Appendix: 56 Prominent Jesuit Geometers

Here is a brief description of the lives and some of the geometrical works of the 56 better-known Jesuit geometers, taken from Sommervogel. There is little point in giving a page reference to Sommervogel since all are listed in alphabetical order. Because of the variety of spellings, the Sommervogel versions are used here. References to professional journals such as the Dictionary of Scientific Biography (DSB), the Philosophical Transactions of the Royal Society of London (TRS) and Le Journal des Savants (also "Scavans": JSV) are indicated for further reading. The number of entries in Sommervogel does not always correspond to the number of books the man has written, since Sommervogel does not list all publications and also some of the numbers refer to repeated editions. These numbers, however, do give some indication of how busy the man was.

1. Francois D'Aguilon (French) b 1546 in Brussels d 1617 in Antwerp

Reference to him in the Dictionary of Scientific Biography is found in v 1 p81, and v12 p74.

1 entry is found in Sommervogel:

Opticorum libri sex (Antwerp, 1613)

He founded a Belgian school for mathematics in Antwerp. In his work the word "stereographic" to describe the projections of Hipparcus appears for the first time. The first edition of his book, which went into several editions, was dedicated to the governor Inigo Borgia (a relative of Francis Borgia, S.J.). Peter Paul Rubens designed the engravings for the illustrations of the book. D'Aguilon planned to write books on catoptrics and dioptrics but died before he finished them.

2. Fran�ois X Alegre (Mexican) b 1729 in Vera Cruz d 1788 in Bologna

14 entries are found in Sommervogel; an example is the following:

Elementorum geometriae Lib. XIV sectionum conicarum Lib.IV una cum tractatu de gnomonica (Bologna, 1770)

A crater on the moon was named in his honor: it was found in the sixth octant of the early editions of lunar maps, but has since been renamed. A century (1889) after his death all his unpublished works were collected and published.

3. Joseph M Amiot (French) b 1718 in Toulon d 1793 in Peking

28 entries are found in Sommervogel; some examples are the following:

Art Militaire des Chinois (Paris, 1772) Dictionnaire Tartar (Paris, 1790)

Positions gŽographiques Turkestan (Lyon, 1880)

His specialties included geometry and physics, but he also had great talent for music. He had earned the confidence of the Chinese emperor Kien-Long, and after the suppression he continued his work in Peking with the support of the same French government that suppressed the Jesuits.

4. AndrŽ Arzet (French) b 1604 in Constance d 1675 in Constance

3 entries are found in Sommervogel; an example is the following:

Clavis Mathematica (Constance, 1634)

He taught in Constance for his whole life and was praised by Riccioli in Almagistum novum for his work on eclipses. A lunar crater was named for him.

5. Mario Bettini (Italian) b 1582 in Bologna d 1657 in Bologna

7 entries are found in Sommervogel; an example is the following:

Aerarium Philosophiae Mathematicae (Bologna, 1648)

He taught the geometry of military art, stereometry and conics. A crater on the moon is named in his honor.

6. Jacques de Billy (French) b 1602 in Compiegne d 1679 in Dijon

Reference to him in the Dictionary of Scientific Biography is found in v 2 p131, v 4 p574,

v 5 p528, v 13 p253.

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in v 1 p 324, v 2 p 568-575 and v 6 p 2185.

Le Journal des Savants (Scavans) (6 sept.1666) published his method for finding a date in the Julian calender.

15 entries are found in Sommervogel; some examples are the following:

Nova Geometriae Clavis Algebra (Paris, 1643) Opus Astronomicum (Paris, 1661) De Proportione Harmonica (Paris, 1658) Discours de la Comete (Paris, 1665)

Doctrinae analyticae inventum novum (Toulouse 1670)

He taught mathematics at Pont a Mousson, Rheims and finally at Dijon, where he became quite friendly with Fermat. Fermat edited one of his books, while he preserved the algebraic discoveries of Fermat in his Doctrinae analyticae . There was abundant correspondence between the two men concerned with topics such as indeterminate analysis, diophantane equations, and harmonic ratios. De Billy is frequently mentioned in Cajori's History of mathematical notations .

7. Jean Bonfa (French) b 1638 in Nimes d 1724 in Avignon

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in v 14 p715-720, 1686, p175.

Le Journal des Scavans (Jan 1679, p24-26) published his "Lettre touchant une nouvelle invention de faire des pendules," in which he describes some of measuring instruments he invented. His "Binocle GŽomŽtrique" was published in the Journal de Trevoux ( Jan. 1702).

7 entries are found in Sommervogel; an example is the following:

Carte Geographique du Com�te Venaissin (Marseille, 1699)

One of his correspondents, Dominic Cassini, along with others admired his astronomical observations as well as his geometrical instruments. He taught mathematics at Avignon and Marseilles.

8. Roger J Boscovich (Croatian) b 1711 in Ragusa d 1787 in Milan

Reference to him in the Dictionary of Scientific Biography is found in v 1 p462,

v 2 p326-332, v 3 p156, 539, v 4 p529, v 6 p 86, 335, v 8 p159, 360, v 11 p142,

v 12 p608, v 13 p39, 235, 375, v 14 p70, v 15 p309, 352, 376.

