Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World (58 page)

alchemy

Alcibiades, Albert

Aldobrandini, Cardinal

Alexander VI, Pope

algebra

Algebra
(Clavius)

algebraic numbers

“all the lines”

“all the planes”

Alvarado

Ammannati, Bartolommeo

Anabaptists

analysis

Angeli, Stefano degli

Anglican Church,
see
Church of England

Antwerp Cathedral

Apiaria universae philosophiae mathematicae
(Bettini)

Apollonius

Apostolic Clerics of St. Jerome,
see
Jesuats

Archimedes

Archimedian spiral

architecture

Aristotelian physics

Aristotle; indivisibles opposed by

Aristotle’s wheel

arithmetic

Arithmetica infinitorum
(Wallis)

Arriaga, Rodrigo de

Arti, Duke of

Arundel, Earl of

Assayer, The
(Galileo)

Assembly of Divines

astrolabe

Astronomia nova
(Kepler)

astronomy

atoms

Aubrey, John

Augsburg

Austria

authority

axiom of Archimedes

Babbage, Charles

Bacon, Francis

Bacon, Roger

Baldi, Bernardino

Bamberg

Barberini, Antonio

Barberini, Francesco

Barberini, Maffeo (Pope Urban VIII)

barometers

Barrow, Isaac

Basilica of Santa Croce

Bavaria

Beaugrand, Jean

Belgium

Bellarmine, Robert; death of; heliocentrism edict of; papal supremacy defended by

Benedictines

Berkeley, George, infinitesimals mocked by

Bernini, Gian Lorenzo

Bernoulli, Daniel

Bettini, Mario

Biberus, Nithard

Bible; science vs.

Biblioteca Nazionale Centrale

Bibliotheca selecta
(Possevino)

Bidermann, Jacob

black holes

Black Robes

black swans

blood, circulation of

Bockelson, Jan

Bohemia

Boleyn, Anne

Bologna, University of

Bolognese Senate

Bolsheviks

Borgia, Cesare

Borgia, Francis, Duke of Gandia

Borgia, Gaspar

Borromeo, Federico

Boscovich, Roger

Bosse, Abraham

Botticelli, Sandro

Boulliau, Ismael

Boulonois, E. de

Bourbons

Boyle, Robert

Brahe, Tycho

Bramante, Donato

Brazil

Breitenfeld, Battle of

Briggs, Henry

Brouncker, Lord

Brunelleschi, Filippo

Bucer, Martin

Burke, Edmund

business models

calculus; creation of; infinitesimal

calendar reform

Calvin, John

Calvinism

Cambridge University

Campion, Edmund

Canisius, Peter

Canons Regular

Cappon, Ignace

Carafa, Vincenzo

Cardano, Gerolamo

Cartesian philosophy

Castelli, Benedetto

Castel Sant’Angelo

Catherine of Aragon

Catherine of Siena

Catholic Church, Catholicism; Bible requiring interpretation in; on good works; hierarchy of; Hobbes’s criticism of; infinitesimals and; Luther’s opposition to; Protestantism vs.; suppressed in England

Cavalieri, Bonaventura; Angeli as disciple of; background of; Bettini’s dispute with; on composition of continuum; conservatism of; death of; Guldin’s dispute with; indivisibles supported by; Jesuats joined by; Jesuits’ attack on; mathematics taught by; method of indivisibles created by; paradoxes as seen by; parallelogram proof of; Tacquet’s dispute with; Torricelli vs.

Cavaliers

Cavendish, Charles

Cavendish, Margaret

Cavendish, William

Cavendish family

centers of gravity

Centrobaryca
(Guldin)

Cesarini, Virginio

Cesi, Federico

Charlemagne

Charles I, King of England

Charles II, King of England; restoration of

Charles V, Emperor

chemistry

China

Christina of Lorraine

Church of England; creation of; indivisibles opposed by; reform of

Church of St. Ignatius

Ciampoli, Giovanni

circle, area of

civil engineering

Civil War, English; causes of; as context of
Leviathan
; threat of anarchy in

Clarendon, Earl of

Clavis mathematicae
(Oughtred)

Clavius, Christopher; calendar reformed by; death of; Galileo’s astronomical discoveries accepted by; geometry seen as central by; Hobbes vs.; Jesuit reverence for; lack of originality of; mathematical academy created by; mathematical curriculum of; mathematics seen as key to religious disputes by; mathematics seen as stable by; mathematics taught by; received into Society of Jesus; textbooks written by

Clement VII, Pope

Clement VIII, Pope

Clement IX, Pope

codes

cohesion

College of Cardinals

Collegio Romano; founding of; Galileo honored by; Galileo’s dispute with; indivisibles banned by; mathematics academy created at; Pallavicino’s defense of dissertation in

Cologne

Colombini, John

comets

Commandino, Federico

compass

conatus

Concis
(Apollonius)

Constitutions
(Ignatius of Loyola)

constructive proofs

continuum: Cavalieri on; Galileo and; indivisibles in; paradoxes of,
see
paradoxes; physical reality and

contradictions,
see
paradoxes

Copernicus, Nicolaus, heliocentric theory of

cossists

Council of Constance

Council of Nicea

Council of Trent

Counter-Reformation

Crick, Francis

Cromwell, Oliver

Cromwell, Richard

curing wounds at a distance

Cursus philosophicus
(Arriaga)

Cylindrica et annularia

Cylindricorum et annularium
(Tacquet)

d’Alembert, Jean

Darwin, Charles

d’Aviso, Urbano

Decameron physiologicum
(Hobbes)

