Maria Gaetana Agnesi s Analytical Institutions

1. Maria Gaetana Agnesi�s Analytical Institutions Chelsea Sprankle Hood College Frederick, Maryland Chelsea�s talk at MathFest 2007.Chelsea�s talk at MathFest 2007.

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 father�s home Agnesi was born in Milan, Italy on May 16, 1718 to her parents, Pietro and Anna. Pietro came from a wealthy family who made their money from the trade of silk textiles. Since Pietro was wealthy, he could afford wonderful tutors in languages, philosophy, mathematics, natural science, and music for Agnesi. By the time she was an adolescent she could speak Greek, Hebrew, French, Spanish, Latin, and many other languages fluently. Agnesi was a child prodigy. Her father would hold gatherings of scholars in his home and Agnesi would partake in these gatherings by disputing with them on abstract mathematical and philosophical topics such as elasticity, Newton's gravitation theory, planetary motion, and the ebb and flow of tides. Many accounts of individuals who attended these meetings describe Agnesi as amazing since she could converse with people in their own languages about these complicated subjects. However, Agnesi did not like participating in these discussions since she was a shy person by nature. She had also always been very religious and had an extreme desire to live a simple life caring for the poor. Agnesi was born in Milan, Italy on May 16, 1718 to her parents, Pietro and Anna. Pietro came from a wealthy family who made their money from the trade of silk textiles. Since Pietro was wealthy, he could afford wonderful tutors in languages, philosophy, mathematics, natural science, and music for Agnesi. By the time she was an adolescent she could speak Greek, Hebrew, French, Spanish, Latin, and many other languages fluently. Agnesi was a child prodigy. Her father would hold gatherings of scholars in his home and Agnesi would partake in these gatherings by disputing with them on abstract mathematical and philosophical topics such as elasticity, Newton's gravitation theory, planetary motion, and the ebb and flow of tides. Many accounts of individuals who attended these meetings describe Agnesi as amazing since she could converse with people in their own languages about these complicated subjects. However, Agnesi did not like participating in these discussions since she was a shy person by nature. She had also always been very religious and had an extreme desire to live a simple life caring for the poor.

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 Agnesi wrote 191 theses in Latin on philosophy and natural science which her father had published in 1738 (when she was 20). These were the theses that she defended during the disputes in her father�s house. When she was 21, she asked permission from her father to enter a convent since she wanted to devote her life to religious services and helping those that were less fortunate. However, her father denied her request since she was dear to him and he didn�t want to lose her. She agreed to stay at his house under 3 conditions: she could go to church whenever she wanted, could dress more simply, and wasn�t forced to attend extravagant societal amusements like balls or the theater. After the death of Pietro�s 3rd wife, Maria had taken over the household duties. By this time she had 20 younger siblings so she was busy. Her real mother had died after the birth of her eighth child and Pietro had remarried. Also during this time, she started to study theology and mathematics heavily, claiming mathematics was the only province of the literary world where peace reigns.Agnesi wrote 191 theses in Latin on philosophy and natural science which her father had published in 1738 (when she was 20). These were the theses that she defended during the disputes in her father�s house. When she was 21, she asked permission from her father to enter a convent since she wanted to devote her life to religious services and helping those that were less fortunate. However, her father denied her request since she was dear to him and he didn�t want to lose her. She agreed to stay at his house under 3 conditions: she could go to church whenever she wanted, could dress more simply, and wasn�t forced to attend extravagant societal amusements like balls or the theater. After the death of Pietro�s 3rd wife, Maria had taken over the household duties. By this time she had 20 younger siblings so she was busy. Her real mother had died after the birth of her eighth child and Pietro had remarried. Also during this time, she started to study theology and mathematics heavily, claiming mathematics was the only province of the literary world where peace reigns.

