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{{Short description|Italian Jesuit mathematician (1648–1737)}}
{{Infobox scientist
| name              = Tommaso Ceva
| image             = Tommaso Ceva.jpg
| image_size        = 150px
| caption           = Tommaso Ceva
| birth_date        = {{birth-date|December 20, 1648}}
| birth_place       = [[Milan]], [[Duchy of Milan]]
| death_date        = {{death-date and age|February 3, 1737|December 20, 1648}}
| death_place       = Milan, Duchy of Milan
| occupation        = {{hlist|Jesuit priest|Poet|Scientist}}
| parents           = Carlo Francesco Ceva and Paola Ceva (née de' Colombi)
| residence         =
| citizenship       = 
| nationality       = [[Italy|Italian]]
| ethnicity         = 
| field             = [[mathematics]], [[geometry]], [[physics]]
| work_institutions = {{nowrap|Jesuit College of Brera, Milan}}
| alma_mater        = {{nowrap|Jesuit College of Brera, Milan}}
| doctoral_advisor  = 
| doctoral_students = 
| known_for         = Cycloid of Ceva
| author_abbrev_bot = 
| author_abbrev_zoo = 
| notable_students  = {{flatlist|
* [[Giovanni Girolamo Saccheri]]
* [[Carlo Archinto]]
}}
| prizes            = 
| religion          = 
| footnotes         = 
| signature         =  
}}

'''Tommaso Ceva''' (December 20, 1648 &ndash; February 3, 1737) was an Italian [[Jesuit]] [[mathematician]] from [[Milan]].  He was the brother of [[Giovanni Ceva]]. His work aided in spreading a knowledge of [[Isaac Newton|Newton]]'s discovery of the [[Newton's law of universal gravitation|law of gravitation]].

== Biography ==
Tommaso Ceva was born into a wealthy Milanese family in 1648. After studying at the Collegio di Brera, a Jesuit college in Milan, on 24 March 1663 he entered the [[Jesuits|Society of Jesus]]. He taught mathematics and [[rhetoric]] at the Jesuit College of Brera in Milan for thirty-eight years.<ref>{{cite book|title=The Jesuits and Italian Universities, 1548-1773|page=379|first=Paul F.|last=Grendler|year=2017|publisher=[[CUA Press]]|language=en|isbn=9780813229362}}</ref> His most famous student was [[Giovanni Girolamo Saccheri]]. Under the tutelage of Ceva, Saccheri wrote his first work, titled ''Quaesita geometrica'' (Geometric Investigations, 1693). Ceva was one of the main representatives of [[Clelia Grillo Borromeo]]'s Academia Vigilantium.{{sfn|Gronda|1980}} [[Joseph I, Holy Roman Emperor|Joseph I]] named him Caesarian Theologian early in the 18th century.{{sfn|Gronda|1980}}

His first scientific work, ''De natura gravium'' (The Nature of Gravity, 1699), dealt with physical subjects - such as [[gravity]] and [[free fall]] - in a philosophical way. His only mathematical work, published in 1699 was the ''Opuscula Mathematica'' (Mathematical Essays), which dealt with [[geometry]], gravity and [[arithmetic]]. Ceva designed an instrument to divide a [[right angle]] into a specified number of equal parts.<ref>''Instrumentum pro sectione cujuscunque anguli rectilinei in partes quotcunque aequales'' (Milan, 1695; repr. In ''Acta eruditorum'' [1695], p. 290).</ref> His device, described in the ''[[Acta Eruditorum]]'' in 1695, won him the attention of [[Gottfried Wilhelm Leibniz|Leibniz]].<ref>{{cite book|title=The Sun in the Church. Cathedrals as Solar Observatories|author-link=John L. Heilbron|first=John L.|last=Heilbron|year=2009|isbn=9780674038486|page=213|publisher=[[Harvard University Press]]}}</ref> This same instrument was described in 1704 by the [[France|French]] [[mathematician]] [[Guillaume de l'Hôpital]].{{sfn|Oettel|1981|page=183}}

In his ''Philosophia novo-antiqua'' (New-Ancient Philosophy, 1704) Ceva defended [[scholasticism]] against the systems [[René Descartes|Descartes]] and [[Pierre Gassendi|Gassendi]] and tried to reconcile the best of ancient and modern [[natural philosophy]].{{sfn|Lindon|2002}} The work comprises six dissertations, dealing with topics ranging from mathematics to [[cosmology]] and [[mechanics]], and engages with live issues for the science of the time ([[Copernican heliocentrism|Copernican theory]]; Descartes's physics and denial of animal souls; Gassendi's [[atomism]]). Ceva accepted Galileo's theory of motion but not his cosmology. As far as [[Cartesian physics]] is concerned, he especially criticized the identification of the [[essence]] of [[matter]] with [[Res extensa|extension]].<ref>{{cite book
 |chapter= "Italy Did Not Want to Be Cartesian" And For Good Reason
 |title= The Oxford Handbook of Descartes and Cartesianism
 |year= 2019
 |last= Belgioioso
 |first= Giulia 
 |publisher= [[Oxford University Press]]
 |location= New York
 |page= 527
 |isbn= 978-0192517210
}}</ref> Ceva's ''Philosophia novo-antiqua'' was reissued in Wien in 1719, in Florence in 1723 and in Venice in 1732.

