Blasius of Parma

(b. Parma, Italy, ca 1345; d. Parma, 1416)

natural philosphy.

Although presumably he was born in in Parma, the first known reference to Blasius is found in the records for 1377 of the University of Pavia, where he took his doctorate, perhaps in 1374 (the latter date makes 1345 a plausible birth year). Listed as an examiner in March 1378, Blasius probably left Pavia by October of that year for the University of Bologna, where he remained at least until 1382 (for 1379–1380, he was officially described as a teacher of logic, philosophy, and astrology), and probably through 1383. On 20 May 1384, he agreed to teach at the University of Padua for four years; his name appears in the university records from February 1386 to 11 May 1387 and again on 16 December 1388 as the sponsor of a doctoral candidate who was represented by another scholar, probably because in 1387 Blasius had returned to Bologna as professor of philosophy and astrology for the period 1387–1388. On 29 July 1388, he was appointed a lecturer in natural philosophy at the University of Florence, where he remained until 1389.

During the next decade, when he reached the summit of his career, Blasius was again at Pavia as professor of “mathematical arts and both philosophies” (i.e., moral and natural). His whereabouts between 1400 and 1403 are unknown, but in subsequent years he taught at the University of Pavia (1403–1407) and the University of Padua (1407–1411). In October 1411 he was dismissed from the latter because he lacked students and was deemed no longer fit to teach, conditions that were probably caused by the infirmities of old age. He died five years later.

A sojourn in Paris, where he received his doctorate (so we are told in an explicit to his Questio de tactu corporum duorum, which was disputed at Bologna no later than 1388), is mentioned in his Questiones supertractatum de ponderibus¹. It was probably while in Paris that he absorbed the new ideas of the Parisian Scholastics, ideas that he was to disseminate and popularize in Italy.

Blasius was not merely an Aristotelian commentator, but also wrote independent treatises on important scientific topics. Prior to 16 October 1396, when he was compelled to recant unspecified transgressions against the Church² (by this time he had probably written the bulk of his extant treatises), Blasius seems to have been a materialist and determinist, accepting as true certain articles condemned at Paris in 1277. In his Questiones de anima (Padua, 1385) he denied that the intellective soul was separable from the body, insisting that it was produced from transient matter. It was only by authority of the Church and faith—not by natural reason or evidence—that one ought to believe in its separability. Furthermore, he denied the immortality of the intellective soul while accepting the eternity of the world and a necessary determinism exerted by the celestial bodies and constellations on terrestrial and human events. Such opinions, characteristic of earlier Bolognese Averroists, were probably instrumental in provoking the ecclesiastical authorities. Blasius capitulated and complied swiftly. During 1396–1397, in lectures delivered at Pavia on the Physics of Aristotle, he repudiated all these views; and in 1405 he attacked astrological determinism (but not astrology) in his Iudicium revolutionis anni 1405, declaring that while the stars influenced men and events, the will of God and human free will could resist if they chose.

Of his numerous scientific treatises, only those on optics, statics, and intension and remission of forms have received more than cursory examinations, resulting in partial or complete modern editions. In addition to relevant discussions on optics in his Questiones de anima and Meteorologica, Blasius also wrote Quaestiones perspectivae (dated 1390 in one manuscript), a lengthy commentary on some of the propositions of John Peckham’s enormously popular thirteenth-century optical treatise, Communis perspectiva. Guided by an empiricist outlook derived ultimately from the optics of Ibn al-Haytham (Alhazen), and perhaps influenced by fourteenth-century nominal-ism, he made visual sensation the basis for human certitude and knowledge; consequently he placed heavy emphasis upon the psychology of perception. Traditional geometric optics was placed in the broader matrix of a theory of knowledge and congnitive perception based on vision.