108 entries are found in Sommervogel; some examples are the following:

De Circulis Osculatoribus (Rome, 1740) Trigonometriae sphaericae (Rome, 1737) De natura et usu infinitorum (Rome, 1741) Elementorum Matheseos (Rome, 1752)

Philosophiae naturalis theoria (Rome, 1758)

Born eighth of nine children, he had an older brother, Barthelemy (1699-1770), who also was a Jesuit mathematician, and on occasion took Roger's place teaching when he was needed elsewhere. He taught at the Roman College for 20 years, although the Jesuit General Luigi Centurione, S.J. (1755-1757) thought his teachings dangerous. When his admirer Laurence Ricci, S.J., became the Jesuit General, however, Boscovich was made a Visitor of the whole Jesuit Society. He did not suffer fools gladly. He argued against some of the Jesuits' blind loyalty to Aristotelean physics; when shown the treasures of the Jesuit school at Sens, which included a rib of the prophet Isaiah, he told the rector to throw it away, in the interest of truth. Correspondent for the Royal Society, he was also a frequent contributor to the Jesuit MŽmoires des TrŽvoux. The famous astronomer/mathematician Joseph Lalande said there was no scholar in all Italy like Boscovich nor did he know any geometer as profound. After the suppression Lalande accompanied Boscovich on a journey through France using a salvus conductus (safe-conduct pass) given Boscovich by Louis XV.

He developed the first coherent description of atomic theory in his work Theoria Philosophiae Naturalis , which is one of the great attempts to explain the universe in a single idea. His influence on modern atomic physics is undoubted, and his works are kept as the Boscovich Archives in the Bancroft Library of Rare Books at Berkeley. On the anniversaries of his publications, his birth, and his death, symposia are held throughout the world to honor this amazing polymath.

Boscovich was a creative scientist whose inventions included the ring micrometer and the achromatic telescope. He was the first to apply probability to the theory of errors, as was later acknowledged by Laplace and Gauss. It was his influence that minimized the hostility of Catholic churchmen to the Copernican system, and he convinced Pope Benedict XIV to remove Copernicus from the Index of Forbidden Books. During his life he had been commissioned by popes and emperors to do such jobs as repair the fissures in St Peter's dome as well as other cathedral domes, direct the drainage of the Pontine marshes and survey the meridian of the Papal states.

He traveled very often as a Visitor of the Society of Jesus, but also as a geometer. He gathered data to define the shape of the earth while on an excursion to Brazil. Another scientific expedition to California had to be canceled because of growing hostility to the Jesuits. After the suppression of the Jesuits he became captain of optics in the French navy.

Born in Ragusa (now Dubrovnik, Yugoslavia), Boscovich lived a long, fruitful life. Incisive in thought, adventuresome in spirit, and independent in judgment, he was a man of the eighteenth century in some respects, but far ahead of his time in others.

9. Joachim Bouvet (French) b 1662 in Mans d 1732 in Peking

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in v 20 p244.

10 entries are found in Sommervogel; an example is the following:

Elementa geometriae (Peking, 1690)

He was one of the party of six Jesuits, along with de Fontaney, Tachard, Visdelou, Lecompte and Gerbillon, who accompanied de Chaumont to Siam in 1685 as "MathŽmaticiens Royal." He later proceeded to China. His Portrait de l'Empereur de la Chine was translated into German by Leibniz in 1699, and an English translation appeared the same year. He was a frequent correspondent of the king's confessor, the Jesuit P�re la Chaise (after whom is named the famous cemetery in the middle of Paris).

10. Louis B Castel (French) b1688 in Montpellier d 1757 in Paris

Reference to him in the Dictionary of Scientific Biography is found in v 3 p114-115,

v 5 p54, v 5 p510, v 15 p58, v 15 p270.

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London.

21 entries are found in Sommervogel; some examples are the following:

Plan d'une MathŽmatique (Paris, 1727) MathŽmatique universelle (Paris, 1778)

Sommervogel lists his correspondence with other mathematicians, 23 articles in MŽmoires des TrŽvoux and 13 in Mercure de France . The Bibliotheque Royal in Brussells now holds many of his manuscripts. In 1730, he was elected to the Royal Society of London, and to the Bordeaux Academy in 1746, despite his opposition to the teachings of Newton. He reproached Newton with wanting to reduce man to "using only his eyes," because Newton's experimental proofs were all visual. He was especially remembered throughout Europe for his ocular harpsichord, a scheme for making colors and musical tones correspond.

11. Thomas Ceva (Italian) b 1648 in Milan d 1737 in Milan

Reference to him in the Dictionary of Scientific Biography is found in v 2 p182,

v 3 p183-184, v 12 p 55.

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London.