4. Analytical Institutions (Instituzioni Analitiche) She began writing her famous text, Analytical Institutions, when she was 20 for the purpose of educating her younger brothers. The entire title can be seen on the cover of her book shown on the slide. Instituzioni means �elementary principles for the teaching of� or �foundations.� A modern-day translation of the entire title would be Foundations of Analysis for the use of Young Italians. On the cover of her book there is a reclining woman sketching geometrical figures on a board. Cupid is holding the board for her; this records her as already being a member of the Academy of Sciences at the University of Bologna. She published it in 1748, so it took her about ten years to write. She wrote it in Italian (purified Tuscan then) for her own enjoyment and to help her brothers (she did not originally intend for it to be published). She had it published in Italian rather than Latin since publishing a work in the language it was written followed examples of famous mathematicians and because she didn�t want the labor of translating it. She said later that she would have written it in Latin had she known it would be published so more of Europe could read it. She began writing her famous text, Analytical Institutions, when she was 20 for the purpose of educating her younger brothers. The entire title can be seen on the cover of her book shown on the slide. Instituzioni means �elementary principles for the teaching of� or �foundations.� A modern-day translation of the entire title would be Foundations of Analysis for the use of Young Italians. On the cover of her book there is a reclining woman sketching geometrical figures on a board. Cupid is holding the board for her; this records her as already being a member of the Academy of Sciences at the University of Bologna. She published it in 1748, so it took her about ten years to write. She wrote it in Italian (purified Tuscan then) for her own enjoyment and to help her brothers (she did not originally intend for it to be published). She had it published in Italian rather than Latin since publishing a work in the language it was written followed examples of famous mathematicians and because she didn�t want the labor of translating it. She said later that she would have written it in Latin had she known it would be published so more of Europe could read it.

5. The book has served as a model of mathematical typography. She designed it herself and even monitored the processes of production and printing in her father�s home. The local publishing house, Richini, installed its presses in her home so Agnesi could direct the process. The paper is handmade, has wide margins, and large font. There are 59 fold-out pages of engraved figures in the back done by Marc�Antonio Dal Re. I got a chance to look at these in the Rare Books room of the Library of Congress, and they are incredible. The book has served as a model of mathematical typography. She designed it herself and even monitored the processes of production and printing in her father�s home. The local publishing house, Richini, installed its presses in her home so Agnesi could direct the process. The paper is handmade, has wide margins, and large font. There are 59 fold-out pages of engraved figures in the back done by Marc�Antonio Dal Re. I got a chance to look at these in the Rare Books room of the Library of Congress, and they are incredible.

6. Dedication Empress Maria Theresa of Austria Proud to publish during time of woman ruler Maria Teresa gave her a gift Agnesi designated her book to the Holy Roman Empress and Duchess of Austria, Maria Teresa. She said she was proud to publish this book during a time when there was a great woman ruler. Agnesi was a promoter of the education of women, so she looked at Maria Teresa as a role model figure for other women. In response to her dedication, Maria Teresa gave Agnesi a rock-crystal box encrusted with diamonds, and a ring.Agnesi designated her book to the Holy Roman Empress and Duchess of Austria, Maria Teresa. She said she was proud to publish this book during a time when there was a great woman ruler. Agnesi was a promoter of the education of women, so she looked at Maria Teresa as a role model figure for other women. In response to her dedication, Maria Teresa gave Agnesi a rock-crystal box encrusted with diamonds, and a ring.