Blasius composed at least two treatises on statics: one Scholastic, the other longer and non-Scholastic in form. The longer work, Tractatus de ponderibus, drew heavily on the thirteenth-century statical treatises associated with the name of Jordanus de Nemore. It was probably from the Elementa Jordani super demonstrationem ponderum that Blasius adopted the important concept of “positional gravity,” which involved a resolution of forces where the effective “heaviness” or weight of a body in a constrained system is proportional to the directness of its descent as measured by the projection of an arbitrary segment of its path onto the vertical drawn through the fulcrum of a lever or balance. Ignoring straightforward and available definitions of positional gravity, Blasius presents the concept in Pt. I, Supps, 6 and 7, proving in the first of these that “in the case of equal arcs unequally distant from the line of equality (i.e., the line of horizontal balance) that which is a greater distance intercepts less of the vertical [through the axis],” and in the second that “one body is heavier than another by the amount that its movement toward the center [of the world] is straighter.”³ But the more of the vertical cut off by a projected arc, the straighter its descent and, therefore, the greater its positional gravity.

In Pt. II, Prop, 4 (probably based upon Elementa Jordani, Th. 2), Blasius misapplied the concept of positional gravity in demonstrating that “when the equal arms of a balance are not parallel with the horizon and equal weights are hung [on their ends], the beam assumes a horizontal postition.”⁴ In Figure 1, let arms AB and BC be equal but not parallel to the horizon, DF. If equal weights are suspended at the ends of the equal arms, the latter would become parallel to the horizon, or DF. This will occur because, being heavy bodies, a and c will seek to descend, c to F and a to G. Assuming, quite improperly, that arcs CF and AG are equal, but unequally distant from DF, Blasius applies Pt. 1, Supp. 6, to show that arc

CF cuts off more of the vertical along HG than does arc AG, and concludes that c’s downward motion to F is more direct than a’s to G. Consequently (by Pt. I, Supp. 7, which is not cited but is clearly required), c is positionally heavier than a and will descend, forcing a upward until horizontal equilibrium is attained. The basic error in all this lies in assuming a simultaneous descent of c with the ascent of a and the ascent of c with the descent of a. The equality of these two ratios would have yielded the desired proof.

Positional gravity was more felicitously applied in proving the law of the lever (Pt. II, Prop. 10) and in demonstrating that equilibrium is attained on a bent lever when equal weights are suspended on its unequal arms, which terminate equidistantly from the axis of support (Pt. II, Prop. 11). A brief third part concerned the specific gravities of fluids and solids. Dynamic considerations played a role, since Blasius says (Pt. III, Prop. 1) that of two solid bodies descending in water, the heavier will descend more quickly. For comparison of liquids, a hydrometer was used, and its principle was utilized in the comparison of two solid, similarly shaped floating when Balsius advocated that each be divided into twelve equally spaced parts.

In one of two treatises on intension and remission of forms, Questiones de latitudinibus formarum, Blasius included both the English (arithmetic) and French (geometric) fourteenth-century versions of the mean speed theorem⁵ that demonstrated the equality of the distances traversed during the same time by one body moving with a uniform speed equal to the velocity acquired by the body in uniform acceleration at the middle instant of its period of acceleration (i.e., S= V₀t + at²/2, where S is distance; V₀ initial velocity; a acceleration; and t time). Blasius may have introduced both versions into Italy.

Over a long career, Blasius discussed many traditional scientific concepts. Initially an apparent supporter of the impetus theory, he later denied, in his Questiones super octo libros physicorum (1397), that it could explain acceleration in free fall or the rebound of bodies. ⁶ He accepted “Bradwardine’s function,” ⁷ which described the relationship between the speeds of two bodies as F₂/R₂ = (F₁/R₁)^v₂/v₁, where F is motive power; R, the resistive force of the body in motion; and V, velocity. He also reflects reflects common Parisian arguments when he denies the natural existence of vacuum inside or outside the cosmos⁸ and then allows (contrary to Aristotle) that if a separate vacuum did exist, bodies could undergo motion and change⁹ (in his Questio de tactu corporum duorum, Blasius holds that if a vacuum actually existed, many difficulties and contradictions involving the physical contact of two bodies could be resolved).¹⁰

Although not an original thinker, Blasius sympathetically absorbed the scientific ideas current among the “moderns” at the University of Paris during the fourteenth century. He helped disseminate these in Italy, where they were widely discussed until the time of Galileo.