35 entries are found in Sommervogel; some examples are the following:

De cycloide (Milan, 1690) Opuscula mathematica(Milan 1699)

Ceva carried on an extensive correspondence with the famous mathematician Guido Grandi, a Camaldolese monk. An essay of his appears at the end of one of Grandi's works. He invented a device to divide an angle into an arbitrary number of parts; ten years later the device was claimed by L'Hospital, with no mention of Ceva. He brought Newton's theory of gravitation to Italy.

Thomas Ceva was a poet as well as a geometer and his poem "Jesus Puer " (Milan 1690) went through many printings, was translated into several languages, and occasioned many commentaries. In fact, he has been called "the greatest Jesuit poet-genius." He came from a famous Italian family. "Ceva's theorem" is named for his brother Giovanni.

12. Claude F. M. de Chales (French) b 1621 in Chambery d 1678 in Turin

Reference to him in the Dictionary of Scientific Biography is found in v1 p81, v 3 p621-622, v 4 p452, v 4 p505,v 13 p320.

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in v 9 p229-233.

8 entries are found in Sommervogel; some examples are the following:

Euclidis elementorum libri octo (Lyons, 1660)

Cursus seu Mundus Mathematicus (Lyons,1674)

Principles gŽnŽraux de la gŽographie mathŽmatique (Paris, 1672)

He was a distinguished mathematician and was appointed Royal Professor of hydrography at Marseilles by Louis XIV. He wrote, as well, on navigation and the art of fortification.

13. Jean Ciermans (Belgian) b 1602 in Bois le duc d 1648 in Portugal

4 entries are found in Sommervogel; some examples are the following:

Repetito menstrua (Louvain, 1639) Annus Positionum Mathematicarum (Louvain, 1641)

Anticipating Pascal by a few years, he invented the first calculator capable of adding and subtracting "with no chance of error." He engaged in a well-publicized philosophical dispute with Descartes. His Repetito menstrua included a different science for each month and was based on the Moslem calendar. He wanted to work in the China mission but died at the age of 46 in Portugal while on his journey to China.

14. Christopher Clavius (German) b 1538 in Bamberg d 1612 in Rome

Reference to him in the Dictionary of Scientific Biography is found throughout

but especially in v 3 p311-312.

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in v 1 p135, v 1 p353-254, v 1 p289-294, v 12 p1030-1035,

v 14 p721-726.

24 entries are found in Sommervogel; some examples are the following:

In Sphaeram Joannis de Sacrobosco (Rome, 1570 Gnomonices libri Octo (Rome, 1581)

Euclid elementorum (Rome, 1589) Epitome Arithmeticae practicae (Rome,1584) Novi calendarii (Rome, 1588) Astrolobium (Rome, 1593)

Geometrica practica (Rome, 1604) Opera mathematica (Rome, 1611)

Born before the start of the Society of Jesus, he was one of its earliest members. His name and his date of birth have been incorrectly given by some historians. One such name was Christopher Schluessel (key), but his name in German was Christopher Claus (from klais = key). He was professor of mathematics at the Roman College for forty-five years; and during this time he won the respect and friendship of numerous astronomers and mathematicians, among whom are numbered Viete, Kepler and Galileo. He was a life-long friend of Galileo, and a 1611 report from Clavius and his Jesuit colleagues confirmed Galileo's discoveries. He was an outstanding astronomer and mathematician. He exerted a wide influence on the schools of Europe as well as China through his Jesuit pupils laboring there. The historian of science George Sarton calls him "the most influential teacher of the Renaissance."

Recently (7/6/79) a front page article in the New York Times credits "chronicler" Clavius with furnishing the 16th century astronomical records as evidence for Princeton astronomers' claim that the sun was shrinking. A total eclipse of the sun no longer displays the noticeable ring which had been seen by Clavius.

Clavius anticipated a number of mathematical developments: e.g., the decimal point, parenthesis, use of logarithms and the vernier scale. It was Clavius who replaced the Julian calendar with the Gregorian calendar. Later mathematicians such as Leibniz became interested in mathematics by reading his works. In his Tractatus triangulorum Clavius summarized nearly all contemporary knowledge of plane and spherical trigonometry. His Euclidis elementorum contains all the known books of Euclid and a vast collection of comments and elucidations. Later editions of this work became the standard text in the 16th- and l7th-century European schools. In this work, Clavius showed concern for the axioms of Euclid and noted the absence of an axiom guaranteeing the existence of a fourth proportional to three given magnitudes. This work led to his being called "the Euclid of the l6th Century."

15. HonorŽ Fabri (French) b 1607 in Dauphined 1688 in Rome

Reference to him in the Dictionary of Scientific Biography is found in v 4 p505-506,

v 5 p544, v 8 p267.

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in v 1 p325-327, v 1 p69-73, v 2 p626, v 4 p925-928,

v 5 p2055-2057, v 5 p2057-2059, v 5 p2082-2083, v 9 p78-83, v 16 p314-323.

