“In disciplinas mathematicas prolegomena” (Clavius)
indivisibles: Aristotle’s opposition to; Cavalieri’s support for; in continuum; experimental math and; Fermat’s criticism of; fixed vs. nonfixed; Fontenelle’s acceptance of; Galileo’s acceptance of; general acceptance of; hierarchy and; Hippasus and; Hobbes’s rejection of; incommensurables and; Jesuit rejection of, see Society of Jesus, indivisibles opposed and banned by; in measuring centers of gravity; method of, see method of indivisibles; Newton’s acceptance of; political significance of; seeming end of; Sorbière’s rejection of; Torricelli’s acceptance of; trouble with; Wallis’s acceptance of
induction
indulgences
infinite parabola
infinitesimal calculus
infinity; absolute vs. relative
infinity sign
“In Guldinum” (Cavalieri)
innovation
Inquisition
Institutes of the Christian Religion (Calvin)
integral calculus
intensity of qualities
“Inter gravissimas”
Invisible College
irrational numbers
Istoria del Concilio di Trento (Pallavicino)
Italy; decline of mathematics in
James I, King of England
James II, King of England
Japan
Java
Jerusalem
Jesuats; fall of; formation of; training of
Jesuits, see Society of Jesus
Joachim of Fiore
Johann Georg of Saxony
Julian calendar
Julius II, Pope
Jupiter
Kazimierz, Jan II
Kelvin, Lord
Kepler, Johannes
Kircher, Athanasius
Kunsthistorisches Museum
Lagrangia, Giuseppe Luigi (Joseph-Louis Lagrange)
Laplace, Pierre-Simon
Laud, William
Lavoisier, Antoine-Laurent
law of falling bodies
Laynez, Diego
Leibniz, Gottfried Wilhelm; calculus of; method of indivisibles formalized by
Leonardo da Vinci
Leoni, Ottavio
Leo X, Pope
Letters on Sunspots (Galileo)
“Letter to the Grand Duchess Christina” (Galileo)
Levellers
Leviathan (Hobbes); Civil War as context of
liberal democracy
liberalizers
Lilius, Aloysius
Lincean Academy, see Accademia dei Lincei
Lindemann, Ferdinand von
lines; composition of; definition of; indivisible; plane composed of
Lipsius, Justus
Locke, John
Longomontanus
Long Parliament
Louis XIII, King of France
Louis XIV, King of France
lunar calendar
Luther, Martin; called to Rome; death of; at Diet of Worms; Ninety-Five Theses of; on omnipresence of Christ; Peasants’ Revolt and; princely support for
Lützen, Battle of
Machiavelli, Niccolò
Maestlin, Michael
Magini, Giovanni Antonio
Magiotti, Raffaello
magnetism
Marston Moor, Battle of
Mary I, Queen of England
Mary II, Queen of England
Mass, sacrament of
materialism
mathematical induction
mathematics: Bacon’s mistrust of; experimental; in Jesuit education; as key to religious disputes; physical world matched with; prestige of; Royal Society’s mistrust of; stability of; as tool of dogmatists; see also geometry
Mathesis universalis (Wallis)
matter
Maurizio of Savoy, Cardinal
Mazarin, Cardinal
Medici, Cosimo, II
Medici court
Mengoli, Pietro
Mennonites
Mersenne, Marin
Messina
metaphysics
method of exhaustion
method of fluxions
method of indivisibles
Mexico
Michelangelo
Miracle of St. Ignatius, The
modernity
“Modus quo disciplinas mathematicas in scholis Societatis possent promoveri” (Clavius)
Moluccas
Monck, George
Montaigne, Michel de
moon
motion
Münster
Münsterian anarchy
Müntzer, Thomas
music theory
Nadal, Jerónimo
Nardi, Antonio
Naseby, Battle of
navigation
Netherlands, English war with
New Atlantis (Bacon)
New Model Army
New Philosophy
Newton, Isaac; calculus of; indivisibles accepted by; method of fluxions of; method of indivisibles formalized by
Niccolini, Francesco
Nickel, Goswin
Ninety-Five Theses
Norway
Nova stereometria doliorum vinariorum (Kepler)
Novum organum (Bacon)
Nuñez, Pedro
Nuremberg
Oldenburg, Henry
Opera geometrica (Torricelli)
Opera mathematica (Tacquet)
Opera omnia (Torricelli)
Ordinatio pro studiis superioribus
“Ordo servandus in addiscendis disciplinis mathematicis”
