson (1931, p. 234).
- 53.
Statutes of 1549, in Gibson (1931, p. 344): “Mathematices professor, si cosmographiam docet, Melam, Plinium, Strabonem aut Ptolomeum enarret.”
- 54.
Statutes of 1564–1565, in Gibson (1931, p. 378). On Sacrobosco’s Sphere and its influence, see Thorndike (1949). For the close connection between Sacrobosco and the Theorica, see Pedersen (1981, pp. 114–115).
- 55.
Gibson (1931, pp. 389–390): “hos potissimum ad explicandum adhibento … Orontium de Sphaera vel Iohannem de Sacrobosco in astronomia.”
- 56.
MS Savile 29, fol. 2v: “Monstruosas Alfonsinorum dicam hypotheses, an delirantium senum fabulas ad artis praescriptionem si revocaro, haeream in vado necesse est. et tamen revocare certum est. Si liberam de mathematicis omnibus dixero sententiam, quantus, dii boni, subeundus ardor invidiae?”
- 57.
His dismissal of the hypotheses as the “stories of raving old men” was clearly intended to recall Johannes Regiomontanus’s furious attack on the Theorica published in 1476, entitled Disputationes contra Cremonensia in planetarum theoricas deliramenta. The Theorica was very occasionally attributed to Alfonso of Castille, the great patron of astronomy, with whom it had no connection. Nor, pace Regiomontanus, did it most likely have anything to do with Gerard of Cremona. See Pedersen (1981).
- 58.
MS Savile 29, fol. 20v: “Astrologiam autem eam intelligo, quae progressus, regressus, conversiones luminum errantium fixarum[que] demonstrat, non eam quam plerique solam esse opinantur, qua circuli definiuntur, describuntur, exemplis illustrantur, quae cum video, tantum absum ab ea quam extuli providentiae cogitatione, tantum ab admiratione fabricae divinae, ut nihil pene admirer, quam eorum impudentem vanitatem, qui frugibus inventis tantopere glandibus delectarentur.” Emphasis mine in Latin and translation.
- 59.
John Chamber’s 1575 lecture notes (see Conclusion, at p. 190) were largely copied from Savile’s. On the Cambridge lecture notes of Henry Briggs, see Goulding (2002).
- 60.
MS London, British Library, Harley 6494, fols 57–77.
- 61.
Regiomontanus (1550, sigs A2r–A3r). Many of the opinions Savile expressed in his protreptic on the decline of mathematics and the measures needed to restore it to its proper place echoed those of yet another mathematical humanist, Francesco Maurolyco. Maurolyco’s thoughts were stated in manuscript works which Savile could not have seen; this does, however, illustrate how men who were educated in both the philological tradition of humanism and the mathematics of antiquity tended independently to very similar conclusions. See Rose (1975, ch. 8). The similarity to Ramus’s model of decline is also apparent.
- 62.
MSS Savile 29, 31 and 32. MS Savile 30 contains John Chamber’s lecture notes (see p. 190).
- 63.
Geminus’s division of the sciences was recorded by Proclus in his Commentary on Euclid. See Proclus (1992, pp. 31–35). In his copy of the Commentary Savile made many annotations to this section, summarizing Geminus’s division in the margin (Savile W.9, p. 11). He defended this division, over the more usual quadrivial division into arithmetic, geometry, music and astronomy, at MS Savile 29, fol. 8r.
- 64.
The list begins on the page following his translation of book V of the Almagest in MS Savile 28. He thus must have drawn up the list after he had translated this part of the Almagest, and before the 1570 lectures, in which he puts to work his research on mathematical authors – that is, between late 1568 and October 1570. The translation ends on fol. 28r; the list of authors begins on fol. 28v. After starting the list, Savile renumbered fols 29 to the end of the manuscript starting from 1. Here I shall refer to what originally was, say, fol. 30, as fol. *2, using the new numbering
- 65.
The list is arranged in several roughly alphabetical sequences. It seems that Savile compiled the list over some time, making notes on mathematical authors (in papers that have not survived), which he periodically copied out into MS Savile 28 in alphabetical order, after which he continued to compile new authors.
- 66.
On the rear flyleaf of MS Savile 28, Savile wrote “Gesneri bibliotheca, Balaei centuria, Diogenes Laertius, Peuceri Sphaerum, Prooemium Mathematicum,” and scribbled Ramus’s name several times elsewhere on the page. None of Savile’s copies of these sources have survived (except, perhaps, the Peucer, a copy of which is in the Savile collection of the Bodleian Library (shelfmark Savile Aa. 14; the copy is without annotations or markings)).