31 entries are found in Sommervogel; some examples are the following:

Theses de universa mathematica (Lyons, 1646) Philosophis Universa (Lyons, 1646)

Opusculum geometricum (Rome, 1659) De Homine (Lyons, 1666)

He wrote more than thirty works, many of them on scientific topics, some of which were reviewed in the Philosophical Transactions. In his treatise De Homine Fabri claimed to have discovered the circulation of the blood prior to Harvey. Sommervogel implies that the most Fabri can claim is that he discovered it without knowing of Harvey's work, since Harvey published so much earlier than Fabri. He was a member of the Holy Office, so when he stated his opinion that the Catholic Church would adopt a figurative meaning to the offending biblical passages if it was shown that the earth does indeed move, he was thrown into prison by Pope Alexander VII for 50 days, and even then he was only released because King Ferdinand intervened.

16. Jean C de la Faille (Belgian) b 1597 in Antwerp d 1654 in Barcelona

Reference to him in the Dictionary of Scientific Biography is found in v 7 p583,

v 7 p557-558, v 8 p26, v 12 p436, v 13 p561.

3 entries are found in Sommervogel; some examples are the following: Theses Mechanicae (Dolae, 1625) Theoremata de Centro Gravitatis (Antwerp, 1632)

He taught at the Imperial College. He is the subject of a well-known painting of Van Dyke which stands in the Brussels Plantin Museum of fine arts; it was on loan to the New York Metropolitan Museum in 1984. Since he was the tutor of Don Juan of Austria, he went on the latter's campaigns, and met his death during one such battle.

17. Jean de Fontaney (French) b 1645 in Bretagne d 1710 in la Fl�che

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in v 13 p145-149, v 14 p715-720, v 20 p371-373.

15 entries are found in Sommervogel; an example is the following:

Observations sur la com�te (Paris, 1681)

He was professor of mathematics at Clermont College, Paris. He was a distinguished astronomer and a corresponding member of the AcadŽmie des Sciences. Fontaney was superior of the group of "Royal Mathematicians" sent by Louis XIV to Siam in 1685. He went on to China, returning to Europe later. In Le Journal des Scavans 21 Nov. 1678, pp. 213-6, he is credited with recording an occultation of Saturn along with Cassini, de la Hire and others. He was a correspondent of the famous Jesuit P�re la Chaise.

18. Aegidus F. de Gottignies (Belgian) b in Brussels 1630 d 1689 in Rome

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in v 1 p209-210, v 5 p2054-2055.

14 entries are found in Sommervogel; some examples are the following:

Elementa Geometriae Planae (Rome, 1669) Logistica (Rome, 1675)

Problema duplatio (Rome, 1681) Logistica Universalis sive mathesis (Naples, 1687)

Aegidus (Gilles) de Gottignies was sent to study at Rome, and he was later appointed professor of mathematics at the Roman College. He was an industrious scholar of wide interests, and published many scientific works. His correspondence with Cassini concerning the eclipse of Jupiter was published in Bologna in 1665. He published a study on the anatomy of the eye of a fly which was later translated into French by the famous naturalist Buffon.

19. Christopher Grienberger (Swiss) b1564 in Tyrol d 1636 in Rome

9 entries are found in Sommervogel; some examples are the following: Euclidis sex primi (Rome, 1655) Elementa trigonometrica (Rome, 1630)

Correspondent with Galileo as well as with Cardinal Robert Bellarmine, he was Clavius' replacement as professor of mathematics at the Roman College. As such he had to make a difficult decision regarding the publication of St. Vincent's great work, Opus geometricum . Grienberger verified Galileo's discovery of the four moons of Jupiter; then later in 1611 he organized a convocation honoring Galileo. At this gathering of cardinals, princes and scholars, the students of Clavius and Grienberger expounded Galileo's discoveries to the delight of Galileo. He is said to have observed that if Galileo had heeded the advice of the Jesuits and proposed his teachings as hypotheses, he could have written on any subject he wished, including the rotation of the earth.

20. Francesco M Grimaldi (Italian) b 1613 at Bologna d at Bologna 1663

Reference to him in the Dictionary of Scientific Biography is found in v 3 p100, 528,

v 4 p506, v 5 p 542, v 6 p 195, 545, v 9 p485, v 10 p59, v 11 p411, v 14 p461.

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in v 6 p3069-3070, v 16 p314-323.

2 entries are found in Sommervogel; an example is the following:

Physico-mathesis de Lumine (Bologna, 1665)

He was professor at Bologna for many years, and was one of the great geometer-physicists of his time. He was an exact and skilled observer, especially in the field of optics. He discovered diffraction and anticipated the invention of the diffraction grating. He was one of the earliest physicists to suggest that light was wavelike in nature. He formulated a geometrical basis for a wave theory of light in his Physico-mathesis; this treatise attracted Isaac Newton to the study of optics. Newton deals with the diffraction problems of Grimaldi in Part III of his Opticks (1704), after having first learned of Grimaldi's diffraction from the writings of another Jesuit geometer, HonorŽ Fabri.

