His solution was extremely long and complicated and may not have been understood by mathematicians reading him in Latin translation. Elkin, an actuarian. The Kitab al-Manazir Book of Optics describes several experimental observations that Alhazen made and how he used his results to explain certain optical phenomena using mechanical analogies. For example, to explain refraction from a rare to a dense medium, he used the mechanical analogy of an iron ball thrown at a thin slate covering a wide hole in a metal sheet. A perpendicular throw breaks the slate and passes through, whereas an oblique one with equal force and from an equal distance does not.
The obvious answer to the problem of multiple rays and the eye was in the choice of the perpendicular ray, since only one such ray from each point on the surface of the object could penetrate the eye. Alhazen argued against Ptolemy's refraction theory, and defined the problem in terms of perceived, rather than real, enlargement.
He said that judging the distance of an object depends on there being an uninterrupted sequence of intervening bodies between the object and the observer. When the Moon is high in the sky there are no intervening objects, so the Moon appears close. The perceived size of an object of constant angular size varies with its perceived distance. Therefore, the Moon appears closer and smaller high in the sky, and further and larger on the horizon. The earth as a whole is a round sphere whose center is the center of the world.
It is stationary in its [the world's] middle, fixed in it and not moving in any direction nor moving with any of the varieties of motion, but always at rest. Ptolemy himself acknowledged that his theories and configurations did not always agree with each other, arguing that this was not a problem provided it did not result in noticeable error, but Alhazen was particularly scathing in his criticism of the inherent contradictions in Ptolemy's works. Ptolemy assumed an arrangement hay'a that cannot exist, and the fact that this arrangement produces in his imagination the motions that belong to the planets does not free him from the error he committed in his assumed arrangement, for the existing motions of the planets cannot be the result of an arrangement that is impossible to exist Having pointed out the problems, Alhazen appears to have intended to resolve the contradictions he pointed out in Ptolemy in a later work.
Alhazen believed there was a "true configuration" of the planets that Ptolemy had failed to grasp. He intended to complete and repair Ptolemy's system, not to replace it completely. Truth is sought for itself [but] the truths, [he warns] are immersed in uncertainties [and the scientific authorities such as Ptolemy, whom he greatly respected are] not immune from error He held that the criticism of existing theories—which dominated this book—holds a special place in the growth of scientific knowledge.
Only one damaged manuscript has been found, with only the introduction and the first section, on the theory of planetary motion, surviving. There was also a second section on astronomical calculation, and a third section, on astronomical instruments. In general, his model didn't try to provide a causal explanation of the motions, but concentrated on providing a complete, geometric description that could explain observed motions without the contradictions inherent in Ptolemy's model. He developed a formula for summing the first natural numbers, using a geometric proof to prove the formula.
The lunes of Alhazen. The two blue lunes together have the same area as the green right triangle. Alhazen discovered the sum formula for the fourth power, using a method that could be generally used to determine the sum for any integral power. He could find the integral formula for any polynomial without having developed a general formula.
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Influence of Melodies on the Souls of Animals. It appears to have been concerned with the question of whether animals could react to music, for example whether a camel would increase or decrease its pace. In "tying the visual perception of space to prior bodily experience, Alhazen unequivocally rejected the intuitiveness of spatial perception and, therefore, the autonomy of vision. Without tangible notions of distance and size for correlation, sight can tell us next to nothing about such things. Alhazen was a Muslim; it is not certain to which school of Islam he belonged.
Alhazen wrote a work on Islamic theology in which he discussed prophethood and developed a system of philosophical criteria to discern its false claimants in his time. There are occasional references to theology or religious sentiment in his technical works, e. Truth is sought for its own sake Finding the truth is difficult, and the road to it is rough.
For the truths are plunged in obscurity. God, however, has not preserved the scientist from error and has not safeguarded science from shortcomings and faults. If this had been the case, scientists would not have disagreed upon any point of science From the statements made by the noble Shaykh, it is clear that he believes in Ptolemy's words in everything he says, without relying on a demonstration or calling on a proof, but by pure imitation taqlid ; that is how experts in the prophetic tradition have faith in Prophets, may the blessing of God be upon them.
But it is not the way that mathematicians have faith in specialists in the demonstrative sciences. I constantly sought knowledge and truth, and it became my belief that for gaining access to the effulgence and closeness to God, there is no better way than that of searching for truth and knowledge. Alhazen made significant contributions to optics, number theory, geometry, astronomy and natural philosophy. Alhazen's work on optics is credited with contributing a new emphasis on experiment.
His work on catoptrics also contains the problem known as " Alhazen's problem ". Some of his treatises on optics survived only through Latin translation. In episode 5 The Music of the Spheres , Bronowski remarked that in his view, Alhazen was "the one really original scientific mind that Arab culture produced", whose theory of optics was not improved on till the time of Newton and Leibniz. After the death of Archimedes no really great physicist appeared until Ibn al-Haytham.
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If, therefore, we confine our interest only to the history of physics, there is a long period of over twelve hundred years during which the Golden Age of Greece gave way to the era of Muslim Scholasticism, and the experimental spirit of the noblest physicist of Antiquity lived again in the Arab Scholar from Basra. According to medieval biographers, Alhazen wrote more than works on a wide range of subjects, of which at least 96 of his scientific works are known. Most of his works are now lost, but more than 50 of them have survived to some extent.