7. Influences on Maria Descartes, Newton, Leibniz, Euler Belloni, Manara, Casati Ramiro Rampinelli Reyneau�s Analyse d�montr�e Jacopo Riccati Maria Teresa of Austria-role model There were certain people who probably influenced Agnesi�s mathematics that she incorporated into Analytical Institutions and I thought it would be good to mention some. Of course she was influenced by mathematicians like Descartes, Newton, Leibniz, Euler, and others. Three of her teachers in mathematics included Carlo Belloni, who was a supporter of new experimental sciences, priest Francesco Manara (professor of logic and experimental physics at the University of Pavia), and Michele Casati (Turin). In her preface she credits her teacher, Father Don Ramiro Rampinelli, professor of mathematics at the University of Pavia, with assisting and guiding her in writing this text. He had actually encouraged her to write the book. During her study under Rampinelli, she read Charles Rene Reyneau�s text, Analyse demontre (1708). This book was an attempt to bring the mathematical discoveries of the 17th century together-it included differential and integral calculus. Agnesi praised it in her preface, although there have been many criticisms of the book by other mathematicians. She used this book as a model for her own text. While writing her book, Agnesi corresponded with Count Jacopo Riccati, a famous mathematician. This exchange of letters began on July 20, 1745 (7 years after she began writing it and 3 years before it was published). In her first letter she mentioned Rampinelli because Riccati knew him (all that was known of Agnesi was that she was a child prodigy). Some of these letters show that Agnesi was a beginner in the field of differential calculus. However, she always made sure she understood the answers and could confirm/verify everything herself before putting it into her book. These letters also show that she was looking for simple routines to follow when solving a problem, rather than concepts to master. There were certain people who probably influenced Agnesi�s mathematics that she incorporated into Analytical Institutions and I thought it would be good to mention some. Of course she was influenced by mathematicians like Descartes, Newton, Leibniz, Euler, and others. Three of her teachers in mathematics included Carlo Belloni, who was a supporter of new experimental sciences, priest Francesco Manara (professor of logic and experimental physics at the University of Pavia), and Michele Casati (Turin). In her preface she credits her teacher, Father Don Ramiro Rampinelli, professor of mathematics at the University of Pavia, with assisting and guiding her in writing this text. He had actually encouraged her to write the book. During her study under Rampinelli, she read Charles Rene Reyneau�s text, Analyse demontre (1708). This book was an attempt to bring the mathematical discoveries of the 17th century together-it included differential and integral calculus. Agnesi praised it in her preface, although there have been many criticisms of the book by other mathematicians. She used this book as a model for her own text. While writing her book, Agnesi corresponded with Count Jacopo Riccati, a famous mathematician. This exchange of letters began on July 20, 1745 (7 years after she began writing it and 3 years before it was published). In her first letter she mentioned Rampinelli because Riccati knew him (all that was known of Agnesi was that she was a child prodigy). Some of these letters show that Agnesi was a beginner in the field of differential calculus. However, she always made sure she understood the answers and could confirm/verify everything herself before putting it into her book. These letters also show that she was looking for simple routines to follow when solving a problem, rather than concepts to master.

8. Analytical Institutions (Instituzioni Analitiche) Two-volume work (4 books) Tomo I Libro Primo � Dell� Analisi delle Quantit� finite Tomo II Libro Secondo � Dell Calcolo Differenziale Libro Terzo � Del Calcolo Integrale Libro Quarto � Del Metodo Inverso delle Tangenti Analytical Institutions is a two volume work in 4 books of about 1,020 pages. It was considered the most clear and comprehensive mathematics text at the time it was published. The first volume contains Book 1 which is on finite mathematics and it begins with basic elementary algebra concepts. She establishes her notation and even goes so far as defining what negative integers and positive integers are. She uses many examples and helpful figures to assist the reader in understanding the topics. She also poses problems to the reader and provides solutions to these problems written in a step-by-step type fashion. The second volume contains the analysis of infinitesimal quantities. It contains Books 2-4. Book 2 covers differential calculus, Book 3 covers integral calculus, and Book 4 covers the Inverse Method of Tangents. It is amazing how she was able to bring all of these concepts from many mathematicians into one �natural order� and present them so clearly. Even though I can�t read Italian, I was able to figure out a lot of what she was saying and I could tell just from the brief time I had with the original book, that it was written carefully and clearly.Analytical Institutions is a two volume work in 4 books of about 1,020 pages. It was considered the most clear and comprehensive mathematics text at the time it was published. The first volume contains Book 1 which is on finite mathematics and it begins with basic elementary algebra concepts. She establishes her notation and even goes so far as defining what negative integers and positive integers are. She uses many examples and helpful figures to assist the reader in understanding the topics. She also poses problems to the reader and provides solutions to these problems written in a step-by-step type fashion. The second volume contains the analysis of infinitesimal quantities. It contains Books 2-4. Book 2 covers differential calculus, Book 3 covers integral calculus, and Book 4 covers the Inverse Method of Tangents. It is amazing how she was able to bring all of these concepts from many mathematicians into one �natural order� and present them so clearly. Even though I can�t read Italian, I was able to figure out a lot of what she was saying and I could tell just from the brief time I had with the original book, that it was written carefully and clearly.