Ceva was also a noted [[poet]] and dedicated a significant amount of his time to this task. In the literary field Ceva shared the Arcadian reaction against [[marinism]], and summed it up in his oft-quoted definition of poetry as ‘un sogno che si fa in presenza della ragione’ (“a dream made in the presence of reason”).{{sfn|Lindon|2002}} His Latin poem ''Jesus Puer'', dedicated to the Holy Roman emperor [[Joseph I, Holy Roman Emperor|Joseph I]], was translated into many languages including [[German language|German]] and [[Italian language|Italian]]. Two other collections of Latin verses, ''Sylvae'' (1699; “Woods”) and ''Carmina'' (1704; “Poems”), range over philosophic, scientific, religious, and literary subjects. Ceva was made a fellow of the [[Pontifical Academy of Arcadia|Arcadia]] in 1718 and was in correspondence with [[Vincenzo Viviani]] and [[Luigi Guido Grandi]].{{sfn|Gronda|1980}} He was a close friend of the mathematician [[Pietro Paolo Caravaggio]] and his son Pietro Paolo Caravaggio junior.{{sfn|Ulivi|1989|page=93}}

His ''Opuscula mathematica'' brought him international fame and his ''Carmina'' were favourably reviewed in ''[[Acta Eruditorum]]''.<ref>''Actorum eruditorum quae Lipsiae publicantur. Supplementa'' 3 (1702): 423–5.</ref> His work was highly praised by [[Gotthold Ephraim Lessing]] and [[Christian Friedrich Daniel Schubart]].{{sfn|Oettel|1981|page=184}}

In his latter years, Ceva suffered from [[paralysis]]. He died in Milan on 3 February 1737.{{sfn|Gronda|1980}}

== The Cycloid of Ceva ==
[[File:Cycloid of ceva.gif|thumb|Cycloid of Ceva]]
Prompted by the familiar "insertion" method of [[Archimedes]], Ceva devised in 1699 a curve for [[Angle trisection|trisection]] which was called the "Cycloidum anomalarum".<ref>{{MathWorld |title=Cycloid of Ceva |id=CycloidofCeva}}</ref> The principle involved is that of doubling angles. The cycloid of Ceva has the [[polar equation]]

:<math>r=1+2\cos(2\theta)</math>.

In [[Cartesian coordinate]]s the equation of this curve is
:<math>(x^2+y^2)^3=(3x^2-y^2)^2</math>.

To trisect the angle <math>\angle ABC </math>, construct a line parallel to the polar axis (the positive <math>x</math> axis). Let <math>D</math> be the point of intersection of the cycloid and the line. Then the angle <math>\angle ABD </math> is one-third of the angle <math>\angle ABC </math>.

Proof: let angle <math>\angle ABD </math> be <math> \theta</math> and let the point <math>F</math> on the <math>x</math> axis be such that <math>|BE| = |EF| = 1</math>. Let <math>G</math> be the [[orthogonal projection]] of <math>F</math> on the line <math>BD</math>. The angle <math>\angle DEF = 2\theta</math>, so <math>|BG| = 1 +\cos(2\theta)</math>. Since <math>|BD| = 1 + 2\cos(2\theta)</math>, <math>|EG| = |GD|</math>, <math>|DF| = |EF| = 1</math>. So angle <math>\angle DFH </math> equals <math>4\theta-\angle EFA=3\theta</math>, but <math>\angle DFH=\angle CBA </math>.

==See also==
*[[List of Jesuit scientists]]
*[[List of Roman Catholic scientist-clerics]]

