1,721,286 research outputs found
Niccolò Tartaglia. Re-thinking the Role Played by Science of Weights in the Sixteenth-Century
No full textNotes on the Concept of Force in Kepler
No full textIn this paper we present some historical and epistemological notes
to trace a general picture of the concept of force in Kepler with the aim to
provide: a) conceptual bases of Keplerian notion of force; b) a stimulus to the
Kepler Forschung as to this concept
Fibonacci and the Abacus Schools in Italy. Mathematical Conceptual Streams-Education in its Changing Relationship with Society
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The Fiction of Infinitesimals in Newton’s Works. On the Metaphorical use of Infinitesimals in Newton
No full textNotes on mechanics and mathematics in Torricelli as physics-mathematics relationship in the history of science
Full text linkIn ancient Greece, the term “mechanics” was used when referring to machines and devices in general and
intended to mean the study of simple machines (winch, lever, pulley, wedge, screw and inclined plane) with
reference to motive powers and displacements of bodies. Historically, works considering these arguments
were referred to as Mechanics (from Aristotle, Heron, Pappus to Galileo). None of the treatises entitled
Mechanics avoided theoretical considerations on its object, particularly on the lever law. Moreover,
there were treatises which exhausted their role in proving this law; important among them are the book
on the balance by Euclid and On the Equilibrium of Planes by Archimedes. The Greek conception of
mechanics is revived in the Renaissance, with a synthesis of Archimedean and Aristotelian routes. This
is best represented by Mechanicorum liber by Guidobaldo dal Monte who reconsiders Mechanics by
Pappus Alexandrinus, maintaining that the original purpose was to reduce simple machines to the lever.
During the Renaissance, mechanics was a theoretical science and it was mathematical, although its
object had a physical nature and had social utility. Texts in the Latin and Arabic Middle Ages diverted
from the Greek and Renaissance texts mainly because they divide mechanics into two parts. In particular,
al-Farabi (ca. 870-950) differentiates between mechanics in the science of weights and that in the science
of devices. The science of weights refers to the movement and equilibrium of weights suspended from a
balance and aims to formulate principles. The science of devices refers to applications of mathematics
to practical use and to machine construction. In the Latin world, a process similar to that registered in
the Arabic world occurred. Even here a science of movement of weights was constituted, namely Scientia
de ponderibus. Besides this there was a branch of learning called mechanics, sometimes considered an
activity of craftsmen, other times of engineers (Scientia de ingeniis). In the Latin Middle Ages various
treatises on the Scientia de ponderibus circulated. Some were Latin translations from Greek or Arabic, a
few were written directly in Latin. Among them, the most important are the treatises attributed to Jordanus
De Nemore, Elementa Jordani super demonstratione ponderum (version E), Liber Jordani de ponderibus
(cum commento) (version P), Liber Jordani de Nemore de ratione ponderis (version R). They were the
object of comments up to the 16th century. The distribution of the original manuscript is not well known;
what is certain is that Liber Jordani de Nemore de ratione ponderis (version R), finished in Tartaglia’s
(1499-1557) hands, was published posthumously in 1565 by Curtio Troiano as Iordani Opvsculum de
Ponderositate. In order to show a mechanical tradition dating back to Archimedes’ science, at least till
the 40s of the 17th century, we present Archimede’s influence on Torricelli’s mechanics upon the centre of
gravity (Opera geometrica)
Galileo a Padova: un itinerario tra, architettura, fortificazioni, matematica e scienza “pratica”
No full textOpen problems in mathematical modelling and physical experiments: exploring exponential function
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On popularization of Scientific Education in Italy between 12th and 16th Century
Full text linkMathematics education is also a social phenomenon because it is influenced both by the needs of the labour market and by the basic knowledge of mathematics necessary for every person to be able to face some operations indispensable in the social and economic daily life. Therefore the way in which mathematics education is framed changes according to modifications of the social environment and know–how. For example, until the end of the 20th century, in the Italian faculties of engineering the teaching of mathematical analysis was profound: there were two complex examinations in which the theory was as important as the ability in solving exercises. Now the situation is different. In some universities there is only a proof of mathematical analysis; in others there are two proves, but they are sixth–month and not annual proves. The theoretical requirements have been drastically reduced and the exercises themselves are often far easier than those proposed in the recent past. With some modifications, the situation is similar for the teaching of other modern mathematical disciplines: many operations needing of calculations and mathematical reasoning are developed by the computers or other intelligent machines and hence an engineer needs less theoretical mathematics than in the past. The problem has historical roots. In this research an analysis of the phenomenon of “scientific education” (teaching geometry, arithmetic, mathematics only) with respect the methods used from the late Middle Ages by “maestri d’abaco” to the Renaissance humanists, and with respect to mathematics education nowadays is discussed. Particularly the ways through which mathematical knowledge was spread in Italy between late Middle ages and early Modern age is shown. At that time, the term “scientific education” corresponded to “teaching of mathematics, physics”; hence something different from what nowadays is called science education, NoS, etc. Moreover, the relationships between mathematics education and civilization in Italy between the 12th and the 16th century is also popularized within the Abacus schools and Niccolò Tartaglia. These are significant cases because the events connected to them are strictly interrelated. The knowledge of such significant relationships between society, mathematics education, advanced mathematics and scientific knowledge can be useful for the scholars who are nowadays engaged in mathematics education research
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