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 John Colson was the 5th Lucasian professor at Cambridge and was known for translating Newton�s Latin Method of Fluxions into English. He was so impressed with Agnesi�s work that he began learning Italian late in life for the sole purpose of translating it into English. His English edition is laid out in the same way as Agnesi�s. The huge difference I noticed was that his geometrical figures are found within the pages rather than as fold-out pages in the back of the book. He added in several notes on the side to clarify what Agnesi was saying in certain places. Colson died in 1760 before he could publish it. Reverend John Hellins took up the book and became its editor. He said that he did nothing to change what Colson had done except to correct any mathematical errors he found. The English edition was published in 1801. John Colson was the 5th Lucasian professor at Cambridge and was known for translating Newton�s Latin Method of Fluxions into English. He was so impressed with Agnesi�s work that he began learning Italian late in life for the sole purpose of translating it into English. His English edition is laid out in the same way as Agnesi�s. The huge difference I noticed was that his geometrical figures are found within the pages rather than as fold-out pages in the back of the book. He added in several notes on the side to clarify what Agnesi was saying in certain places. Colson died in 1760 before he could publish it. Reverend John Hellins took up the book and became its editor. He said that he did nothing to change what Colson had done except to correct any mathematical errors he found. The English edition was published in 1801.

10. Colson�s Rendition Wrote The Plan of the Lady�s 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� Colson began to write The Plan of the Lady�s System of Analyticks in an attempt to make the book easier for the women of Britain to read. I read some of it and it is basically a description of each section in Agnesi�s text. Colson claimed that he wanted to show that the ladies of his country could not be outdone by a foreign woman. However, he didn�t even get past a rough draft of the first book before he died. Typically, the one thing people remember or say they �know� about Maria Agnesi is the curve she studied (y = a^3 / (x^2 + a^2) that is now known as �the witch of Agnesi�. Even though Fermat studied this curve originally, thanks to Colson�s translation error, Agnesi is now associated with it. Colson began to write The Plan of the Lady�s System of Analyticks in an attempt to make the book easier for the women of Britain to read. I read some of it and it is basically a description of each section in Agnesi�s text. Colson claimed that he wanted to show that the ladies of his country could not be outdone by a foreign woman. However, he didn�t even get past a rough draft of the first book before he died. Typically, the one thing people remember or say they �know� about Maria Agnesi is the curve she studied (y = a^3 / (x^2 + a^2) that is now known as �the witch of Agnesi�. Even though Fermat studied this curve originally, thanks to Colson�s translation error, Agnesi is now associated with it.

11. The Mistake of the Witch Original Italian version: a versiera � versed sine curve Derived from Latin vertere � to turn Colson�s version: avversiera � witch Colson mistranslated the Italian word aversiera which means versed sine curve and is derived from the Latin vertere which means to turn. He mistakenly took the word to be avversiera which means witch or wife of the devil. ��will be the equation of the curve to be described, which is vulgarly called the Witch.�Colson mistranslated the Italian word aversiera which means versed sine curve and is derived from the Latin vertere which means to turn. He mistakenly took the word to be avversiera which means witch or wife of the devil. ��will be the equation of the curve to be described, which is vulgarly called the Witch.�

