Apollonius Dyscolus’ use of ambiguity in grammatical problem-solving has in recent years had the benefit of two scholarly studies. David Blank, in the course of his analysis of the Syntax as a whole, has described the broad functions which Apollonius assigns to ambiguity. Jean Lallot's 1988 paper, ‘Apollonius Dyscole et l'ambigüité linguistique: problemes et solutions’, is devoted exclusively to the treatment of linguistic ambiguity in Apollonius’ work. Yet it is to be feared that the flood of (...) light thrown by these scholars on what had been an unregarded corner of ancient grammar has shown up rather more than Apollonius would have cared to admit, both about the nature, and about the prospects for success, of the enterprise on which he was engaged. At the same time, certain structural features of ancient grammar, at least of the ancient grammar which Apollonius himself constructed, have come into sharper focus: features clear enough with the benefit of hindsight, but glimpsed, it appears, all too dimly by Apollonius himslf. It is now worryingly clear not only that ambiguity was ambiguous for Apollonius, but also that the ambiguity of ambiguity represented a genuine threat to the coherence and value of his work. In this paper I set out to justify both these claims. (shrink)

Regarding the influence of François Rabelais on the Giordano Bruno‟s works, up to now the criticism have only taken into consideration the lexical and thematic analogies. This article individualizes, in a passage of the Oratio Valedictoria, a literal quotation from the Gargantua et Pantagruel, showing that Rabelais was a direct source of inspiration for Bruno. The protagonist of the passage is the pythagorean Apollonius of Tyana, a character well known by the Nolan, who mentioned him in many occasions. He (...) represents the ideal medium with the oriental wisdom, that had so much influence on the thought of Bruno. Besides, he embodies the model of the "natural magician" in which the philosopher repeatedly identified himself, both in his works and life. (shrink)

The article includes a short biography of Hermann of Dalmatia and gives an account of his translations and philosophical and scientific work. In order to have a better understanding of Hermann’s philosophy, a reminder of Greek and Arabic philosophy of nature, on which he relies in his interpretation of the world picture, needs to be presented. Cosmological models by Plato, Aristotle, Eudoxus, Heraclides of Pont, Apollonius of Perga, Hipparchus, Ptolemy, and the Arab scientist Abu Ma’shar, are presented. The main (...) focus of interest is on Hermann’s translations. The immense importance of his translations from Greek and Arabic into Latin is due to the fact that some of the seminal Greek and Arabic works became known in Western Europe in the middle of the twelfth century. Hermann is also important as the author of the original work De essentiis, which presented a blend of Platonian and Aristotelian as well as Western European and Arab traditions. (shrink)

Regarding the influence of Francois Rabelais on the Giordano Bruno’s works, up to now the criticism have only taken into consideration the lexical and thematic analogies. This article individualizes, in a passage of the "Oratio Valedictoria", a literal quotation from the Gargantua et Pantagruel , showing that Rabelais was adirect source of inspiration for Bruno. The protagonist of the passage is the pythagorean Apollonius of Tyana, a character well known from the Nolan, who mentioned him in many occasions. He (...) represents theideal medium with the oriental wisdom, that had so much influence on the thought of Bruno. Besides, heembodies the model of the "natural magician" in which the philosopher repeatedly identified himself, both inhis works and life. (shrink)

During 17th century a scientific controversy existed on the derivation of Snell’s laws of reflection and refraction. Descartes gave a derivation of the laws, independent of the minimality of travel time of a ray of light between two given points. Fermat and Leibniz gave a derivation of the laws, based on the minimality of travel time of a ray of light between two given points. Leibniz’s calculus method became the standard method of derivation of the two laws. We demonstrate in (...) this article that Snell’s law of reflection follows from simple results of geometry. We do not use the concept of motion or the time of travel in our demonstration. That is, time plays no role in our demonstration. (shrink)

Alhazen problem of reflection at a concave spherical surface is one of the most discussed problems in optics. It was solved by Alhazen, The number of solution points vary from zero to a maximum of four. However, his solution is known to be prolix. Huygens solved the problem and identified the solution points to be points of intersection of the given circle and a hyperbola. Many other lines of attack were attempted with their solutions. New solutions are offered from time (...) to time. In this paper we offer a solution based on the criterion to be satisfied by reflection of a ray of light at a concave spherical surface. Based on that criterion we show that it is impossible for a circle containing both end points of the path of the ray inside it, to reflect rays from one point to the other. However, for every point on the given circle, we can construct two orthogonal circles (orthogonal conics in general) which reflect rays from one given point to the other, while the given circle is a non-reflector. (shrink)