NOTES

1. Quoted by Marshall Clagett in Marshall Clagett and E. A. Moody. The Medieval Science of Weights, pp. 413–414.

2. The brief document has been translated by L. Thorndike in University Records and Life in the Middle Ages, pp. 258–259.

3. Clagett and Moody, op. cit., p. 243.

4.Ibid., p. 251. The figure appears on p. 250.

5. Marshall Clagett, Science of Mechanics, pp, 402–403.

6. A. Maier, Zwei Grundprobleme der scholastischen Naturphilosophie, pp. 271–273.

7.Questions super tractatu De proportionibus Thome Berduerdini, questions 10, 11 (MS Vat, lat, 3012, 15lr-153v).

8.Questions super octo libros physicorum, MS Vat, lat. 2159, 120v, c. 1.

9.Ibid., 124r, c. 2–124v. c. 1.

10. G. F. Vescovini, “problem di fisica aristotelica in un maestro del XIV secolo: Biagio Pelacani da Parma,” in Rivista di filosofia, 51 (1960), 196.

BIBLIOGRAPHY

I. Original Works. All but a few of Blasius’ works are unpublished. References to manuscripts of these treatises can be found in L. Thorndike and P. Kibre, “Blasius of Parma,” in A Catalogue of Incipits of Mediaeval Scientific Writings in Latin (rev. and enl. ed., Cambridge, Mass., 1963), c. 1764; and, in an earlier but more conveniently arranged list, in L. Thorndike, A History of Magic and Experimental Science, IV (New York, 1934), app. 40, pp. 652–662.

Questions or commentaries on the following works of Aristotle are extant: Questiones librorum de caelo et mundo (Milan, Ambros. P. 120 Sup., 1–69; Bodleian Library, Canonicus Misc. 422, 1–52; Rome, Angelica 592 [F.6.4], 1–34; Rome, Angelica 595 [folio numbers unavailable]; Vienna, National Bibliothek, 2402, 1–63v); Commentaria in Aristotelis de generatione et corruptione (Vienna, National Bibliothek, 2402, 99r-123v); Questiones de anima (Vat. Chigi O IV 41, 112–217v; Vat. Urbinas lat. 1489, 74-[terminating folio number unavailable]; Bodleian Library, Canonicus Misc. 393, 1–78; Turin 1247 [folio numbers unavailable]); Questiones in libros metheororum (Vat. lat. 2160, 63–138v, which is immediately preceded by Blasius’ Conclusiones super libris methaurorum Aristotelis, a work differing from the Questiones; Florence, Ashburnham 112, 1–60; Vat. Chigi O IV 41, 62–108v; University of Chicago 10, 39 ff.). On the Physics of Aristotle, Blasius left at least three versions: (1) Expositio per conclusiones super octo libros physicorum Aristotelis (Vat. lat. 2159, 1–98v); (2) Questions super octo libros physicorum, preserved, with variant titles, in separate versions, one written in or before 1385 at Padua, of which only the first two books remain (Vat. Chigi O IV 41), and the other, copied in 1397 in Pavia, differing somewhat and embracing all eight books (Vat. lat. 2159, 6lr-230r; despite an apparent overlap in pagination with the Expositio, it immediately follows the latter with independent pagination beginning with 6lr); an incomplete and mutilated version of the Pavia copy is contained in Vat. lat. 3012, 2v-110v; and (3) an arrangement of Buridan’s Questiones super octo phisicorum libros Aristotelis made around 1396 (Venice, S. Marco X, 103, 83–84).