- 67.
In his quite extensive entry on Proclus (at fol. *13r), for example, he gave a comprehensive list of Proclus’s mathematical works and a little biographical color. Some of the bibliographical information he drew from editions of Proclus’s work in his own library; but most of the information (particularly the philosopher’s biography, his worth as a mathematician and the existence of other ancient Procluses) he took from pp. 154–155 of the Prooemium (p. 37 of the Scholae mathematicae), for which he cited the page references.
- 68.
For instance, his entries for Caspar Peucer and Conrad Dasypodius, both on fol. *6v, read in their entirety “281 Rami” and “284 Rami” respectively.
- 69.
MS Savile 28, fol. 28v: “Diophantus. de numeris polygoniis. item lib. 2 Arith. cum scholiis max. planudis, et alteri innominati. graece servantur Romae, et alibi in Italia. Ramus: 6 libros cum tamen author 13 polliceatur graecos habemus. citatus a Theone.”
- 70.
Gesner’s entry (Gesner, 1545, fol. 214r) reads: “Diophanti scriptoris Graeci arithmetices libri duo (alias, sex) cum scholiis Max. Planudis et alterius innominati. Harmonica, et quaedam de numeris polygoniis. Omnia Graece servantur Romae et alibi in Italia.”
- 71.
Ramus Prooemium mathematicum, p. 120 (= p. 37 of the Scholae mathematicae): “Diophantus, cujus sex libros, cum tamen author ipse tredecim polliceatur, graecos habemus de arithmeticis admirandae subtilitatis artem complexis, quae vulgo Algebra arabico nomine appellatur; cum tamen ex authore hoc antiquo (citatur enim a Theone) antiquitas artis appareat.”
- 72.
MS Savile 26, fol. 81v.
- 73.
On the difficult question of the length of Savile’s series of lectures, see Appendix B.
- 74.
MS Savile 29, fol. 2r: “Socraticus Aristippus, cum ex naufragio Rhodiorum ad littus proiiceretur non multis comitatus eiusdem periculi fortunaeque sociis, pertimescentibus caeteris, partim ne sibi qui superatis iam fluctibus omni se molestia defunctos arbitrabantur, nova necessitas instaret in agro deserto fame pereundi, partim ne pelago iam usi scopuloso atque barbaro, bestiis uterentur deinceps aestu quovis immanioribus, et partim ne in homines inciderent belluis infestiores, nihil humani praeter faciem habentes; primus conspectis mathematicorum diagrammatis et illo numquam satis laudato pulvere ad bene sperandum de salute omnium quasi signum aliquod amplissimum extulit. Maximas molestiarum moles et turbulentissimas tempestates effugimus. En illum, comites, pulverem et abacum. En circumductos circulos, descripta trigona, tetragona, polygona, quorum me contemplatio maerentem delectat, iacentem erigit, afflictum excitat. Non ego vobis, ut augur ab avibus, non ut aruspex ab extis, non a stellis, ut astrologus, quorum occultis mysteriis carere me non moleste fero, sed ab hisce depictis formulis, ut non imprudens forte rerum aestimator, salutem et miseriarum omnium finem denuntio. Figurae sunt humanitatis indices, graecae disciplinae non leve vestigium. Mihi credite, comites, harum artium studia in animum agrestem non cadunt. Ingenuae sunt, ab ingenuis discuntur, nec quisquam, nisi liberaliter institutus, liberales artes complecti potest. De moribus insularum bene sperate. Sciunt misereri qui sciant geômetrein.”
- 75.
See passage cited at n. 61 of first chapter.
- 76.
See, for instance, Trinkaus (1960); Vickers (1988, pp. 744–745); and Plett (2004, p. 146).
- 77.
MS Savile 29, fol. 23r: “Quid igitur, inquiet aliquis, nihilne adiecit Copernicus, nihil tot de astronomia perscripti libri? Caeteros quidem omnes non dubitabo mea sententia condemnare. Quid enim tot sphaericis libellis continetur, quod non extet apud Ptolemaeum multo uberius, multo illustrius? Copernicus, quem laudes immortales meruisse constat, non aliquod novum caput ad astronomiam adiecit, quod non esset a Ptolemaeo pertractatum, sed ipse easdem res nova quadam ratione variatis hypothesibus illustravit.
- 78.