12. As we know, Newton and Leibniz independently discovered calculus at about the same time and used different notation. Newton used �The method of fluxions� and thereby used fluxional notation when finding derivatives. In fluxional notation, the first derivative of x would be written as x with a dot over it. The second derivative of x would be written as x with two dots over it and so forth. The English used Newton's fluxional notation. Leibniz used differential calculus and thereby used differential notation, which is what we are used to seeing today in mathematics--with powers of d representing number of the derivative you are taking. The rest of Europe was associated with this notation. The dot notation can still be found in textbooks of other disciplines, especially physics texts when taking derivatives with respect to time. During the time of Agnesi and Euler there was a dispute about which one was better, but people were starting to realize that both were beneficial to know. Euler in particular stated that one should know both notations in order to benefit the most from reading different texts. As we know, Newton and Leibniz independently discovered calculus at about the same time and used different notation. Newton used �The method of fluxions� and thereby used fluxional notation when finding derivatives. In fluxional notation, the first derivative of x would be written as x with a dot over it. The second derivative of x would be written as x with two dots over it and so forth. The English used Newton's fluxional notation. Leibniz used differential calculus and thereby used differential notation, which is what we are used to seeing today in mathematics--with powers of d representing number of the derivative you are taking. The rest of Europe was associated with this notation. The dot notation can still be found in textbooks of other disciplines, especially physics texts when taking derivatives with respect to time. During the time of Agnesi and Euler there was a dispute about which one was better, but people were starting to realize that both were beneficial to know. Euler in particular stated that one should know both notations in order to benefit the most from reading different texts.

13. Notational Controversy Myth: Agnesi didn�t mention fluxions Myth: Colson eliminated Agnesi�s references to differences *Agnesi used both words *Colson used both words Truth: Colson did change Agnesi�s differential notation to fluxional notation There is a myth that all Agnesi mentioned in her text were differences and that she did not ever mention fluxions. There is also a myth that John Colson changed everywhere Agnesi used the word difference to the word fluxion. After looking at the Italian copy of the text, I saw that Agnesi did in fact use the word �fluxion�. She often would say difference or fluxion (deferens o flussioni). I also saw in Colson�s English copy that he used both words. He did insert the word fluxion more often than Agnesi, and did take out the word difference in some places and replaced it with fluxion, but he usually used both words. One thing that is true is that Colson changed Agnesi�s differential notation into fluxional notation.There is a myth that all Agnesi mentioned in her text were differences and that she did not ever mention fluxions. There is also a myth that John Colson changed everywhere Agnesi used the word difference to the word fluxion. After looking at the Italian copy of the text, I saw that Agnesi did in fact use the word �fluxion�. She often would say difference or fluxion (deferens o flussioni). I also saw in Colson�s English copy that he used both words. He did insert the word fluxion more often than Agnesi, and did take out the word difference in some places and replaced it with fluxion, but he usually used both words. One thing that is true is that Colson changed Agnesi�s differential notation into fluxional notation.

14. Here is an example I took from the beginning of Book I of Agnesi's Italian copy of Analytical Intitutions when she is defining basic terms and establishing her notation. I thought number five was a good example since it shows that Agnesi did use both words and it shows her differential notation. In #5 she is explaining how higher orders of differences/fluxions are represented. Colson did replace this notation with Newtonian fluxions and he inserted the word fluxion more places than Agnesi. Try to keep this slide in your mind for the next one which shows Colson's translation.Here is an example I took from the beginning of Book I of Agnesi's Italian copy of Analytical Intitutions when she is defining basic terms and establishing her notation. I thought number five was a good example since it shows that Agnesi did use both words and it shows her differential notation. In #5 she is explaining how higher orders of differences/fluxions are represented. Colson did replace this notation with Newtonian fluxions and he inserted the word fluxion more places than Agnesi. Try to keep this slide in your mind for the next one which shows Colson's translation.

15. The same example, as translated by Colson.The same example, as translated by Colson.

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. I thought that the very first problem Agnesi poses in Book I was extremely interesting in that it shows her character and how her problems are very similar to problems we would see in a textbook today. They would probably be worded slightly differently but we see the same types of problems in pre-algebra texts. It is a basic word problem about giving certain amounts of money to a certain number of poor people. I thought that the very first problem Agnesi poses in Book I was extremely interesting in that it shows her character and how her problems are very similar to problems we would see in a textbook today. They would probably be worded slightly differently but we see the same types of problems in pre-algebra texts. It is a basic word problem about giving certain amounts of money to a certain number of poor people.

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. Her solution starts with defining the variable as we would teach students to do first today. She then sets up expressions to represent the problem and sets them equal to solve for her variable. I just wanted to give an idea of how basic she starts out in her text. Her solution starts with defining the variable as we would teach students to do first today. She then sets up expressions to represent the problem and sets them equal to solve for her variable. I just wanted to give an idea of how basic she starts out in her text.