The two works on statics are Questiones super tractatum de ponderibus, containing five questions and known only in a single manuscript (Milan. Ambros. F. 145 Sup., 18r-28r), edited and translated by Father Joseph Brown in a thesis, “The Scientia de ponderibus in the Later Middle Ages” (Univ. of Wis., 1967); and Tractatus de ponderibus, edited and translated by Marshall Clagett in Marshall Clagett and E. A. Moody, The Medieval Science of Weights (Madison, Wis., 1952), pp. 238–279. On intension and remission of forms, Blasius left two treatises, De intensione et remissione formarum and Questiones super tractatu de latitudinibus formarum: for manuscripts of both, see Marshall Clagett, The Science of Mechanics in the Middle Ages (Madison, Wis., 1959), pp. 404, 685–686; the second treatise was published in 1482 and 1486 at Padua and in 1505 at Venice, while part of the third and final question of the second treatise was edited and translated by Clagett in Science of Mechanics, pp. 402–408. On problems of motion, he wrote Questions super tractatu De proportionibus Thome Berduerdini (i.e., Bradwardine); for manuscripts, see Marshall Clagett, The Science of Mechanics in the Middle Ages, p. 686; and De motu iuxta mentem Aristotelis (MS Vat. Barb. 357, 1–16v).

Of the three books and twenty-four questions of the Quaestiones perspectivae, Book I, quests. I-10 were edited by F. Alessio as “Questioni inedite di ottica di ottica di Biagio Pelacani da Parma,” in Rivista critica di storia della filosofia, 16 (1961), 79–110, 188–221; Book I, quests. 14 and 16, and Book III, quest. 3 (ultima questio), were edited by G. F. Vescovini as “Le questioni di ‘Perspectiva’ di Biagio Pelacani da Parma,” in Rinascimento, 1 (1961), 207–243-the text is preceded by a lengthy discussion of the questions and their historical context on pp. 163–206. The 1505 edition of Questiones super tractatu de latitudinibus formarum includes Blasius Questio de tactu corporum duorum, which is summarized by G.F. Vescovini in “Problemi di fisica aristotelica in un maestro del XIV secolo: Biagio Pelacani da Parma,” in Rivista di filosofia, 51 (1960), 179–200.

On astronomy, Blasius wrote Questions super tractatum sperae Johannis de Sacrobosco (MS Parma 984) and a Theorice planetarum (Vat. lat. 4082, 47r-60v; Venice, S. Marco VIII.69, 175r-216v). The Latin text of the titles of the problems discussed by Blasius in the latter treatise was published by L. Thorndike in Isis, 47 (1956), 398–400. Thorndike mentions that the Latin texts of the first three problems and the last were published by G. Boffito and U. Mazzia in Bibliofilia, 8 (1907), 372–383, where they are mistakenly ascribed to Peter of Modena. In the same article, Thorndike (Isis, 47 [1956], 401–402) cites another astronomical work by Blasius, Demonstrationes geometrice ub theorica planetarum, printed anonymously by Octavianus Scotus (Venice, 1518), fols. 143r–152v (a possible manuscript version of this treatise is Vat. lat. 3379, 52r–61r, which bears the slightly variant title Blasii parmensis demonstrationes geometrie in theoricam planetarum). An astrological prediction constitutes Blasius’ Indicium revolutonis anni 1405 (Bibliothèque Nationale MS 7443, 11v–17r).

The diverse treatises cited below conclude the list of Blasius’ scientific and philosophic works known thus far: Questiones super tractatus loyce [i.e., logice] magistri Petri Hyspani [i.e., Peter of Spain] (Bodleian Library, Canonicus Misc. 421, 92–222); Questiones undecim de locis (Venice, S. Marco X, 208, 82–92); Queritur utrum spericum tangat planum (Bodleian Library, Canonicus Misc. 177, 153–154); Questiones viginti sex predicamentis (Venice, S. Marco X. 208, 43–82 and perhaps also Vat. Barberini 357); De motu (Vat. Barberini 357, 1–16v); Elenchus questionum Buridani (i.e., A Refutation of Questions of Buridan; Venice, S. Marco X, 103, 83–84); and a De terminis naturalibus (Bodleian Library, Canonicus Misc. 393, 78–83), of uncertain attribution. A theological work, De predestinatione, has also been preserved (Venice, Bibl. de’ Santi Giovanni e Paolo 163).