Ottoman Empire
Oughtred, William
Owen, John
Oxford Philosophical Society
Oxford University
Pallavicino, Pietro Sforza
Papacy; fight for supremacy of; Jesuits favored by
Papal States
parabola, cubic
parabolas; infinite; quadrature of
paradoxes; as acceptable to Galileans; of bowl circumference; of continuum; of indivisibles; of Zeno
parallelogram
Parlement of Paris
Parliament, English; Long; Rump; universities reformed by
Paul III, Pope
Paul V, Pope
Peasants’ Revolt
Pell, John
Peloponnesian War (Thucydides)
Pepys, Samuel
Percy, Henry
Percy family
Pereira, Benito; on infinitely divisible continuum
perspective
Peru
Petrarch, Francesco
Philip of Hesse
Philosophical Transactions of the Royal Society of London
philosophy; see also freedom to philosophize
physical world, mathematics matched with
physics; Aristotelian
Physics (Aristotle)
pi
Piccolomini, Francesco
Pico della Mirandola, Giovanni
Pierrepont, Lord
plane, composition of
plane geometry
planes
planets; paths of
Plato
points, definition of
Polanco, Juan de
Poland
Possevino, Antonio
Presbyterians
Pride’s Purge
Principia mathematica (Newton)
Problemata geometrica sexaginta (Angeli)
projectiles
Protestants, Protestantism; Bible accessible in; calendar reform and; Catholicism vs.; conversion to; on faith and good works; in France; and “priesthood of all believers”
Ptolemy
Puritans
Pythagoras
Pythagoreans
Pythagorean theorem
Quadratura parabola (Valerio)
quadrature of circle
Quakers
radio
Rafael
Raleigh, Walter
Raleigh family
; Ranters
rational order
Ratio studiorum (Ignatius of Loyola)
Reformation; and Counter-Reformation
regula
“Regulations for Higher Studies”
relative infinity
relativity
Restoration
Ricci, Matteo
Ricci, Michelangelo
Riccioli, Giambattista
Richelieu, Cardinal
Roberval, Gilles Personne de
Rocca, Giannantonio
Rodriguez
Rome
Rosco
Roundheads
Royalists
Royal Society; experimentalism of; mathematics distrusted by
Rubens, Peter Paul
Rump Parliament
Rusconi, Camillo
Russian Orthodox Church
Rutherford, Ernest
sacraments
Sacrobosco
St. Georges Hill
St. Peter’s Basilica
St. Vincent, Gregory; circle allegedly squared by
Sangallo
Santarelli, Antonio
Santi, Leone
Sarpi, Paolo
Saxony
Scaliger, Joseph Justus
Scheiner, Christoph
scholasticism
school divinity
Schwenckfeld, Caspar von
science: authority in; faith and
scientific revolution
scientists
Scotland
Seekers
semi-gnomons
Senate: Bolognese; Venetian
Serious and Faithful Representation, A
Sforza
Shakespeare, William
Sidereus nuncius (Galileo), see Starry Messenger, The
Sigismund III, King of Poland
Sistine Chapel
Six Lessons to the Professors of Mathematics, One of Geometry, the Other of Astronomy (Hobbes)
Society of Jesus: absolute truth as belief of; banned from teaching in France; calendar reform and; Castelli’s application to; colleges of; creation of; early leaders of; eclipse of; educational system of; Galileo’s tension with; geometry as core of mathematical practice of; growing interest in indivisibles in; growth of; guiding principles of; hierarchy of; mathematics as core discipline in; as meritocracy; orderliness of; Pallavicino’s challenge to; papal supremacy defended by; Revisors General of; training in; travels of
Society of Jesus, indivisibles opposed and banned by; Angeli’s dispute with; Cavalieri attacked by; hidden facets of; legal track of; St. Vincent’s work and; victory in
Socinians
solar calendar
solids, composition of
Sorbière, Samuel; English Republican spirit disdained by; Hobbes praised by
Sorbonne
Sover, Bartholomew
Soviet Union
Spain
Spallanzani, Lazzaro
Spanish Armada
specchio ustorio, Lo (Cavalieri)
spheroids
spirals
Spiritual Exercises, The (Ignatius of Loyola)
Sprat, Thomas
squaring of circle, see quadrature of circle
Stalin, Joseph
