Title: Maria Gaetana Agnesi
1Maria Gaetana Agnesis Analytical Institutions
- Chelsea Sprankle
- Hood College
- Frederick, Maryland
2Biographical 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
3Biographical 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
4Analytical Institutions (Instituzioni Analitiche)
5Table of Contents
Page 1
6Dedication
- Empress Maria Theresa of Austria
- Proud to publish during time of woman ruler
- Maria Teresa gave her a gift
7Influences on Maria
- Descartes, Newton, Leibniz, Euler
- Belloni, Manara, Casati
- Ramiro Rampinelli
- Reyneaus Analyse démontrée
- Jacopo Riccati
- Maria Teresa of Austria-role model
8Analytical 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
9English 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
10Colsons 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
11The 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.
12Notational Controversy
- Newtons fluxions (English)
- 1st Derivative 2nd Derivative
- Leibnizs differentials
- 1st Derivative 2nd Derivative
- or
13Notational 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
145. 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 .
-
16Problem 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.
17Solution
- 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.
18Comparison 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
19After 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
20Recognition
- Streets, scholarships, and schools have been
named in her honor - Instituzioni is the first surviving mathematical
work of a woman
21Special Thanks!
Thanks to the Summer Research Institute of Hood
College!
22References
- 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.