II. Secondary Literature. There is relatively little literature on Blasius. To what has already been cited, we may add L. Thorndike, A History of Magic and Experimental Science, IV, ch. 39; G. F. Vescovini, Studi sulla prospettiva medievale (Turin, 1965), ch. 12; A. Maier, Die Vorläufer Galileis 14. Jahrhundert (Rome, 1949; 2nd ed., 1966), pp. 279–299, and Zwei Grundprobleme der scholastischen Naturphilosophie, 2nd ed. (Rome, 1951), pp. 270–274; and F. Amodeo, “Appuntisu Biagio Pelacani da Parma,” in Atti del IV Congresso Internazionale dei Matematici, 3 (Rome, 1909), 549–553.

Edward Grant

BLASIUS OF PARMA

(b. Costamezzana, Parma, Italy, ca. 1345;d. Parma, 1416)

natural philosophy. For the original article on Blasius of Parma see DSB, vol. 2.

The recent critical edition of some of the most important of Blasius’s works has allowed for a more complete acquaintance with his thought, as well as a more informed appreciation of his great importance in the history of science and philosophy of the later Middle Ages, particularly in terms of the European dissemination of debates that occurred at the University of Paris and at Oxford.

Blasius of Parma’s importance in medieval scientific thought can be found in his promotion, in Italian universities, of the outcome of fourteenth-century Parisian and English debates on logic and natural philosophy (John Buridan, Albert of Saxony, Thomas Bradwardine). The great importance of the University of Pavia in the fifteenth century as a center where the Parisian and, above all, the English works on natural philosophy were commented on (with Giovanni Marliani as a prominent master) is at least partly due to Blasius’s presence as a master there. Blasius’s works, even those not originating from his university teaching, are addressed to an academic audience, with the exceptions of two astrological iudicia given in 1386 (Padua) and 1405.

Natural Philosophy. In addition to Aristotle’s natural philosophy (Physics,On the Heavens, On Becoming and Passing Away, Metereologics, On the Soul) Blasius wrote commentaries on two of the most common university manuals: some parts of Peter of Spain’s Tractatus logicales and John of Holywood’s On the sphere. His strong interests in natural philosophy, as well as in relying on the new languages of proportions and intension and remission, occasioned an original way of introducing and dealing with physical problems in his lectures on logical works and even in his commentaries on Aristotle. In particular, he tackled explicitly the problem of the relationship between the point and the line in his commentary on Peter of Spain’s Tractatus (III, 10 “whether points are in the line” [utrum puncta sint in linea], presenting one of the topic arguments against indivisibles), and introduced a way of treating limits (incipit/desinit) in discussions about the quality of categorical propositions (I, 16).

In discussing contrariety he openly declared a preference for analysing the problem physically rather than logically, which led him to cursorily introduce the problem of intension and remission (III, 3), discussed in a lengthier form in III, 16. In his commentaries on Aristotle’s physical works Blasius included some of the relevant topics of fourteenth century Parisian and English natural philosophy: in On the Soul the way in which to measure the perfection of a form (II, 6 “whether the essential perfection in living substances is to be measured by the proximity to the highest degree” [“utrum in latitudine viventium sit essen-tialis perfectio penes accessum ad summum attendenda”]). In the Physics commentary the intension and remission of qualities is discussed in the last question of the fifth book (V, 10), whereas in the questions on the seventh book he dealt with the way of calculating the speed (“penes quid attendenda est velocitas”) in the three different Aristotelian motions (local motion, alteration, and augmentation/diminution: VII, 6–8), the way of calculating the speed considering the ratios of the speed and those of the movers (VII, 9 “utrum in motibus proportio velocitatum sit sicut proportio causarum”) and the limits of natural agents as well (VII, 10 “utrum agens naturale sit limitatum”).

Role of Mathematics. Blasius maintained, following Aristotle, the primacy of mathematics as far as certitude is concerned. The main problem, however, was the abstract character typical of mathematical and geometrical notions, which made them unfit for physical research. Blasius’s reductionist attitude in ontology did not let him consider proportions, points, lines, and surfaces as real objects. It was very urgent, therefore, to solve this semantic problem if one wanted to take advantage from the clear and cogent procedures of mathematics. Blasius relied on logic in order to solve this problem and to enable the application of mathematics in dealing with natural philosophy problems. He maintained that geometrical and mathematical notions are very useful tools, because they are the outcome of complex operations of human reason, which need not denote specific objects, but rather relations between real objects. He relied explicitly on the semantic theory of appellatio rationis, as did many late medieval thinkers, John Buridan included. He did not uphold the theory according to which propositions denote something different from the subject term. Truth and falsehood, moreover, do not refer to true or false propositions, as for the main part of the terminists taking their lead from William Ockham. They are rather the two ways of referring of propositions.