21. Paul Guldin (Swiss) b 1577 in Saint Galld 1643 in Gratz

Reference to him in the Dictionary of Scientific Biography is found in v 1 p164, v 3 p152,

v 4 p110, v 5 p 527, 588-9, v 7 p 583, v 9 p97, v 10 p301, v 13 p561, 615.

7 entries are found in Sommervogel; some examples are the following: Problema Arithmeticum (Vienna, 1622) de Centro Gravititatis Trium (Vienna, 1635)

Born a Jew and named Habakuk Guldin, after his conversion he changed his name to Paul. The author D. E. Smith., in a rather hostile mood, changed Paul's name back again to Habakuk and spoke with scorn of Habakuk's humble start in life as an apprentice to a goldsmith. Paul entered the Jesuit Society as a Coadjutor Brother, and after a few years he was asked to become a Jesuit Scholastic, then was later ordained. "Guldin's rule," named in his honor, has recently been changed to "Pappus rule" by textbook authors who have been intimidated by recent careless historians.

22. Maximilian Hell (Hungarian) b 1720 in Schemnitz d 1792 in Vienna

Reference to him in the Dictionary of Scientific Biography is found in v 2 p599,

v 6 p233-235, v 7 p580-1, v 10 p34, v 13 p39.

35 entries are found in Sommervogel; some examples are the following: Ephemerides Astronomiae Anni, 1758-1806 Elementa Mathematica (Claudipoli, 1755)

He taught mathematics in the Jesuit college at Leutschau, Hungary (now in Czechoslovakia). Later he was made director of the astronomy observatory in Vienna. After the Suppression of the Jesuits he continued working there as director, along with other members of the Society. He fell victim to the public defamation of Jesuits then in vogue when he was accused of altering his findings during a transit of Venus. His name was not cleared until a century later when in 1883 the famous astronomer Simon Newcomb found his readings to be correct, and his scholarship above suspicion.

23. Johann Helfenzrieder (Swiss) b 1724 in Landsberg d 1803 in Reittenhaslach

26 entries are found in Sommervogel; some examples are the following:

Abhandlung von der Geodasie (Ingolstadt, 1775)

Abhandlung vom Gebrauche der Erden (Ausburg, 1794)

He taught physics at Fribourg, then geometry at Ingolstadt. He authored very accurate almanacs and published treatises on the use of telescopes, as well as on the construction of surveying apparatus. His later works include practical mechanics and the study of hydraulics.

24. Pierre Jartoux (French) b 1669 in Embrum d 1720 in Peking

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in v 28 p237-247.

7 entries are found in Sommervogel; an example is the following:

Principes pour trouver les lignes trigonomŽtriques au moyen des sŽries infinies.

In his time he was considered the best Jesuit mathematician on the China mission. He presented nine remarkable theorems on infintie series, one of which concerned the direction of arcs and chords of a common circle.

25. Athanasius Kircher (German) b 1602 in Geisad 1680 in Rome

Reference to him in the Dictionary of Scientific Biography is found in v 7 p 324-328

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in v 1 p 125-127, v 1 p 109-117, v 2 p 484-488, v 3 p 779-784, v 4 p 1093, v 4 p 967-969, v 6 p 3056-3058, v 10 p 533-542. v 12 p 1027-1029,

v 13 p 208-221, v 15 p 1036-1040, v 15 p 1184-1185, v 17 p 615-617,

v 17 p 865-870, v 20 p 433- 439, v 21 p 337-338, v 22 p 487 -508, v 26 p2-35.

39 entries are found in Sommervogel; some examples are the following:

Primitiae gnomonicae (Avignon, 1635) Ars magna lucis et umbrae (Rome, 1646)

Itinerarium extaticum (Rome, 1656) Mundus subteraneus (Amterdam, 1665)

Ars magna sciendi (Amsterdam, 1669) Phonurgia nova (Kempten, 1673)

He taught at the Roman College for many years and wrote on numerous scientific subjects, many of which were reviewed in the JSV. With his contributions on subjects such as mathematics, astronomy, harmonics, acoustics, chemistry, microscopy and medicine, he played a significant part in the early scientific revolution. In his 39 large books on the sciences, he shows learning of the past, ever open to the developments and possibilities of the future. His Museum Kircherianum was considered one of the best science museums in the world. Among his inventions are found the megaphone, the pantometrum for solving geometrical problems, and a counting machine. His discoveries include sea phosphorescence as well as microscopically small organisms which cause the transfer of epidemic diseases.

Kircher's works were quoted by very many scholars of the day. It was by facilitating a wide diffusion of knowledge, by stimulating thought and discussion by his vast collections of scientific information, that Kircher earned a place among the fathers of modern science and the titles of "universal genius " and "master of a hundred arts ."

26. Jacques Kresa (Moravian) b 1645 in Smrschitz d 1715 in Brunn

6 entries are found in Sommervogel; two examples are the following:

Elementos geometricos de Euclides (Cadiz, 1689)

Analysis trigonometriae sphericae (Prague, 1720)

He held "la chaire de controverse" in Prague for a number of years. In addition to his native tongue, he could converse in Latin, German, Greek, Hebrew, Italian, French, Spanish, and Portuguese.