Starry Messenger, The (Galileo)
steam engines
Stevin, Simon
Strafford, Earl of
straightedge
Strassburg
strings, vibration of
Stubbe, Henry
Suárez, Francisco
sunspots
surfaces: definition of; as indivisible
Sweden
Swift, Jonathan
Swiss Confederacy
Switzerland
syllogisms
Tacquet, André; Angeli’s dispute with; Cavalieri disputed by
tangents
Tartaglia, Niccolò Fontana
technology
telescope
Theodosius
theology
thermodynamics
Thirty-Nine Articles
Thirty Years’ War
Thomas Aquinas
Thomson, William, Lord Kelvin
Thucydides
tides
Tilly, Count
time, as indivisible
Titian
Torricelli, Evangelista; Cavalieri vs.; conservatism of; continuum as seen by; death of; indivisibles supported by; mathematics professorship offered to; paradoxes as seen by; Wallis influenced by
Torricellian experiment
totalitarianism
Tractatus de Sphaera (Sacrobosco)
transcendental numbers
Treatise on Angular Sections (Wallis)
Treatise on Heresy … (Santarelli)
Treatise on the Power of the Supreme Pontiff in Temporal Affairs (Bellarmine)
Trew Law of Free Monarchies, The (James I)
triangles
Trinity
trisection of angle
truth, hierarchy of
Truth Tried (Wallis)
Turner, Peter
Unitarians
universal gravitation
Urban VIII, Pope
Urbino, Duchy of
vacuum; nature’s abhorrence of
Valerio, Luca; resignation from Lincean Academy
Valois
van Schooten, Frans
Venetian Senate
Vere, Horatio
Vere, Lady Mary
Vesalius
Viète, François
Villamena, Francisco
Vindicationes Societatis Iesu (Pallavicino)
Vitelleschi, Mutio
Viviani, Vincenzo
Volta, Alessandro
Voltaire
volumes, calculation of
voting rights
Voyage to England, A (Sorbière)
Wallenstein, Albrecht von
Wallis, Joanna
Wallis, John; appointed Oxford professor; commoners mistrusted by; death of; deductive proofs of; dogmatism abhorred by; experimental mathematics of; Hobbes’s dispute with; indivisibles defended by; infinite series in proofs of; infinity sign invented by; introduction to mathematics of; material notions in mathematics of; mathematics as pragmatic for; as Parliamentarian; plurality in politics of; Royal Society joined by; Scholasticism mastered by; sensory basis of knowledge as belief of; textbooks written by
Wallis, John, Sr.
Ward, Seth
wars of Castro
Watson, James
Westphalia, Peace of
White, Richard
White Mountain, Battle of
Wiles, Andrew
William III, King of England
Winstanley, Gerrard
Wittenberg
women, right to vote of
Woods, Anthony
Worms, Diet of
Wright, John Michael
Zeno the Eleatic
Zwingli, Huldrych
ALSO BY AMIR ALEXANDER
Duel at Dawn: Heroes, Martyrs, and the Rise of Modern Mathematics
Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice
A NOTE ABOUT THE AUTHOR
Amir Alexander is the author of Geometrical Landscapes and Duel at Dawn: Heroes, Martyrs, and the Rise of Modern Mathematics. His work has been featured in Nature, The Guardian, and other publications. He teaches history at UCLA and lives in Los Angeles, California.
Scientific American / Farrar, Straus and Giroux
18 West 18th Street, New York 10011
Copyright © 2014 by Amir Alexander
All rights reserved
Printed in the United States of America
First edition, 2014
An excerpt from Infinitesimal originally appeared, in slightly different form, in Scientific American.
Library of Congress Cataloging-in-Publication Data
Alexander, Amir R., author.
Infinitesimal: how a dangerous mathematica
l theory shaped the modern world / Amir Alexander. — First edition.
pages cm
Includes bibliographical references and index.
ISBN 978-0-374-17681-5 (hardback)
1. Calculus—History. 2. Geometry, Infinitesimal—History. 3. Mathematics—Europe—History—16th century. 4. Mathematics—Europe—History—17th century. 5. Science, Renaissance. I. Title.
QA24. A544 2014
511—dc23
2013033923
Designed by Jo Anne Metsch
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