The first chapter of this thesis traces the history of probability from the origins to the beginning of the XX century; in particular, it focuses on the studies of those Mathematicians who dealt with the so-called social applications of the Theory of Probabilities (demography, criminal and civil trials) and with the theory of errors. The thesis points out the main achievements that the Theory reached at the end of the XIX century, and continues with the researches done by the professors of the University of Pavia. Following this approach, the present elaborate analyzes the work of Gregorio Fontana, who succeded to Ruggero Boscovich as professor of Mathematics at the University. Deeply influenced by the works of his contemporaries, his studies granted him a chair in the Royal Society. He wrote an accurate Appendix for his Italian translation of the Course of Lectures on the Principles of Natural Philosophy by George Atwood. Fontana pointed out how researchers should deal with the errors of measurements.Antonio Bordoni, another important professor of the University of Pavia, showed enthusiasm for the achievements of his colleagues and gave his contribute with the Saggio Sopra Gli Esami Scolastici. In his work he made an investigation on the examination procedure used at University also solving a problem of inverse probability: what is the probability that the grade given to a student reflects his real knowledge of a discipline? In the XIX century, thanks to Gauss’ studies, the theory of errors was improved with the least squares method. Using this method a researcher could use a faster way, opposite to the one proposed by Fontana, to determine the mean errors of n observations. The least squares method was used massively in the geodetic studies. The last chapter of the thesis illustrates how the teaching of Geodesy at University of Pavia followed Gauss’ method and theories.
Si è avanzati nell'analisi del lavoro di Gregorio Fontana che succedette a Ruggero Boscovich sulla cattedra di Matematica dell'Ateneo pavese. Membro della Royal Society , Fontana dimostrò una grande conoscenza del lavoro dei contemporanei ed uno spiccato acume. Compilò una ricca ed articolata Appendice per la sua traduzione del trattato Course of Lectures on the Principles of Natural Philosophy di George Atwood. La Dissertazione illustra le principali metodiche di cui uno sperimentatore può servirsi per trattare gli errori che inevitabilmente affliggono le misurazioni. Antonio Bordoni si cimentò in una complessa riflessione legata alle procedure con cui si conducevano gli esami universitari che fu compendiata nel Saggio Sopra gli Esami Scolastici. Bordoni affrontò anche alcuni problemi di probabilità inversa: in particolare riuscì a stabilire quale fosse stata la probabilità che il voto assegnato ad un esaminato potesse riflettere la sua reale preparazione. L’Ottocento visse l’affermazione del metodo dei minimi quadrati per lo studio degli errori di misura. Questa metodo, elaborato da Gauss, permetteva di stimare in modo agevole, rispetto a quanto proposto da Fontana, gli errori di misura. Il metodo divenne uno strumento indispensabile per coloro che si occupavano di osservazioni geodetiche. Il quarto, ed ultimo capitolo della tesi, evidenzia come siano cambiate le metodologie per la stima degli errori di misura geodetici dopo gli studi di Gauss; in particolare si è fatto vedere come, nei corsi universitari di Geodesia Teoretica dell’Università di Pavia il metodo fosse stato insegnato ed applicato con interesse.
ALCUNE APPLICAZIONI DEL CALCOLO DELLA PROBABILITA' ALL'UNIVERSITA' DI PAVIA FRA IL 1783 ED IL 1920
LAZZARINI, ANTONIO MARIA
2014/2015
Abstract
The first chapter of this thesis traces the history of probability from the origins to the beginning of the XX century; in particular, it focuses on the studies of those Mathematicians who dealt with the so-called social applications of the Theory of Probabilities (demography, criminal and civil trials) and with the theory of errors. The thesis points out the main achievements that the Theory reached at the end of the XIX century, and continues with the researches done by the professors of the University of Pavia. Following this approach, the present elaborate analyzes the work of Gregorio Fontana, who succeded to Ruggero Boscovich as professor of Mathematics at the University. Deeply influenced by the works of his contemporaries, his studies granted him a chair in the Royal Society. He wrote an accurate Appendix for his Italian translation of the Course of Lectures on the Principles of Natural Philosophy by George Atwood. Fontana pointed out how researchers should deal with the errors of measurements.Antonio Bordoni, another important professor of the University of Pavia, showed enthusiasm for the achievements of his colleagues and gave his contribute with the Saggio Sopra Gli Esami Scolastici. In his work he made an investigation on the examination procedure used at University also solving a problem of inverse probability: what is the probability that the grade given to a student reflects his real knowledge of a discipline? In the XIX century, thanks to Gauss’ studies, the theory of errors was improved with the least squares method. Using this method a researcher could use a faster way, opposite to the one proposed by Fontana, to determine the mean errors of n observations. The least squares method was used massively in the geodetic studies. The last chapter of the thesis illustrates how the teaching of Geodesy at University of Pavia followed Gauss’ method and theories.È consentito all'utente scaricare e condividere i documenti disponibili a testo pieno in UNITESI UNIPV nel rispetto della licenza Creative Commons del tipo CC BY NC ND.
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https://hdl.handle.net/20.500.14239/23860