Nearly half of his surviving works are on mathematics, 23 of them are on astronomy, and 14 of them are on optics, with a few on other subjects. Known as a conservative theologian, he opposed Aquinas' views on the nature of the soul. After a brief stint in Rome, he was appointed Archbishop of Canterbury in His time as archbishop was marked by efforts to improve discipline in the clergy as well as reorganize the estates of his see. Before and during his time as archbishop, he wrote a number of works on optics, philosophy, and theology, as well as writing hymns.
Numerous manuscripts of his works survive. He was born about and was educated at Lewes Priory. For years Peckham taught at Paris, where he was in contact with many of the leading scholars of his time, including Thomas Aquinas. He famously debated Aquinas on at least two occasions during and , during which Peckham defended the conservative theological position, and Thomas put forth his views on the soul.
Where Peckham met Bacon is not known, but it would have been at either Paris or Oxford. Queen Eleanor persuaded him to write for her a scholarly work in French, which was later described as "unfortunately rather a dull and uninspired little treatise. His heart, however, was buried with the Franciscans under the high altar of their London church. His tomb still survives. A number of his works have survived, and some have appeared in print in various times: Perspectiva communis Collectarium Bibliae Registrum epistolarum Tractatus de paupertate Divinarum Sententiarum Librorum Bibliae Summa de esse et essentia Quaestiones disputatae Quodlibeta Tractatus contra Kilwardby Expositio super Regulam Fratrum Minorum.
Danach war er für etwa zwei Jahre — Rektor der Pariser Universität. In der Optik behandelt er u. Auch darüber hinaus war Peckhams Werk noch Gegenstand universitärer Ausbildung. In die Zeit seines Rektorates fiel die Verurteilung von 13 averroistischen Irrtümern Vom November datiert ein Brief des Johannes Peckhams, in dem er über Siger von Brabant und Boetius von Dacien mit Befriedigung vermerkt, dass die beiden in Italien ein jämmerliches Ende gefunden hätten.
Band 3, Bautz, Herzberg , Sp. Vitellonis Thuringopoloni opticae libri decem Vgl. Seine weiteren Lebensdaten sind unbekannt. Da sie die Katoprik von Heron zitiert, deren Übersetzung Wilhelm von Moerbeke erst Ende abschloss, kann sie nicht vor entstanden sein, wahrscheinlich mehrere Jahre später. Das Werk galt lange Zeit als ein Meisterwerk, das sowohl physikalische geometrische als auch metaphysische religiöse Aspekte des Phänomens Licht behandelte.
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Sein Einfluss auf spätere Autoren ist schwer von dem von Alhazen zu trennen, zumal ein gemeinsamer Druck ihrer Arbeiten erschien. Nürnberg hrsg. Witelonis Perspectivae Liber primus, ed. Wroclaw Vitellionis mathematici doctissimi Band 24, Bautz, Nordhausen , Sp. Filosofo della natura del XIII sec.
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Una biografia. Studien zur Intelligibilität des Seienden im Kontext der mittelalterlichen Lichtspekulation. Aschendorff, Münster David C. Egli distingue questa luce divina dalla luce sensibile che ne è una manifestazione e rappresenta la prima delle entità sensibili del cosmo. Biblioteca e Centro di studi a Roma, Conferenze, 87, Encyclopedia of Physical Science. Infobase Publishing; XV, XXVII, Kelso, University of Missouri-Columbia, Le fonti storiche e una serie di documenti autografi testimoniano la sua attiva partecipazione alla vita politica di Firenze.
Nel fu risarcito del torto subito, con il titolo di Segretario del Consiglio della repubblica, stimato ed onorato dai suoi concittadini. La sua influenza divenne tale che a partire dal si trova a malapena nella storia di Firenze un avvenimento pubblico importante al quale Brunetto non abbia preso parte. Nel Brunetto Latini fu elevato alla dignità di Priore. Questi magistrati, in numero di dodici, erano stati previsti nella costituzione del La sua parola si faceva frequentemente sentire nei Consigli generali della repubblica.
Era uno degli arringatori, od oratori, più frequentemente designati. Dante, che era stato allievo di Brunetto, è profondamente scosso, e non nasconde verso il maestro una persistente ammirazione. Brunetto è il primo nell'opera a toccare fisicamente il poeta, tirandolo per la veste. Il protagonista, sconfortato dalla notizia della disfatta di Montaperti, si perde in una "selva diversa". L'opera, della quale Alfonso D'Agostino ha segnalato ottantacinque testimoni manoscritti 61 completi, 11 incompleti, 13 frammentari , consta di tre libri e risulta la prima enciclopedia volgare in senso proprio.
Nel secondo libro si tratta dei vizi e delle virtù, attingendo sostanzialmente dall' Etica Nicomachea. Di Taller del infante Fadrique de Castilla m. Dei tre libri, il primo tratta "de la naissance de toutes choses" la nascita di tutte le cose. Tratta dell'arte di governare che secondo l'autore era la più importante e nobile di tutte le scienze. Il manoscritto è composto da pagine e miniature e rilegato in pelle marrone con motivi sotto forma di mosaici. I margini di 18 fogli sono pieni di numerosi arabeschi e costituiscono una delle serie più evolute ed antiche di questo genere nella storia della miniatura europea.
Le illustrazioni della storia naturale usano schemi tradizionali che ricordano ai bestiari della tradizione romanica. Clark Marlboro College , I.