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Jacques de Billy

Jacques de Billy 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 Jacques de Billy rather than just read about it. In short: For the English patristic scholar and Benedictine abbot, see Jacques de Billy (abbot) (1535–1581). Jacques de Billy (March 18, 1602 – January 14, 1679) was a French Jesuit mathematician.

Jacques de Billy — main illustration
Jacques de Billy — illustration

Key takeaways

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

Reference excerpt

For the English patristic scholar and Benedictine abbot, see Jacques de Billy (abbot) (1535–1581).

Jacques de Billy (March 18, 1602 – January 14, 1679) was a French Jesuit mathematician. Born in Compiègne, he subsequently entered the Society of Jesus. From 1629 to 1630, Billy taught mathematics at the Jesuit College at Pont-à-Mousson. He was still studying theology at this time. From 1631 to 1633, Billy taught mathematics at the Jesuit college at Rheims. From 1665 to 1668 he was professor of mathematics at the Jesuit college at Dijon. One of his pupils there was Jacques Ozanam. Billy also taught in Grenoble. He also served as rector of a number of Jesuit Colleges in Châlons-en-Champagne, Langres and in Sens. The mathematician Claude Gaspard Bachet de Méziriac, who had been a pupil of Billy's at Rheims, became a close friend. Billy maintained a correspondence with the mathematician Pierre de Fermat. He died January 14, 1679 in Dijon, France.

Work and legacy Jacques de Billy wrote multiple books on mathematics. In 1637, he published his first book called Abregé des Preceptes d’Algebre. This book helped teach basic principles and rules of algebra. In 1643, he published his second book called Nova Geometriae Clavis Alegrba, which was designed as a way to help solve geometric problems using algebra. French mathematician Bachet introduced Billy to indeterminate analysis at the Jesuit College at Rheims. Later on, in his time at the College of Dijon, Billy with the help of Pierre Fermat published his ideas on number theory. Billy's mathematical works also include Diophantus Redivivus. The foundational text for number theory was written in these volumes. Oldenburg and Rahn use this book as a reference to their own. Billy also wrote Diophantus Geometria Sive Opus Contextum ex Arithmetica et Geometrie Simul, which states a large number of solutions to algebraic equations, what we now call Diophantine equations. In the field of astronomy, he published several astronomical tables. First published in Dijon by Pierre Palliot in 1656, Billy's tables of eclipses is called Tabulae Lodoicaeae seu universa eclipseon doctrina tabulis, praeceptis ac demonstrationibus explicata. Adiectus est calculus, aliquot eclipseon solis & lunae, quae proxime per totam Europam videbuntur. The tables were calculated for the years 1656 to 1693. This work also contains solar and lunar tables based on the Paris meridian. It also includes a detailed examination of problems involved in astronomical calculations. In 1665, Jacques de Billy wrote Discors de la comète qui a paru l'an 1665, au mois d'Auril. In this pamphlet, Billy talks about a comet observed in the sky in April of 1665. He talks about the path it took across the sky, its position to the stars and its appearance. He goes on to reject the common idea that comets were signs in the sky, and he states that they are actually a natural event that could be studied scientifically. Jaques De Billy wrote the book Barlaam and Josaphat in 1692 which is a Greek hagiography, later leading to a Spanish translation by Antonio de Borja leading to a turning point in foreign literature in the Philippines, as well as the first book written there. Billy put together a book called Doiphantus with Fermat’s Notes, from various of Fermat’s letters. This was a key role in making Fermat’s number-theoretic methods accessible to other mathematicians. In this book were several numerical problems that others were not able to solve. Many other mathematicians such as Ozanam were influenced by many Jesuits, one of them being Jacques de Billy. Earlier in life, Billy wrote an analysis called Epilogue or Specious Analysis which was a book of mathematical problems that he didn’t revisit until later in his life after reading what Ozanam did in similar problems. Billy was one of the first scientists to reject the role of astrology in science. He also rejected old notions about the malevolent influence of comets. Jacques de Billy edited most Greek works in Latin, this was mainly due to his inability to find people who would publish his work. In 1935, Jacques de Billy was honored with the naming of a lunar crater, which now bears the name Billy.

Works

Diophanti redivivi (in Latin). Vol. 1. Lyon: Jean Thioly. 1670. Diophanti redivivi (in Latin). Vol. 2. Lyon: Jean Thioly. 1670.

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

References O'Connor, John J.; Robertson, Edmund F., "Jacques de Billy", MacTutor History of Mathematics Archive, University of St Andrews Moon Watch Polybiblio

Further reading Itard, Jean (1970–1980). "Billy, Jacques de". Dictionary of Scientific Biography. Vol. 2. New York: Charles Scribner's Sons. p. 131. ISBN 978-0-684-10114-9.

References

Illustrations

Jacques de Billy: Diophanti redivivi, 1670
Diophanti redivivi, 1670

Worked examples

Example 1 — a first encounter with Jacques de Billy

Start with the simplest possible case. Write down what Jacques de Billy 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 Jacques de Billy 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 Jacques de Billy 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 Jacques de Billy

In research
Jacques de Billy 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 Jacques de Billy 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
Jacques de Billy is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1602 births, 1679 deaths, 17th-century French Jesuits, so understanding it makes those chapters shorter.
In everyday life
Look for Jacques de Billy 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 Jacques de Billy in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Jacques de Billy 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 Jacques de Billy out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Jacques de Billy in simple terms?

For the English patristic scholar and Benedictine abbot, see Jacques de Billy (abbot) (1535–1581). Jacques de Billy (March 18, 1602 – January 14, 1679) was a French Jesuit mathematician.

Why does Jacques de Billy 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 Jacques de Billy?

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 Jacques de Billy.

Tags

  • 1602 births
  • 1679 deaths
  • 17th-century French Jesuits
  • 17th-century French mathematicians
  • Catholic clergy scientists
  • French number theorists
  • Jesuit scientists

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