mathematics

Paolo Casati

Paolo Casati 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 Paolo Casati rather than just read about it. In short: Paolo Casati (Latin: Paulus Casatus; 23 November 1617 – 22 December 1707) was an Italian Jesuit mathematician. He belonged to the Jesuit scientific school founded in the Provincia Veneta by Giuseppe Biancani, and represented later by Niccolò Cabeo, Niccolò Zucchi, Giovanni Battista Riccioli and Francesco Maria Grimaldi.

Key takeaways

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

Reference excerpt

Paolo Casati (Latin: Paulus Casatus; 23 November 1617 – 22 December 1707) was an Italian Jesuit mathematician. He belonged to the Jesuit scientific school founded in the Provincia Veneta by Giuseppe Biancani, and represented later by Niccolò Cabeo, Niccolò Zucchi, Giovanni Battista Riccioli and Francesco Maria Grimaldi.

Biography Born in Piacenza to a Milanese family, Casati joined the Jesuits in 1634. From 1636 to 1637 he studied physics and metaphysics at the College of Ferrara. One of the most famous Jesuits scientists of the time, Niccolò Cabeo (1586–1650), was teaching at Ferrara when Casati arrived there. In 1640 he moved to the Roman College, where he studied theology for four years. He was then sent to teach logic at the Jesuit college of Bologna. Bologna Jesuits had developed a strong program of experimentation, such as with falling bodies. During his time in Bologna, Casati frequented the scientific circle gathered around Giovanni Battista Riccioli and Francesco Maria Grimaldi. In Bologna Casati befriended the mathematician Giannantonio Rocca (1607-1656), a disciple of Cavalieri and one of the first Italian supporters of Cartesian philosophy. In 1650, Casati moved to Rome, where he assumed the position of professor at the Roman College. He was given the chair in mathematics after teaching philosophy and theology.

Sweden In 1651, Casati was sent on a mission to Stockholm in order to gauge the sincerity of Christina of Sweden's intention to become Catholic. He subsequently returned to his post at Rome. In 1677, he moved to the Jesuit College in Parma, where he remained until his death. Casati was a friend and correspondent of the famous florentine librarian Antonio Magliabechi, and other scientists like Carlo Rinaldini, Giovanni Antonio Rocca and Daniello Bartoli.

Terra machinis mota The astronomical work Terra machinis mota (1658) imagines a dialogue between Galileo, Paul Guldin, and Marin Mersenne on various intellectual problems of cosmology, geography, astronomy and geodesy. For example, they discuss how to determine the Earth's dimensions, floating bodies, the phenomena of capillarity, and also describe the experiment on the vacuum made by Otto von Guericke in 1654. The work is remarkable for the fact that it represents Galileo in a positive light, in a Jesuit work, only 25 years after Galileo's condemnation by the Church.

Theories on the vacuum

Casati discussed the hypothesis of horror vacui, that nature abhors a vacuum, in his thesis Vacuum proscriptum, published in Genoa in 1649. Casati confuted the existence of both vacuum and atmospheric pressure, but he did not rely entirely on scientific observation, and refers to Catholic thought in order to back his claims. The absence of anything implied the absence of God, and hearkened back to the void prior to the story of creation in the book of Genesis (see Vacuum: historical interpretation).

Recognition The crater Casatus on the Moon is named after him.

Other works Fabrica et uso del compasso di proportione [A work explaining the construction and use of proportional compasses] (in Italian). Bologna: Ferroni. 1664. Le ceneri dell'Olimpo ventilate (1673), a dialogue about meteorology. De gli horologi solari (unpublished manuscript): about sundial construction. Mechanicorum libri octo (in Latin). Lyon: Anisson, Posuel et Rigaud. 1684. De igne (in Latin). Venezia: Nicolò Pezzana. 1686. Exercitationes matheseos candidatis exhibitaæ (1698) (unpublished manuscript): a collection of algebraic and geometrical subjects.

Notes

See also List of Jesuit scientists List of Roman Catholic scientist-clerics

Sources

De Ferrari, Augusto (1978). "CASATI, Paolo". Dizionario Biografico degli Italiani (in Italian). Vol. 21: Caruso–Castelnuovo. Rome: Istituto dell'Enciclopedia Italiana. ISBN 978-88-12-00032-6. Gavagna, Veronica (2002). "I gesuiti e la polemica sul vuoto. Il contributo di Paolo Casati". In Gian Paolo Brizzi; Roberto Greci (eds.). In Gesuiti e università in Europa (sec. XVI-XVIII). Bologna. pp. 325–38.{{cite book}}: CS1 maint: location missing publisher (link) Gavagna, Veronica (2011). "Paolo Casati e la scuola galileiana". In Luigi Pepe (ed.). Galileo e la scuola galileiana nelle Università del Seicento. Bologna: CLUEB. pp. 311–26. Elazar, Michael; Feldhay, Rivka (2018). "Jesuit Conceptions of Impetus After Galileo: Honoré Fabri, Paolo Casati, and Francesco Eschinardi". Emergence and Expansion of Preclassical Mechanics. Boston Studies in the Philosophy and History of Science. Vol. 270. pp. 285–323. doi:10.1007/978-3-319-90345-3_10. ISBN 978-3-319-90343-9. Feldhay, Rivka; Even-Ezra, Ayelet (2018). "Heaviness, Lightness and Impetus in the Seventeenth Century: A Jesuit Perspective". Emergence and Expansion of Preclassical Mechanics. Boston Studies in the Philosophy and History of Science. Vol. 270. pp. 255–284. doi:10.1007/978-3-319-90345-3_9. ISBN 978-3-319-90343-9.

Worked examples

Example 1 — a first encounter with Paolo Casati

Start with the simplest possible case. Write down what Paolo Casati 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 Paolo Casati 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 Paolo Casati 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 Paolo Casati

In research: Paolo Casati 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 Paolo Casati 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: Paolo Casati is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1617 births, 1707 deaths, 17th-century Italian Jesuits, so understanding it makes those chapters shorter.
In everyday life: Look for Paolo Casati 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 Paolo Casati in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Paolo Casati means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
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Frequently asked questions

What is Paolo Casati in simple terms?

Why does Paolo Casati 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 Paolo Casati?

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 Paolo Casati.