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Maria Gaetana Agnesi

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Title: Maria Gaetana Agnesi


1
Maria Gaetana Agnesis Analytical Institutions
  • Chelsea Sprankle
  • Hood College
  • Frederick, Maryland

2
Biographical Information
  • Born in Milan on May 16, 1718
  • Parents Pietro Anna Agnesi
  • Fluent in many languages by the time she was an
    adolescent
  • Discussed abstract mathematical and philosophical
    topics with guests at her fathers home

3
Biographical Information
  • Published Propositiones Philosophicae (191 theses
    on philosophy and natural science) in 1738
  • Wanted to enter a convent at age 21
  • Took over household duties
  • Studied theology and mathematics

4
Analytical Institutions (Instituzioni Analitiche)
5
Table of Contents
Page 1
6
Dedication
  • Empress Maria Theresa of Austria
  • Proud to publish during time of woman ruler
  • Maria Teresa gave her a gift

7
Influences on Maria
  • Descartes, Newton, Leibniz, Euler
  • Belloni, Manara, Casati
  • Ramiro Rampinelli
  • Reyneaus Analyse démontrée
  • Jacopo Riccati
  • Maria Teresa of Austria-role model

8
Analytical Institutions (Instituzioni Analitiche)
  • Two-volume work (4 books)
  • Tomo I
  • Libro Primo Dell Analisi delle Quantità finite
  • Tomo II
  • Libro Secondo Dell Calcolo Differenziale
  • Libro Terzo Del Calcolo Integrale
  • Libro Quarto Del Metodo Inverso delle Tangenti

9
English Translation
  • John Colson (1680-1760)
  • Lucasian professor at Cambridge
  • Published Fluxions in English in 1736
  • Learned Italian late in life
  • Died in 1760 before it was published
  • Edited by Reverend John Hellins
  • Published in 1801

10
Colsons Rendition
  • Wrote The Plan of the Ladys System of Analyticks
  • Purpose was to render it more easy and useful
    for the ladies
  • Did not get past the first
  • book
  • Responsible for the witch

11
The Mistake of the Witch
  • Original Italian version a versiera versed
    sine curve
  • Derived from Latin vertere to turn
  • Colsons version avversiera witch

the equation of the curve to be described,
which is vulgarly called the Witch.
12
Notational Controversy
  • Newtons fluxions (English)
  • 1st Derivative 2nd Derivative
  • Leibnizs differentials
  • 1st Derivative 2nd Derivative
  • or

13
Notational Controversy
  • Myth Agnesi didnt mention fluxions
  • Myth Colson eliminated Agnesis references to
    differences
  • Agnesi used both words
  • Colson used both words
  • Truth Colson did change Agnesis differential
    notation to fluxional notation

14
5. In quella quisa che le differenze prime
non-ânno proporzione assegnabile alle quantità
finite, così le differenze seconde, o flussioni
del secondo ordine non ânno proporzione
assegnabile alle differenze prime, e sono di esse
infinitamente minori per mondo, che due quantità
infinitesima del primo ordine, masono assumersi
per equali. Lo stesso si dica delle differenze
terze rispetto alle seconde, e così di mano in
mano. Le differenze seconde si sogliono marcare
condoppia d, le terze con trè d ec. La
differenza adunque di dx, cioè la differenza
seconda di x si scriverà ddx, o pure d2x, e dx2,
perchè il primo significa, come ô deto, la
differenza seconda di x, ed il secondo significa
il quadrato di dx la differenza terza sarà dddx,
o pure d3x ec. Così ddy sarà la differenza di
dy, cioè la differenza seconda di y ec.
15
  • After the same manner that first differences or
    fluxions have no assignable proportion to finite
    quantities so differences or fluxions of the
    second order have no assignable proportion to
    first differences, and are infinitely less than
    they so that two infinitely little quantities of
    the first order, which differ from each other
    only by a quantity of the second order, may be
    assumed as equal to each other. The same is to
    be understood of third differences or fluxions in
    respect of the second and so on to higher
    orders.
  • Second fluxions are used to be represented by
    two points over the letter, third fluxions by
    three points, and so on. So that the fluxion of
    , or the second fluxion of x, is written thus,
    where it may be observed, that and 2
    are not the same, the first signifying (as said
    before,) the second fluxion of x, and the other
    signifying the square of .

16
Problem I
  • Let there be a certain sum of shillings,
    which is to be distributed among some poor
    people the number of which shillings is such,
    that if 3 were given to each, there would be 8
    wanting for that purpose and if 2 were given,
    there would be an overplus of 3 shillings. It is
    required to know, what was the number of poor
    people, and how many shillings there were in all.

17
Solution
  • Let us suppose the number of poor people to
    be x then because the number of shillings was
    such, that, giving to each 3, there would be 8
    wanting the number of shillings was therefore
  • 3x 8.
  • But, giving them 2 shillings a-piece,
    there would be an overplus of 3 therefore again
    the number of shillings was
  • 2x 3.
  • Now, making the two values equal, we shall
    have the equation
  • 3x 8 2x 3,
  • and therefore
  • x 11
  • was the number of poor. And because 3x 8,
    or 2x 3,
  • was the number of the shillings, if we
    substitute 11 instead of x, the number of
    shillings will be 25.

18
Comparison Agnesi Euler
  • Introductio in Analysin Infinitorum and
    Analytical Institutions published in 1748
  • Both thought it was important to know English
    notation and Leibniz notation
  • Began their texts with basic definitions and
    explanations of concepts
  • Used many examples

19
After 1748
  • Appointed as honorary reader at University of
    Bologna by Pope Benedict XIV
  • Later asked to accept the chair of mathematics
  • Devoted the rest of her life to charity
  • Cared for poor older women
  • Died January 9, 1799

20
Recognition
  • Streets, scholarships, and schools have been
    named in her honor
  • Instituzioni is the first surviving mathematical
    work of a woman

21
Special Thanks!
Thanks to the Summer Research Institute of Hood
College!
22
References
  • Agnesi, Maria. Analytical Institutions (English
    translation). John Colson. London Taylor and
    Wilks, 1801.
  • Agnesi, Maria. Instituzioni Analitiche ad uso
    Della Gioventu Italiana. Milan, 1748.
  • Dictionary of Scientific Biography. Agnesi,
    Maria Gaetana. 75-77
  • Findlen, Paula. "Translating the New Science
    Women and the Circulation of Knowledge in
    Enlightenment Italy." Configurations 3.2(1995)
    167-206. 27 June 2007 http//muse.jhu.edu/journal
    s/configurations/v003/3.2findlen.htmlgt.
  • Gray, Shirley. Agnesi. 1 Jan. 2001. California
    State University. 22 Jul 2007 lthttp//instruction
    al1.calstatela.edu/sgray/Agnesi/gt.
  • Mazzotti, Massimo. "Maria Gaetana Agnesi
    Mathematics and the Making of a Catholic
    Enlightenment." Isis 92(2001) 657-683.
  • Mount Holyoke College Library web page.
    lthttp//www.mtholyoke.edu/lits/library/arch/col/ra
    re/rarebooks/agnesi/gt.
  • Mulcrone, T. F. The Names of the Curve of
    Agnesi. The American Mathematical Monthly
    64(1957) 359-361.
  • Archimedes/Newton/Agnesi/Euler A Sampler of Four
    Great Mathematicians. Ohio State University,
    1990.
  • Truesdell, Clifford. "Maria Gaetana Agnesi."
    Archive for History of Exact Science 40(1989)
    113-142.
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