27. Francesco Lana-Terzi (Italian) b 1631 in Brescia d in Brescia 1687

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in v 6 p3060, v 6 p2114-2116, v 7 p4068-4069, v 10 p509-512,

v 18 p33-37.

9 entries are found in Sommervogel; an example is the following:

Prodromo ouero saggio di alcune invenzioni nuove (Brescia, 1670)

After his studies at the Roman College, he was appointed professor of mathematics at Ferrara and Brescia. He carried out investigations on a wide range of problems in physics, and is listed as an inventor. In 1983, Belize issued a commemorative stamp of his flying ship. He earned the title "Father of Aviation" by being the first to present a scientific treatise on heavier-than-air flying machines. Although critical of Lana's flying machine, Robert Hooke wrote eleven pages concerning Lana's "Flying Chariot" in his Philosophical Collections , and Hooke also read long selections from Lana's Prodromo at the meetings of the Royal Society in 1679.

28. Antoine Laval (French) b1664 in Lyon d 1728 in Lyon

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in 25 p2241-2246.

5 entries are found in Sommervogel; an example is the following:

Voyage de la Louisiane...(Paris, 1728)

He was commissioned by the king to undertake astronomical expeditions. He published 54 articles in MŽmoires des TrŽvoux and 11 in Les MŽmoires de l'AcadŽmie des sciences, most of which described results of his observations of planetary motion.

29. Francis Line (English) b in London 1595 d in Liege 1675

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in v 1 p231-239, v 9 p217-219, v 9 p219, v 9 p78-83,

v 10 p386-388, v 10 p499-580, v 10 p500-503, v 10 p503-504, v 11 p556-561,

v 23 p1416-1418.

5 entries are found in Sommervogel; two examples are the following:

De Corporum Inseparabilitate (London, 1661) An Explanation of the Dyall (Liege, 1673)

He was a mathematician, physicist and scientific controversialist and was professor of mathematics at the displaced English College located in Liege. In the records of the English Province, Volume VI, by Henry Foley (London: Burns & Oates, 1880), he seems also to have had other names: Butler, Hall (Thomas) and Lisle among them. Foley mak

29. Francis Line (English) b in London 1595 d in Liege 1675

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in v 1 p231-239, v 9 p217-219, v 9 p219, v 9 p78-83,

v 10 p386-388, v 10 p499-580, v 10 p500-503, v 10 p503-504, v 11 p556-561,

v 23 p1416-1418.

5 entries are found in Sommervogel; two examples are the following:

De Corporum Inseparabilitate (London, 1661) An Explanation of the Dyall (Liege, 1673)

He was a mathematician, physicist and scientific controversialist and was professor of mathematics at the displaced English College located in Liege. In the records of the English Province, Volume VI, by Henry Foley (London: Burns & Oates, 1880), he seems also to have had other names: Butler, Hall (Thomas) and Lisle among them. Foley makes the point that many of the Jesuits at the time just disappeared and were never heard from again, so the time of death is difficult to know. He had a nephew, George Line, who was also a Jesuit. In 1669, a time when Jesuits were hanged, drawn and quartered, Line was chosen by King Charles II to construct a sundial in the garden of his Whitehall home.

30. Antoine de la Louvere (French) b 1600 in Rieux d 1664 in Toulouse

Reference to him in the Dictionary of Scientific Biography is found in v 4 p573,

v 7 p583-584, v 10 p336, v 14 p749.

9 entries are found in Sommervogel; some examples are the following:

Quadratura Circuli (Toulouse, 1651) De Cycloide Galilaei (Toulouse, 1658) Propositiones Geometriae (Toulouse, 1658)

Among the variations in the spelling of his name are found: de la Loubere, de la Louvere, LaLouvere, Lalouere, Loubere. He was the first geometer to study the helix. He inverted Guldin's rule to find centers of gravity; and, by the time he had the work published, he was teaching theology, which he said was much easier and more suited to his advanced age. Then, irked by an accusation of Pascal, he returned to the fray and produced a good deal more geometry concerning cycloids.

31. Paul Mako deKerck (Hungarian) b 1723 in Jasz-Apath d 1793 in Bude

24 entries are found in Sommervogel; some examples are the following:

Calculi differentialis (Trattnern, 1763) Elementa geometrica (Bude, 1790)

He taught geometry and physics in Vienna until the suppression of the Jesuits in1773, then he returned to Hungary. There he received ecclesiastical honors and became president of the University of Buda.

32. Charles Malapert (French) b 1580 in Mons d 1630 in Victoria

10 entries are found in Sommervogel; some examples are the following:

Faciliorum Geometriae (Douai, 1614) Euclidis Elementorum ( Douai, 1620)

He taught at Pologne and Douai. His research at Douai was described in Rosa Ursina by Christopher Scheiner. After serving as rector of the college at Arras, he was asked by King Philip IV to teach mathematics in Madrid. He died on the way to this assignment.