De centro gravitatis
(Guldin)

De centro gravitatis
(Valerio)

De cive
(Hobbes)

deconstruction

De corpore
(Hobbes)

De Corpore Politico, or the Elements of the Law
(Hobbes)

deduction

deductive proofs

De homine
(Hobbes)

De infinitis parabolis
(Angeli)

de la Chaise, François

della Rovere family

del Monte, Guidobaldo

de Lugo, Giovanni

Democritus

de Nemore, Jordanus

Denmark

De revolutionibus
(Copernicus)

Descartes, René; infinitesimals disdained by

De sectionibus conicis
(Wallis)

de Thou, Jacques-Auguste

Dialogue on the Two Chief World Systems
(Galileo)

Dialogues Concerning Two New Sciences
(Galileo)

Diet of Worms

differential calculus

Digby, Kenelm

Diggers

Discourse on Floating Bodies
(Galileo)

Discourses and Mathematical Demonstrations Relating to Two New Sciences
(Galileo)

Disputationes metaphysicae
(Suárez)

divine grace

divine omnipotence

divine right of kings

DNA

Dominicans

Donatello

doubling of cube

Drake, Francis

ductus plani in planum

Duperron, Jacques Davy

Dutch Republic

Easter

Eck, Johann

Edward VI, King of England

Einstein, Albert

electricity

electric motors

electrodynamics

electronics

Elementorum philosophiae sectio tertia de cive
(Hobbes)

Elements, The
(Euclid); Clavius’s edition of

Elenchus geometriae Hobbianae
(Wallis)

Elizabeth I, Queen of England

engineering

England; Catholicism suppressed in; Dutch war with; manners in

Enlightenment

Enthusiasts

Estates-General

Eucharist

Euclid

Euclid
(Clavius)

Euclidean geometry; as construction of world; deduction in; method of presentation in; pure reasoning in; rigidity of

Eudoxus of Cnidus

Euler, Leonhard

evolution

Exercitationes geometricae sex
(Cavalieri)

experiments; in math; as standing for tolerance

Fairfax, Thomas

faith; and scientific research

Faithorne, William

Farnese family

Favre, Pierre

Ferdinand II, Duke of Tuscany

Ferdinand II, Emperor

Fermat, Pierre de

Fifth Monarchy Men

Finland

fluids

fluxions

Fontenelle, Bernard Le Bovier de

Fordinus

fortifications

Foscarini, Paolo

Fourier, Joseph

France; English alliance with; Huguenots expelled from; Jesuits banned from teaching in; manners in; Protestants in

Francisco de Toledo

Francis I, King of France

Francis Xavier

Franck, Sébastian

Franklin, Benjamin

Frederick I, King of Denmark

Frederick the Wise of Saxony

freedom to philosophize

French Academy of Sciences

French Revolution

French Royal Academy of Sciences

Galen

Galileo Galilei; astronomical discoveries of; Barberini’s friendship with; conservatism of; and continuum; death of; denunciation of; fame of; freedom to philosophize advocated by; heliocentrism defended by; Hobbes’s visit to; house arrest and humiliation of; indivisibles accepted by; Jesuits’ tension with; Urban’s discussions and relationship with; Urban’s removal of protection from; Wallis influenced by

Galvani, Luigi

Gandia, Duke of

Gandia, Spain

Gassendi, Pierre

General Congregation

generators

Geneva, Switzerland

geography

Geometria indivisibilibus
(Cavalieri)

geometrical curves

geometry; as embodiment of order; in Plato’s Academy

Germany

Germany, Nazi

Gilbert, William

Giotto

Glorious Revolution

gnomon; semi-

Goa

Gonzaga, Charles, Duke of Nevers

good works, Catholic belief in

Grassi, Orazio

gravitation

Gregorian Calendar

Gregory XIII, Pope

Gregory XV, Pope

Grienberger, Christoph

Guldin, Paul; Cavalieri disputed by

gunpowder

Gustavus I Vasa, King of Sweden

Habsburgs

Hall of the Consistory

Harriot, Thomas

Harvey, William

Hawking, Stephen

heat diffusion

heliocentrism

Henri IV, King of France

Henry VIII, King of England

hierarchy: of Church; Hobbes’s advocacy of; indivisibles and; of Jesuits; of knowledge; and opposition to indivisibles; papal supremacy in; in religion; of truth

Hieronymites

Hippasus

History
(de Thou)

History of the Royal Society
(Sprat)

Hitler, Adolf

Hobbes, Francis

Hobbes, Thomas; as Bacon’s secretary; Clavius vs.; education of; as ejected from ranks of mathematicians; flaws in geometry seen by; Galileo visited by; geometry as model of philosophy of; geometry reformed by; grand tours of; indivisibles interpreted by; indivisibles rejected by; introduction to mathematics of; and knowledge as based on logic; material notions in mathematics of; own philosophy praised by; quadrature of circle and; rigidity of; as Royalist in Civil War; Scholasticism disdained by; Sorbière’s praise for; Wallis’s dispute with

Hobbes, Thomas (father)

Holbeach, Martin

Holy Roman Empire

homogenes

Hooke, Robert

Horace

horror vacui

Huguenots

human nature

Human Nature
(Hobbes)

Huygens, Christiaan

hydrodynamics

Ignatius His Conclave
(Donne)

Ignatius of Loyola; Aquinas as authority of; background of; Clavius received into Society of Jesus by; Jesuits created by; mathematical education valued by; order defended by; sainthood of; and start of Jesuit colleges

Imperial Cortes

impetus

incommensurability

Independents

“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