Blasius was resolute in his reliance on the new fourteenth-century tools of analysis. So much so that in question eight of his commentary on Bradwardine’s Treatise on Proportions he blended proportions, latitudes of forms, and a special topics like reaction (reactio) in discussing whether the power of the agent has always to be greater than that of the patient in order to produce an effect (“utrum a proportione equalitatis vel minoris inequalitatis proveniat vel provenire posit aliquis effectus; vel sic: utrum in omni motu potentia motoris debeat excedere potentiam rei mote vel equari ei”). Blasius did not accept Bradwardine’s solution concerning speed: Taking into consideration time, speed depends on the ratio between power and resistance, whereas considering the outcome (effectus productus) only the agent must be considered (q. 10, 2). This solution was coherent with his ontological convictions, according to which proportions are nothing more than the outcome of the comparing soul (and in this sense one can rely on mathematics in comparing times, power, and resistances). If one takes speed for the final result, the only element to be considered is the power of the agent (“proportio velocitatum, id est effectuum productorum vel producibilium, insequitur proportionem agentium absolute”, q. 10, 2). The different ways of attaining the speed, respectively in rectilinear local (speed can be attained through the linear space obtained by the fastest point in a given time) and in downward motion (speed can be attained through the distance from the center of the world), rest upon such ontological commitments.

Ideas on Qualities. In his question On Intension and Remission of Forms (De intensione et remissione formarum) Blasius denied the existence of species in order to explain vision, following his reductionist agenda. Also knowledge, even scientific knowledge, was for him nothing different than the knowing soul. No quality, moreover, could be inherent to the soul without having an infinite degree of intensity, being soul in-extended. In the first part of the question (articulus I) Blasius had a wider project: to limit ontology only to substances, refusing the existence of every kind of accidental qualities. In order to do that concerning the accidental category of quality (admitted by William Ockham), Blasius relied upon the theory of intension and remission in analysing the presence of contrary qualities in natural substances. In particular, he felt himself entitled to refuse the existence of coldness on the basis that it could be considered hotness in a lower degree (the last conclusion of the articulus I: “frigiditas non est aliud quam remissa caliditas”). Between the two contrary qualities, therefore, there is no specific distinction. He rejected, moreover, qualities’s power to produce, in their highest degree, the substantial form, a theory defended by Walter Burley in his On Intension and Remissiom of Forms. For example hot in its highest degree can produce fire. According to his reductionist attitude, Blasius upheld the solution according to which intension and remission concern the natural being, the bearer of the quality, rather than quality itself. This solution permitted Blasius to take into consideration two dimensions of the changing quality: intension of the quality properly and the extension of the quality in the subject. In this way Blasius was able to deal with the topic introducing a way of representing quality’s changes through geometrical figures.

In this question, moreover, Blasius blended some topics of fourteenth-century English and Parisian natural philosophy, as he did in his commentary on Bradwardine’s Treatise on Proportions. In addition to intension and remission, he discussed the ways of attaining speed in local motion and alteration, problems concerning limits (first/last instant, primum/ultimum instans) and reaction (reactio). On this last topic he granted the position of Parisian masters, according to which there is a difference between the power of acting and that of resisting in every quality.

SUPPLEMENTARY BIBLIOGRAPHY. A complete bibliography of Blasius’s works, listing the known manuscripts, has been prepared by Graziella Federici Vescovini in the “Appendix” to Federici Vescovini, Graziella and Barocelli, Francesco, eds., Filosofia, scienza e astrologia nel Trecento Europeo. Biagio Pelacani Parmense, a cura di con un intervento di Raymond. Klibansky. Padova: Il Poligrafo 1992: 181–216.