MS Savile 46v–47r: “… crederem profecto, si pythagorica metempsuchsis mihi probaretur, animum Aristarchi multa secula vagantem in corpus commigrasse Copernici. … et quamvis ex suis ipse scriptis Aristarchus non potest cognosci … eadem fere dicit [Archimedes] de astrologia Aristarchi quae sunt a Copernico nuper in caelo confirmata. itaque caelum hoc copernicianum novum quoddam inventum non est, cum quadringentis ante Ptolemaeum annis sit ab ingeniosissimo artifice constabilitum.” (“If I accepted the Pythagorean doctrine of reincarnation, I should believe that the soul of Aristarchus, having wandered many centuries, had migrated to the body of Copernicus. … And although it is not [now] possible to read Aristarchus’s writings, … Archimedes says almost the same things concerning the astronomy of Aristarchus as were recently affirmed in the heavens by Copernicus. And so this Copernican heaven is not some new invention, since it was established by a brilliant master four hundred years before Ptolemy.”)
- 79.
See Gingerich (1973).
- 80.
MS Savile 29, fol. 64r: “Erasmus Rheynholdus, vir ad amplificanda mathemata natus, et graecis libris eruditus.”
- 81.
See n. 63 above.
- 82.
Savile was referring to Michael Stifel’s Arithmetica integra (Nuremberg 1544). Savile’s unannotated copy of this edition is in the Bodleian Library with shelfmark Savile R.13.
- 83.
Here Savile almost certainly intended Cardano’s Ars magna sive de regulis algebraicis (Nuremberg 1545). Savile’s sparsely annotated copy of this edition is found at Savile N.15(2).
- 84.
MS Savile 29, fols 17r–v: “Quae tamen a me certis de causis non afferrentur, nisi cum historia nostra mathematicos omnes non solum astrologos complexura sit, nec historico more tantum, quo seculo vixerint, quibus moribus extiterint, quo caelo usi sint, sed mathematice magis, quid in quo genere scripserint, quam bene, quam ad instituendos tyrones commoditate. Haec, inquam, cum esse[n]t dicenda disceptationem et de tota mathesi et de singulis formis absque scelere non potui praeterire. Etenim si dicerem erudite scripsisse de isorrhopicis Archimedem, Ptolemaeum de catoptricis, Stifellium de surdis et irrationalibus numeris, de cossicis Cardanum, alium de geodesia, de scrupulis astronomicis alium, non explicata prius artis cuiusque vi et facultate iam plurimis incognita, amens profecto et insanum videatur.”
- 85.
The nuances to the term “history” in the sixteenth century were manifold, as a recent collection of papers has demonstrated (Pomata et al. 2005). See, in particular, Pomata (2005, especially p. 106–114). Savile may have had in mind a common Aristotelian sense of “historia” as “knowledge without causes” – a kind of bare narration of facts, which did not attempt to make an assessment from the point of view of any more specialized ars. Savile’s statement that he would proceed mathematically as well as historically seems to be meant to assure his audience that he will enter into causes from a mathematical point of view – while yet keeping the two approaches distinct.
- 86.
MS Savile 29, fol. 25r.
- 87.
MS Savile 29, fol. 65r and the addition to this page on fol. 1v (garrula mathesis).
- 88.
MS Savile 29, fols 29r–31r. A complete account of the contents of Savile history may be found in Appendix A.
- 89.
Ibid., fol. 29r.
- 90.
Ibid.
- 91.
Ibid. Savile was an implacable opponent of astrology throughout his life; see Goulding (1999, at notes 58–62).
- 92.
On Annius’s forgeries, see Stephens (1984); Grafton (1991, pp. 76–103, especially p. 85); Ligota (1987).
- 93.
MS Savile 29, fol. 29r. The passage Savile was using is found at the very beginning of the third book of “Berosus,” De antiquitate Iani patris; in Annius (1545), it is found at fols 22v–23r.
- 94.
MS Savile 29, fol. 8r: “Arithmeticam … certum est … una cum homine nato natam esse.”
- 95.
Ibid., fol. 8v.
- 96.
What follows is all summarised from MS Savile 29, fols 18r–19v.
- 97.
Savile clearly means to recall Timaeus 47B.
- 98.
Timaeus 47A.
- 99.
MS Savile 29, fol. 29r.
- 100.
MS Savile 29, fol. 30r (“insignem mentiendi impunitatem”). On Callisthenes observations, see Grafton (1991, pp. 134–135).