33. Theodore Moretus (Belgian) b 1601 in Antwerp d 1667 in Breslau

20 entries are found in Sommervogel; some examples are the following:

Mathematici Tractatus (Prague, 1641) De luna pascali et solis motu (Wratislaviae, 1666)

He taught geometry for 14 years in Prague. His eulogy was printed in the Memoria Sachsiana , a medical-physics journal.

34. Pierre Nicolas (French) b 1642 in St. Flour d 1714 in Toulouse

5 entries are found in Sommervogel; some examples are the following:

De lineis logarithmeticis et Spiralibus Hyperbolicis Exercitiones (Toulouse,1696)

De Conchoidibus et Cissoidibus (Toulouse, 1697)

He taught for most of his life in Toulouse, then later became provincial. The historian Montucla mentions the impact Nicolas' studies had on the geometer Tschirnhausen in the effort to find the center of gravity of a surface of revolution.

35. Francois Noel (French) b 1651in Hestrud d 1729 in Lille

12 entries are found in Sommervogel; an example is the following:

Observationes mathematicae (Prague, 1708)

On the occasion of Robert Boyle's new pump and the newly discovered atmospheric pressure he engaged in bitter controversy with Blaise Pascal over the existence of a vacuum. He went to China in 1684, returned to France twice representing China on ceremonial occasions, then finally settled in Prague. He was also skilled in music and art.

36. Ignace G Pardies (French) b 1636 in Pau d 1673 in Bicetre

Reference to him in the Dictionary of Scientific Biography is found in v 6 p130,

v 7 p583, v 10 p54, 314-315.

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in v 6 p3064-3066, v 7 p4087-4090, v 7 p4091-4093,

v 7 p5012-5013, v 7 p5014- 5018, v 7 p4054, v 7 p5150-5151, v 8 p6042-6046,

v 9 p219, v 26 p270-288.

16 entries are found in Sommervogel; some examples are the following:

Horologium Thaumaticum Duplex (Paris, 1662) Elemens de GŽometrie (Paris, 1671)

Discours du Mouvement local (Paris, 1670)

In later life he was appointed professor of mathematics at the Coll�ge Louis-leGrand, Paris. Pardies agreed with Huygens and Hooke in holding to the undulatory theory of light. All physicists of the day knew of his controversy with Newton over this matter, which had been reported in great detail in the Philosophical Transactions.

37. Andrea Pozzo (Italian) b 1642 in Trent d 1709 in Vienna

2 entries are found in Sommervogel; an example is the following:

Perspectiva Pictorum et Architectorum 2 vol. (Rome, 1693-1700)

He was a Jesuit Coadjutor Brother who wrote of perspective geometry applied to art. His book was one of the earliest on perspectivities and was meant to aid artists and architects. It has gone into many editions, even into this century, and has been translated from the original Latin and Italian into numerous languages such as French, German, English and Chinese. He is best known for his perspective paintings on the ceiling of St. Ignatius Church in Rome.

38. Claude Rabuel (French) b 1669 in Ain d 1728 in Lyon

1 entry is found in Sommervogel;

Commentaires sur la gŽometrie de DŽscartes (Lyon, 1730)

He taught for 29 years in Lyons, specializing in conic sections, optics, catoptrics and optical illusions.

39. Giacomo Rho (Italian) b 1593 in Milan d 1638 in Peking

Reference to him in the Dictionary of Scientific Biography is found in v 14 p162.

28 entries are found in Sommervogel; some examples are the following:

Geometria speculativa et practica 10 vol (Wittik, 1622)

Explicatio regularum proportionum (Peking, 1630)

After being ordained by Cardinal Bellarmine he went to China in 1620. There he was commissioned to organize the imperial calendar. His Chinese name was Lo ya kou.

40. Vincent Riccati (Italian) b 1707 in Castel-Franco d 1775 in Italy

Reference to him in the Dictionary of Scientific Biography is found in v 11 p401-402.

28 entries are found in Sommervogel; some examples are the following:

Tomus primus opuscuorum (Bologna, 1757) Institutiones analyticae (Bologna, 1765)

He worked together with Girolamo Saladini in publishing his discovery, the hyperbolic functions - although Lambert is often incorrectly given this credit. Riccati not only introduced these new functions, but also derived the integral formulas connected with them, and then, still using geometrical methods. He then went on to derive the integral formulas for the trigonometric functions. The Institutiones is recognized as the first extensive treatise on integral calculus. The works of Euler and Lambert came later.

Saladini and Riccati also considered other geometrical problems, including the tractrix, the strophoid and the four-leaf rose introduced by Guido Grandi. His father Jacobi (after whom is named the Riccati differential equation) was one of the principal Italian mathematicians of the century, and his brother Giovanni was also a prominent mathematician.

41. Matteo Ricci (Italian) b 1552 in Macerata d 1610 in Peking

Reference to him in the Dictionary of Scientific Biography is found in v 3 p311,

v 4 p457, v 7 p19, v 10 p103, v 11 p402-403, v 14 p162-4.