==Notes==
{{Reflist}}

== Bibliography ==
{{sfn whitelist |CITEREFGronda1980}}
{{Refbegin|30em|indent=yes}}
* {{cite journal|last=Lindon|first=J.|year=2002|title=Ceva, Tommaso|journal=The Oxford Companion to Italian Literature|publisher=[[Oxford University Press]]|access-date=22 May 2023|url=https://www.oxfordreference.com/view/10.1093/acref/9780198183327.001.0001/acref-9780198183327-e-759}}
* {{cite book|author-link=Filippo Argelati|first=Filippo|last=Argelati|title=Bibliotheca scriptorum mediolanesium|pages=417–20|location=Milan|year=1745|volume=1|publisher=in Aedibus Palatinis}}
* {{cite book|first=Pietro|last=Riccardi|title=Biblioteca matematica italiana|volume=1|pages=343–4|location=Modena|year=1870|publisher=tipografia dell'erede Soliani}}
* {{DBI |title= CEVA, Tommaso |url=https://www.treccani.it/enciclopedia/tommaso-ceva_(Dizionario-Biografico)|last= Gronda|first= Giovanna|volume= 24}}
* {{cite book|author-link=Carlos Sommervogel|first=Carlos|last=Sommervogel|title=Bibliothèque de la Compagnie de Jésus|location=Brusels|publisher=Oscar Schepens|year=1891|volume=2|pages=1015–24}}
* Alberto Pascal, ''L'apparecchio polisettore di Tommaso Ceva e una lettera inedita di Guido Grandi'', «Rendiconti dell'Istituto Lombardo di Scienze e Lettere», s. II, 48 (1915), pp.&nbsp;173–181.
* Ramat, Raffaello, "La critica del padre Ceva," ''Civiltà moderna'', 10 (1938), 385-95, and 11 (1939), 139-66. (Reprinted in ''Sette contributi agli studi di storia della letteratura italiana'', (Florence, 1947), pp.&nbsp;5–44.
* Luigi Tenca, ''La corrispondenza epistolare fra Tommaso Ceva e Guido Grandi'', in ''Rendiconti dell'Istituto lombardo di scienze e lettere'', classe di scienze matematiche e naturali, LXXXIV (1951), pp.&nbsp;519–537.
* {{cite journal|first=Vitilio|last=Masiello|title=Critica e gusto di Tommaso Ceva|pages=288–313|journal=Convivium|year=1959|issue=4|volume=XXVII}}
* {{cite journal|first=Vitilio|last=Masiello|title=Le idee estetiche di Tommaso Ceva|pages=298–317|journal=Convivium|year=1960|volume=XXVIII|issue=3}}
* {{cite encyclopedia
 |title= Ceva, Tomasso
 |encyclopedia= [[Dictionary of Scientific Biography]]
 |volume= III
 |year= 1981
 |last= Oettel
 |first= Herbert
 |publisher= [[Charles Scribner's Sons]]
 |location= New York
 |pages= 183–184
 |url= https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/ceva-tomasso
 |access-date= 16 August 2023
}}
* {{cite journal
 |title= Guido Grandi, scienziato e polemista, e la sua controversia con Tommaso Ceva
 |volume= 19
 |issue= 3
 |year= 1989
 |last= Simonutti
 |first= Luisa 
 |journal = Annali della Scuola Normale Superiore di Pisa. Classe di Lettere e Filosofia
 |pages= 1001–1026
 |jstor= 24307638
}}
* {{cite journal|date=1989|first=Elisabetta|issn=0392-4432|last=Ulivi|number=1|periodical=Bollettino di Storia delle Scienze Matematiche|pages=91–137|title=Un tardo seguace di Viète, Pietro Paolo Caravaggio senior|volume=IX}}
* {{cite book|last=Canziani|first=Guido|chapter=Descartes e Gassendi nella Philosophia Novo-antiqua di Tommaso Ceva|title=Per una storia critica della scienza|editor1=Marco Beretta|editor2=Felice Mondella|editor3=Maria Teresa Monti|location=Bologna|publisher=Cisalpino|year=1997|pages=139–64}}
* {{cite journal
 |title= Sleeping with the Enemy: Tommaso Ceva's Use and Abuse of Lucretius in the Philosophia novo-antiqua (Milan, 1704)
 |journal= What Nature Does Not Teach: Didactic Literature in the Medieval and Early-Modern Periods
 |year= 2008
 |last= Haskell
 |first= Yasmin
 |series= Disputatio
 |volume= 15
 |publisher= [[Brepols]]
 |location= Turnhout
 |pages= 497–520
|doi= 10.1484/M.DISPUT-EB.3.3264
 |isbn= 978-2-503-52596-9
 }}
* {{cite journal|title=Milano bilingue: il gesuita Tommaso Ceva (1648-1737)|last=Colombo|first=Emanuele|journal=Studia Borromaica: Saggi e documenti di storia religiosa e civile della prima età moderna|volume=24|year=2010|issue=24 |pages=77–97|doi=10.1400/252020}}
{{refend}}

==External links==
* {{MacTutor Biography|id=Ceva_Tommaso}}
* {{Britannica|103943|author=Clara Silvia Roero}}
* {{treccani|tommaso-ceva|Tommaso Ceva|Bindo Chiurlo and Ettore Bortolotti|1931}}
* {{CathEncy|wstitle=Thomas Ceva}}

{{Jesuits}}
{{Authority control}}

{{DEFAULTSORT:Ceva, Tommaso}}
[[Category:1648 births]]
[[Category:1737 deaths]]
[[Category:Scientists from Milan]]
[[Category:17th-century Italian mathematicians]]
[[Category:18th-century Italian mathematicians]]
[[Category:18th-century Italian Jesuits]]
[[Category:17th-century Italian Jesuits]]
[[Category:Jesuit scientists]]
[[Category:Latin-language writers from Italy]]