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Vitello

Vitello is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Vitello rather than just read about it. In short: Vitello (Polish: Witelon; German: Witelo; c. 1230 – 1280/1314) was a Polish friar, scientist, theologian, natural philosopher and an important figure in the history of philosophy in Poland. Name Vitello's name varies with some sources.

Vitello — main illustration
Vitello — illustration

Key takeaways

  • Vitello belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Vitello to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Vitello from memory before moving on to harder problems.

Reference excerpt

Vitello (Polish: Witelon; German: Witelo; c. 1230 – 1280/1314) was a Polish friar, scientist, theologian, natural philosopher and an important figure in the history of philosophy in Poland.

Name Vitello's name varies with some sources. In earlier publications he was quoted as Erazmus Ciolek Witelo, Erazm Ciołek, Vitellio and Vitulon. Today, he is usually referred to by his Latin name Vitello Thuringopolonis, often shortened to Vitello.

Life Vitello's exact birth-name and birthplace are uncertain. He was most likely born around 1230 in Silesia, in the vicinity of Legnica. His mother came from a Polish knightly house, while his father was a German settler from Thuringia. He called himself, in Latin, "Thuringorum et Polonorum filius" – "a son of Thuringians and Poles." He studied at Padua University about 1260, then went on to Viterbo. He became friends with William of Moerbeke, the translator of Aristotle from Greek language into Latin. Vitello's major surviving work on optics, Perspectiva, completed in about 1270–78, was dedicated to William. In 1284 he described the reflection and refraction of light.

Perspectiva

Vitello's Perspectiva was largely based on the work of the polymath Alhazen (Ibn al-Haytham; d. ca. 1041) and Robert Grosseteste, and he in turn influenced later scientists, in particular Johannes Kepler. Vitello's treatise in optics was closely linked to the Latin version of Ibn al-Haytham's Arabic opus: Kitab al-Manazir (The Book of Optics; De aspectibus or Perspectivae), and both were printed in the Friedrich Risner edition Opticae thesaurus (Basel, 1572). Vitello's Perspectiva, which rested on Ibn al-Haytham's research in optics, influenced also the Renaissance theories of perspective. Lorenzo Ghiberti's Commentario terzo (Third Commentary) was based on an Italian translation of Vitello's Latin Perspectiva. Vitello's treatise also contains much material in psychology, outlining views that are close to modern notions on the association of ideas and on the subconscious. Perspectiva also includes Platonic metaphysical discussions. Vitello argues that there are intellectual and corporeal bodies, connected by causality (corresponding to the Idealist doctrine of the universal and the actual), emanating from God in the form of Divine Light. Light itself is, for Vitello, the first of all sensible entities, and his views on light are similar to those held by Roger Bacon, though he is closer in this to Alhazen's legacy.

Other works In Perspectiva, Vitello refers to other works that he had written. Most of these do not survive, but De natura daemonum and De primaria causa paenitentiae have been recovered.

Legacy The lunar crater Vitello is named after him.

See also History of philosophy in Poland List of Poles List of Catholic clergy scientists

Notes

References Vitello and his thoughts

Witelonis Perspectivae Liber Primus: Book I of Vitello's Perspectiva, edition and English translation by Sabetai Unguru, with introduction and commentary, Warsaw, The Polish Academy of Science Press, Studia Copernicana, vol. XV, 1977. Witelonis Perspectivae Libri Duo - Liber Secundus et Liber Tertius: Books II and III of Vitello's Perspectiva, edition and English translation by Sabetai Unguru, with introduction and commentary, Warsaw, The Polish Academy of Science Press, Studia Copernicana, vol. XXVII, 1991. Witelonis Perspectivae Liber Quartus: Book IV of Vitello's Perspectiva, A Critical Edition and English Translation with Introduction, Notes and Commentary by Carl J. Kelso, University of Missouri-Columbia, 2003. Witelonis Perspectivae Liber Quintus: Books V of Vitello's Perspectiva, edition and English translation by Mark A. Smith of the First Catoptrical Book of Witelo's Perspectiva, with introduction and commentary, Warsaw, The Polish Academy of Science Press, 1983. Studies

Clemens Baeumker, "Witelo: Ein Philosoph und Naturforscher des dreizehnten Jahrhunderts," Beiträge zur Geschichte der Philosophie des Mittelalters, part 3, no. 2, Münster, Aschendorff, 1908. Władysław Tatarkiewicz, Historia filozofii (History of Philosophy), 3 vols., Warsaw, Państwowe Wydawnictwo Naukowe, 1978. Jerzy Burchardt, "The Discovery of the Rainbow in Crystal by Witelo"

External links Online Galleries, History of Science Collections, University of Oklahoma Libraries High resolution images of works by and/or portraits of Witelo in .jpg and .tiff format. Erasmus Ciołek Witelo monument in the Żórawina village, Wrocław County, Lower Silesian Voivodeship, SW Poland. [1]

Illustrations

Vitello: Cover of Vitellonis Thuringopoloni opticae libri decem (Ten Books of Optics by the Thuringo-Pole Witelo)
Cover of Vitellonis Thuringopoloni opticae libri decem (Ten Books of Optics by the Thuringo-Pole Witelo)
Vitello: Page from a manuscript of De Perspectiva, with miniature of its author Vitello.
Page from a manuscript of De Perspectiva, with miniature of its author Vitello.

Worked examples

Example 1 — a first encounter with Vitello

Start with the simplest possible case. Write down what Vitello claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Vitello before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Vitello ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Vitello

In research
Vitello appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Vitello in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Vitello is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1280 deaths, 13th-century German Catholic theologians, 13th-century German philosophers, so understanding it makes those chapters shorter.
In everyday life
Look for Vitello outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Vitello in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Vitello means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Vitello out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Vitello in simple terms?

Vitello (Polish: Witelon; German: Witelo; c. 1230 – 1280/1314) was a Polish friar, scientist, theologian, natural philosopher and an important figure in the history of philosophy in Poland. Name Vitello's name varies with some sources.

Why does Vitello matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Vitello?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Vitello.

Tags

  • 1280 deaths
  • 13th-century German Catholic theologians
  • 13th-century German philosophers
  • 13th-century German scientists
  • 13th-century German writers
  • 13th-century Polish Roman Catholic theologians
  • 13th-century Polish clergy
  • 13th-century Polish historians
  • 13th-century mathematicians
  • 13th-century writers in Latin
  • Canons of Wrocław
  • Catholic clergy scientists

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