WORKS BY BLASIUS OF PARMA

Quaestiones super de anima: Federici Vescovini, Graziella, Le‘Quaestiones de anima’ di Biagio Pelacani da Parma. Firenze: Leo S, Olschki, 1974 (based on two mss.: Città del Vaticano, ms. Chig. 0.IV, 41; Napoli, Biblioteca Nazionale Vittorio Emanuele III, ms. VIII, G., 74). Italian translation: Biagio Pelacani da Parma, Quaestiones de anima. Alle origini del libertinismo, a cura di Valeria Sorge. Napoli: Morano, 1955.

Quaestiones de musica discovered by John E. Murdoch in the ms. Paris: Bibliothèque Nationals, lat. 7372, ff. 1r–72r, published as Murdoch, John, E. “Music and Natural Philosophy:

Hitherto unnoticed “Quaestiones” by Blasius of Parma (?)”, Manuscripta, XX (1976): 119–136. The author maintains that this text cannot be surely attributed to Blasius.

Questio de intensione et remissione formarum: Federici Vescovini, Graziella, “La Quaestio de intensione et remissione formarum di Biagio Pelacani da Parma”, Physis, XXXI (1994): 433–535 from the ms. Venice, Biblioteca Marciana, ms. VI, 62 (2549).

Questiones super Tractaus logice Magistri Petri Hispani. Edited by Joël Biard and Graziella Federici Vescovini, avec la coll. de Orsola Rignani et Valeria Sorge. Paris: J. Vrin, 2001.

Questiones circa Tractatum proportionum Magistri ThomeBraduardini. Edited by Joël Biard et Sabine Rommevaux. Paris: J. Vrin, 2005.

OTHER SOURCES

Biard, Joël. “L’être et la mesure dans l’intension et la rémission des formes (Jean Buridan, Blaise de Parme).” Medioevo 27 (2002): 415–447.

———. “Le système des senses dans la philosophie naturelle du XIVe siècle (Jean de Jandun, Jean Buridan, Blaise de Parme).” Micrologus 10 (2002): 335–354.

———. “Mathématique et philosophie dans les ‘Questions’ de Blaise de Parme sur le ‘Traité des rapports’ de Thomas Bradwardine.” Revue d’Histoire des Sciences 56 (2003): 383–400.

Buzzetti, Dino. “Blasius Pelacani, the Paradoxes of Implication and the Notion of Logical Consequence.” In Medieval and Renaissance Logic in Spain. Acts of the 12th European Symposium on Medieval Logic and Semantics held at the University of Navarra (Pamplona 26-30 May 1997), edited by Ignacio Angelelli and Perez Ilarbe, 97–135. Paloma, Spain: Olms, 1998.

Federici Vescovini, Graziella. “Biagio Pelacani: filosofia, astrologia e scienza agli inizi dell’età moderna.” In Filosofia, scienza e astrologia nel Trecento Europeo. Biagio Pelacani Parmense, edited by Graziella Federici Vescovini and Barocelli, Francesco, 39–52. A cura di con un intervento di Raymond. Klibansky. Padova: Il Poligrafo, 1992.

Rommevaux, Sabine. “L’irrationalité de la diagonale et du côté d’un même carré dans les ‘Questions’ de Blaise de Parme sur le ‘Traité des rapports’ de Bradwardine.”Revue d’Histoire des Sciences 56 (2003): 401–418.

Sorge, Valeria. “‘Contra communiter philosophantes’: a proposito della fisiologia della visione in Biagio Pelacani da Parma.” Atti dell’Accademia di scienze morali e politiche della Società nazionale di scienze, lettere e arti di Napoli 106 (1996): 299–322, 455–474.

———.”L’influenza di Alhazen sulla dottrina della visione in Biagio Pelacani da Parma.” In Filosofia e scienza classica, arabo-latina medievale e l’età moderna, edited by Graziella Federici Vescovini, 113–127. Louvain-La-Neuve: FIDEM, 1999.

Stefano Caroti