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 Since it is the year of Euler, I thought it would be interesting to compare Agnesi to him. Agnesi�s Analytical Institutions was published in the same year as Euler�s Introduction to Analysis of the Infinite (1748). Agnesi's book can almost be seen as an introduction to his. They both began their texts with basic definitions and explanations of concepts. They also were well known for teaching through examples. As mentioned before, they both thought it was important to be aware of both the Newtonian or English notation and the notation of Leibniz. Agnesi was aware of Euler and read some of his work. In fact, she even mentioned him in Book 4, section 3 of her Analytical Institutions. This section is of the construction of more limited equations, by the help of various substitutions. She says to refer to two of the very learned Mr. Euler's dissertations inserted in the Memoirs of the Academy of St. Petersurg, Vol. 6. I have not found any evidence of Euler being aware of her but I would assume he had heard of her famous book.Since it is the year of Euler, I thought it would be interesting to compare Agnesi to him. Agnesi�s Analytical Institutions was published in the same year as Euler�s Introduction to Analysis of the Infinite (1748). Agnesi's book can almost be seen as an introduction to his. They both began their texts with basic definitions and explanations of concepts. They also were well known for teaching through examples. As mentioned before, they both thought it was important to be aware of both the Newtonian or English notation and the notation of Leibniz. Agnesi was aware of Euler and read some of his work. In fact, she even mentioned him in Book 4, section 3 of her Analytical Institutions. This section is of the construction of more limited equations, by the help of various substitutions. She says to refer to two of the very learned Mr. Euler's dissertations inserted in the Memoirs of the Academy of St. Petersurg, Vol. 6. I have not found any evidence of Euler being aware of her but I would assume he had heard of her famous book.

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 The publication of her text in 1748 led to her wide fame throughout Europe. Pope Benedict the 14th was impressed by her work and appointed her as an honorary reader at the University of Bologna. Shortly after, she was asked by the Pope and professors and the University of Bologna to accept the chair of mathematics. She probably neither accepted nor declined since after her father�s death in 1752 she finally felt that she could devote her time to helping the less fortunate. She spent the rest of her life on charitable work and providing shelter for the homeless. She became the director of the Pio Instituto Trivulzo, a home for ill and infirm women. She ended up dying in poverty in Milan on January 9, 1799 and was buried in a mass grave of 15 women. The publication of her text in 1748 led to her wide fame throughout Europe. Pope Benedict the 14th was impressed by her work and appointed her as an honorary reader at the University of Bologna. Shortly after, she was asked by the Pope and professors and the University of Bologna to accept the chair of mathematics. She probably neither accepted nor declined since after her father�s death in 1752 she finally felt that she could devote her time to helping the less fortunate. She spent the rest of her life on charitable work and providing shelter for the homeless. She became the director of the Pio Instituto Trivulzo, a home for ill and infirm women. She ended up dying in poverty in Milan on January 9, 1799 and was buried in a mass grave of 15 women.

20. Recognition Streets, scholarships, and schools have been named in her honor Instituzioni is the first surviving mathematical work of a woman Agnesi did receive wide recognition during her life even though she was a woman. After her death, streets have been named after her, scholarships have been named in her honor, and even schools share her name. Her Analytical Institutions is the first surviving mathematical work done by a woman.Agnesi did receive wide recognition during her life even though she was a woman. After her death, streets have been named after her, scholarships have been named in her honor, and even schools share her name. Her Analytical Institutions is the first surviving mathematical work done by a woman.

21. At the Library of CongressAt the Library of Congress

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/journals/configurations/v003/3.2findlen.html>. Gray, Shirley. Agnesi. 1 Jan. 2001. California State University. 22 Jul 2007 <http://instructional1.calstatela.edu/sgray/Agnesi/>. Mazzotti, Massimo. "Maria Gaetana Agnesi: Mathematics and the Making of a Catholic Enlightenment." Isis 92(2001): 657-683. Mount Holyoke College Library web page. <http://www.mtholyoke.edu/lits/library/arch/col/rare/rarebooks/agnesi/>. 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.