36 entries are found in Sommervogel; some examples are the following:

Ki ho youen pen - Geometrica Practica (Peking, 1595 ;later reprinted in Nanking,1865) Hoen kai tong hien tou cho - Explanation of the celestial sphere (Peking, 1607)

Against his father's wishes, who forbade any talk of religious topics around the home, Matteo Ricci entered the Jesuit Society. When his father came to bring him home from the Jesuit novitiate, he was stricken ill and took this as a sign that Matteo truly had a vocation.

Ricci arrived in China in 1583, worked there for 27 years. He was welcomed to the academies and gained many influential friendships. When the time was ripe, he opened a residence in Nanking for himself, his fellow Jesuits and his scientific instruments. Eventually he became the court mathematician in Peking. His books Geometrica Practica and Trigonometrica were translations of Clavius' works into Chinese. He made Western developments in mathematics available to the Chinese and published in 1584 and 1600 the first maps of China ever available to the West. For the first time the Chinese had an idea of the distribution of oceans and land masses. He introduced trigonometric and astronomical instruments, and translated the first six books of Euclid into Chinese.

His success was due to his personal qualities, his complete adaption to Chinese customs (choosing the attire of a Chinese scholar) and to his authoritative knowledge of the sciences. He is remembered for his Chinese works on religious and moral topics, as well as works on scientific topics such as the astrolabe, sphere, arithmetic, measure and isoperimeters. It is still possible to visit his tomb in the Peking suburbs. The Encyclopedia Britannica reports, "Probably no European name of past centuries is so well known in China as that of Li-ma-teu (Ricci Matteo)."

42. John Baptist Riccioli (Italian) b 1598 in Ferrara d 1671 in Bologna

Reference to him in the Dictionary of Scientific Biography is found in v 1 p483, v 3 p100

v 4 p166, v 5 p527, 542-3, v 6 p364, v 7 p326, v 8 p26, v 10 p53, v 11 p 411.

Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in v 1 p 394-396, v 1 p 120-123, v 1 p 263-28, v 2 p 693-698,

v 5 p 2023, v 6 p 3061-3063, v 8 p 6033-6036, v 9 p 219-222, v 11 p 611,

v 13 p 244-258, v 14 p 721-726, v 16 p 314-323.

20 entries are found in Sommervogel; some examples are the following:

Almagestum Novum Astronomicum (Bologna, 1651) De Nova Cometa ( Bologna, 1664) Vindiciae Kalendarii Gregorii ( Bologna, 1666) Chronologiae Reformatae ( Bologna, 1669)

He was professor of philosophy and theology at Parma. One of the outstanding astronomers of the century, he wrote many books on scientific as well as theological matters. His lunar map stands at the entrance to the moon exhibit at the Smithsonian Institution. It is described in detail in the Philosophical Transactions because it is the first map to name craters after scientists and prominent people instead of abstract concepts. His treatise on refraction was also reported on in the Philosophical Transactions .

43. Claude Richard (Spanish)b 1588 in Ornans d 1664 in Madrid

6 entries are found in Sommervogel; an example is the following:

Euclidis Elementorum geometricorum libri (Antwerp, 1645)

He taught geometry and Hebrew in Rome for 7 years and then requested the China mission. While on his way to China, he stopped in Lisbon, where King Philip IV, after petitioning his superiors, made him professor of mathematics at the University of Madrid, where he taught for the next forty years.

44. Girolamo Saccheri (Italian) b 1667 in San Remo d 1733 in Milan

Reference to him in the Dictionary of Scientific Biography is found in v 1 p541,

v 4 p417, 451, v 6 p76, 202, v 7 p329, 330, v 8 p429, v 12 p 55-57, v 13 p510.

6 entries are found in Sommervogel; some examples are the following:

Euclides ab omni naevo vindicatus (Milan, 1733) Quaesita geometria (Milan, 1694) Logica demonstrativa (Milan, 1701)

One of his teachers was the Jesuit geometer Thomas Ceva, through whom Saccheri met Giovanni Ceva. The latter encouraged him to write his first book on coordinate geometry. He later wrote on logic and was quite concerned with the importance of definitions in mathematics. His last book, Euclides, prepared the way for non-Euclidean geometry. He presumed the first 28 theorems of Euclid's first book, since these did not depend on the fifth postulate, then denied the fifth postulate and attempted to find a contradiction. Eugenio Beltrami rescued this work from oblivion more than a century after it was written and showed that he deserved the title "founder of non-Euclidean geometry."

45. Gregory St. Vincent (Belgian) b 1584 in Bruges d 1667 in Gand

Reference to him in the Dictionary of Scientific Biography is found in v 5 p527, v 6 p 98,

v 7 p557, v 9 p97, v 9 p311, v 10 p336, v 12 p74-76, v 13 p235, v 13 p561,

v 13 p480, v 14 p148.

Articles by him or concerning his work are found in the Philosophical Transactions.

6 entries are found in Sommervogel; an example is the following:

Opus geometricum (Antwerp, 1647)             </