- 101.
fol. 30v: “Mathematicam illam intelligo puram, castam, incorruptam, non physicis coniecturis, aut praedictionibus Chaldaicis contaminatam.”
- 102.
The notion that the Chaldeans were responsible for spoiling ancient mathematics is also found in the writings of Pico della Mirandola (see Popper 2006, p. 91), Savile was influenced by Pico’s anti-astrological arguments, and may have taken from him also this negative assessment of the Chaldean “additions” to astronomy.
- 103.
MS Savile 29, fol. 30v: “et omnium [artium] sanctissimam mathesim nova domicilia conquirere coëgit.”
- 104.
Ibid.: “Illud potius agamus, quomodo possit Oxonium Alexandria transferri, aut si illud maius est, quam ut optari debeat, certe quomodo possit Alexandrinus Ptolemaeus ab Oxoniensibus intelligi.” In the manuscript, Savile has underlined this passage heavily. He goes on afterwards to draw attention to his unwonted departure from the historical narrative, further emphasizing the significance of this passage. (“Sed prope oblitus eram me nondum ad haec tempora discendisse. Domum redeamus.”)
- 105.
The mid-seventeenth-century Savilian professor of Geometry, John Wallis (who was familiar with Savile’s manuscripts) used a similar argument to much the same ends in his own inaugural lecture. See Popper (2006, p. 104).
- 106.
Ramus (1569, p. 67): “Guilielmus Landgravius Hessiae videtur Cassellas Alexandriam transtulisse; sic Cassellis artifices organorum observandis syderibus necessariorum instruxit, sic quotidianis per instructa organa observationibus oblectatur, ut Ptolemaeus ex Aegypto in Germaniam cum armillis et regulis venisse videatur.”
- 107.
There is some irony in the fact that, several years later, Savile would work extensively with an astronomer who had enjoyed the Landgraf’s patronage at Kassel, the “German Alexandria.” His work with this astronomer, Paul Wittich, concerned entirely theoretical problems of planetary astronomy. See Goulding (1995).
- 108.
MS Savile 29, fols 32v–33r.
- 109.
The role Savile assigned to the Greeks bears some resemblance to the historical model put forward by Pico della Mirandola in his work against divinatory astrology. See Popper (2006, p. 91).
- 110.
MS Savile 29, fols 32r–v.
- 111.
Ibid., fol. 34v: “tertius post Thaletem et Pythagoram parens Hippocrates Chius …”
- 112.
Ibid., fol. 35r.
- 113.
See p. 66 above.
- 114.
MS Savile 29, fol. 34v. For Savile’s later researches into Hippocrates’s quadratures, see Goulding (2005).
- 115.
MS Savile 29, fol. 11r: “quanquam ab huiusmodi commemoratione nescio quo rerum externarum fastidio semper animus meus abhorruerit.”
- 116.
Presumably his MA studies, when he would have been reading geometry.
- 117.
MS Savile 29, fol. 5r: “… ut altero iam anno quo animum ad discendum inieci, et in Euclidem, Ptolemaeum, Archimedem praecipue incubui, prope incredibili perfusus animi voluptate, nihil extra quaesiverim vel ad utilitatem vel ad oblectationem.”
- 118.
MS Savile 29, fol. 10v: “Geometriae tamen amore intemperanter ardeo, nec immoderatos hoc loco eos impetus facile cohibeo.”
- 119.
Feingold (1984, pp. 190–192); Taylor (1954, pp. 4–5). Pumfrey (2004) makes the point that the worlds of the universities and the practitioners were more widely separated in England than in anywhere else in Europe: the kind of bricolage common on the Continent, where mathematicians moved back and forth between these sites of knowledge and refashioned their identities as they went, was almost unknown.
- 120.
MS Savile 29, fol. 22r–v: “… ne semper haeream in navigationibus, quas scio plerosque vestrum contemnere …”
- 121.
MS Savile 29, fol. 5r–v.
- 122.
See Feingold (2001). There is clear evidence that, a few years after Savile’s lectures, Ramism was a matter of public discussion in Oxford. In 1583, shortly after Savile returned to England from his European tour, a letter written home by an Oxford undergraduate recorded that Savile was widely tipped to be the university’s champion in a refutation of the Ramist philosophy as advanced from Cambridge by William Temple (MS Oxford, Bodleian Library, Rawlinson D.985, fol. 52v; edited in (Jeffery, 1909), p. 57).
- 123.
