26
the total publications in the field between 1570 and 1770 in Europe, and more elsewhere (as in missionary lands like China).
As for unpublished papers, the numbers are even more stark. In the Roman
College alone, mathematics was taught for 220 years (1553–1773); teachers dictated their lessons, which each student was expected to transcribe completely. Given
an average annual number of 50 students (typical for the seventeenth and eighteenth
centuries), one can hypothesize that 11,000 student manuscripts were produced in
Rome alone. In fact, in Rome’s archives and libraries one can find hundreds of
mathematical works from Jesuits, ranging from simple lessons to mathematical
treatises. By the time of the suppression, there were about 200 Jesuit schools around
the world, and perhaps a fifth of them offered math as a philosophy course. So, at
30–40 colleges—from Europe to Latin America, India, Macau, and in Manila, dating from the sixteenth century—a number of students at times comparable to that in
Rome would be producing manuscripts on mathematics at various levels of
advancement.
The places where knowledge is transmitted should be judged primarily by the
substance, rather than the quantity, of what they transmit. This, however, does not
erase the general historical fact that much of the mathematical literacy of Catholic
Europe between the late 1500s and the mid-1700s came from the schools of the
Society. Descartes is perhaps the most familiar example of a Jesuit product in mathematics. Given the reality of the times, their average standard in the transmission of
consolidated knowledge was significant even in comparison to that of the universities. The manuals produced by their teachers could be found even in non-Jesuit and
non-Catholic schools. They included Clavius’s textbooks (from 1570); those of
A. Tacquet in the mid-1600s (reprinted into the early 1800s) and J. De Billy’s immediately after; R. J. Boscovich’s Elementa universae matheseos (1752–1754), judged
to be the best Italian mathematics textbook of the eighteenth century, and one of the
best in Europe; and the Institutiones analyticae (1765–1767) by V. Riccati and
G. Saladini, a reference text for differential and integral calculus throughout the
second half of the 1700s in Italy, comparable to the best European examples. In the
whole, therefore, one may conclude that Jesuits produced some of the most widespread mathematical education tools in the ancien régime Europe.
Meanwhile, a handful of Jesuit missionaries mapped large parts of multiple continents, determining the positions of dozens of localities in India, Indochina,
Philippines, China (almost the entire Chinese Empire and outer Mongolia), Japan,
and also in the Americas. Their observations of eclipses allowed tests of the accuracy of astronomical tables and ephemerides. Their magnetic declination measurements, carried out over much of the planet (many were collected as early as the
mid-1600s in works by A. Kircher and G.B. Riccioli) allowed the first attempts at
isogonic charts for the measurement of longitude, foreshadowing the work of
Edmund Halley (1700–1702). Add to this the Society’s contribution to the creation
of astronomical observatories, botanical gardens, and laboratories. Even given the
relative vagueness of the term “observatory,” in the eighteenth century the Jesuits
directed about 30 of the 120–130 in existence in Europe; in addition, they created or
U. Baldini
the total publications in the field between 1570 and 1770 in Europe, and more elsewhere (as in missionary lands like China).
As for unpublished papers, the numbers are even more stark. In the Roman
College alone, mathematics was taught for 220 years (1553–1773); teachers dictated their lessons, which each student was expected to transcribe completely. Given
an average annual number of 50 students (typical for the seventeenth and eighteenth
centuries), one can hypothesize that 11,000 student manuscripts were produced in
Rome alone. In fact, in Rome’s archives and libraries one can find hundreds of
mathematical works from Jesuits, ranging from simple lessons to mathematical
treatises. By the time of the suppression, there were about 200 Jesuit schools around
the world, and perhaps a fifth of them offered math as a philosophy course. So, at
30–40 colleges—from Europe to Latin America, India, Macau, and in Manila, dating from the sixteenth century—a number of students at times comparable to that in
Rome would be producing manuscripts on mathematics at various levels of
advancement.
The places where knowledge is transmitted should be judged primarily by the
substance, rather than the quantity, of what they transmit. This, however, does not
erase the general historical fact that much of the mathematical literacy of Catholic
Europe between the late 1500s and the mid-1700s came from the schools of the
Society. Descartes is perhaps the most familiar example of a Jesuit product in mathematics. Given the reality of the times, their average standard in the transmission of
consolidated knowledge was significant even in comparison to that of the universities. The manuals produced by their teachers could be found even in non-Jesuit and
non-Catholic schools. They included Clavius’s textbooks (from 1570); those of
A. Tacquet in the mid-1600s (reprinted into the early 1800s) and J. De Billy’s immediately after; R. J. Boscovich’s Elementa universae matheseos (1752–1754), judged
to be the best Italian mathematics textbook of the eighteenth century, and one of the
best in Europe; and the Institutiones analyticae (1765–1767) by V. Riccati and
G. Saladini, a reference text for differential and integral calculus throughout the
second half of the 1700s in Italy, comparable to the best European examples. In the
whole, therefore, one may conclude that Jesuits produced some of the most widespread mathematical education tools in the ancien régime Europe.
Meanwhile, a handful of Jesuit missionaries mapped large parts of multiple continents, determining the positions of dozens of localities in India, Indochina,
Philippines, China (almost the entire Chinese Empire and outer Mongolia), Japan,
and also in the Americas. Their observations of eclipses allowed tests of the accuracy of astronomical tables and ephemerides. Their magnetic declination measurements, carried out over much of the planet (many were collected as early as the
mid-1600s in works by A. Kircher and G.B. Riccioli) allowed the first attempts at
isogonic charts for the measurement of longitude, foreshadowing the work of
Edmund Halley (1700–1702). Add to this the Society’s contribution to the creation
of astronomical observatories, botanical gardens, and laboratories. Even given the
relative vagueness of the term “observatory,” in the eighteenth century the Jesuits
directed about 30 of the 120–130 in existence in Europe; in addition, they created or
U. Baldini