MS Savile 29, fols 5v–6r: “Dii immortales, mathesin quae hucusque ab omni vitae commodo sacrosancta fuit ad mechanicae tractationem tanquam vilissimum aliquod pistrinum detrudi!”
- 124.
MS Savile 29, fol. 5v: “Hunc tu finem artium liberalissimarum, Rame, cum Platone, Ptolemaeo, Proclo, et reliquis doctioribus philosophis constituisses velim, non illum mechanicum et illiberalem.”
- 125.
MS Savile 29, fol. 5v: “ Istam si tu pro tua singulari in dicendo facultate ad substantias separatas anabasin exornasses, et tuam nobis vehementer probasses eloquentiam, quam nunc quidem in tanta rerum foeditate contemnimus.”
- 126.
MS Savile 29, fol. 11v: “Quem enim non delectaret tam illustris, tam grata, tam iucunda rerum suavissimarum varietas? Me certe vehementer affecit certas esse et statas vices a primis a media, a mediis ad ultima directo quodam ordine proficiscendi. Iuvit in triangulis pedem ponere. De quadrilateris disceptationes mire placebant. Delectabat iam versasse circulos, iam ad praedicta comparasse. Nondum de circulis defessum excepit suaviss. proportionum concentus, in quibus morari semper vellem nisi mori parum geometer noluissem. Itaque irrationalia non sine ratione attigi. Quid multa? Fatigatus discessi. Stereometriam demum vix a primo limine salutans, geometriae vale dixi.”
- 127.
Savile’s personal copy of Euclid is in the Bodleian Library with shelfmark Savile W.9(1) (Euclid, Stoicheia, ed. Simon Grynaeus, Basel, 1533). The volume is heavily annotated, but offers no support for Savile’s account. Note that Savile makes no mention of the arithmetical books of the Elements; his own copy of Euclid, however, suggests that he read them continuously with the geometrical ones.
- 128.
At fol. 9r Savile told his students that the geometrical preparation needed for studying the Almagest was the first six books of the Elements, scarcely anything from the tenth book on irrationals, as well as a theorem or two from the eleventh and thirteenth books (both of which books concern stereometry). From the eleventh book, he no doubt meant the propositions on intersecting planes; it is difficult to see what he might have required from the thirteenth. In any case, Savile was hardly demanding from his students the curriculum that he said he had found essential in his own education. (“In geometria sex primos elementorum libros, et nonnulla undecimi, decimique tertii theoremata, vix decem.”)
- 129.
Republic 528A–B.
- 130.
See passage cited at n. 49 of second chapter.
- 131.
Ramus, Scholae mathematicae, p. 14: “At Elizabetha Anglorum regina, Angliam tuam Galliae discipulam diutius fieri ne sinito, sed Gallos vicissim in Angliam provocato… In duabus eruditissimis regni tui academiis sciscitando didici regiis stipendiis honorari professores linguae graecae, hebraicae, medicinae, juris civilis, theologiae… At mathematicis artibus praemium regale nullum est constitutum… Itaque opto regios reginae Elizabethae in academia et Cantabrigiensi et Oxoniensi mathematicos professores, qui sempiterna praeclarissimi beneficii laude memoriam tuam exornent.” One of Ramus’s correspondents about the state of mathematics in England was John Dee. In a letter to Dee, written in 1565, that was published in Ramus (1599, pp. 174–175), Ramus asked “who in your universities teaches mathematics, and with what authority?” (“quinam in vestris gymnasiis, quaque authoritate mathematicas artes profiteantur.”)
- 132.
MS Savile 29, fols 2v–3r: “quam quidem ingratam et adversam dignitati nostrae famam, scripta non iam pridem severa monitione auctam et amplificatam vidimus.”
- 133.
MS Savile 29, fol. 7v.
- 134.
The statutes are reprinted in Gibson (1931, pp. 528–540). The following paragraphs are summarized from pp. 528–529 and Sect. 5 on p. 531. On the rarity of the notion of “research” as part of a professor’s duty, see Curtis (1959, p. 227).
- 135.
Aubrey (1958, p. 268).
- 136.
See Goulding (2002), where I suggest that Savile’s partial change of heart may be connected with the criticisms of the universities put forward by his chosen successor, Henry Briggs, and the perceived threat in the foundation of Gresham College.
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Goulding, R. (2010). “To Bring Alexandria to Oxford:” Henry Savile’s 1570 Lectures on Ptolemy. In: Defending Hypatia. Archimedes, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3542-4_4
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