Tesi sul tema "Newton, Isaac (1642-1727) – Religion"

Isaac Newton remarqua dans la conclusion de ses fameux Principes mathématiques de la philosophie naturelle (1687) : « Les idolâtres s’imaginaient que le soleil, la lune, les astres, les âmes des hommes et toutes les autres parties du monde étaient des parties du Dieu suprême et que, par conséquent, on devait leur rendre un culte, mais c’était une erreur. » Le mathématicien observait de façon similaire en concluant son Traité d’optique : « A la vérité, si les païens n’eussent pas été aveuglés par le culte des faux dieux, ils auraient poussé leur philosophie morale bien au-delà de ce qu’ils nommaient les quatre vertus cardinales ; et au lieu d’enseigner la transmigration des âmes, le culte du soleil et de la lune, et des héros décédés, ils auraient enseigné la raison suprême pour laquelle notre souverain Bienfaiteur et véritable Auteur doit être adoré. » Une question se pose au lecteur contemporain : comment rendre compte de l’insertion de ces considérations théologiques en conclusion de deux traités de nature essentiellement mathématique ?Des éléments de réponse se trouvent dans un manuscrit inachevé de Newton intitulé « Les origines philosophiques de la théologie païenne » (Theologiæ gentilis origines philosophicæ), un traité d’histoire des religions comportant plus de 130.000 mots répartis sur quelque 200 folios. Newton y soutient notamment que la cosmologie des Anciens était de nature théologique du fait qu’elle procédait en partie de la projection sur les éléments du cosmos des âmes des ancêtres de l’humanité déifiés. C’est ainsi que Newton voit dans la catastérisation des premiers hommes l’origine de l’animisme astral, de l’astrolâtrie et de l’astrologie. A ses yeux, la chute originelle de l’homme dans l’idolâtrie aurait corrompu aussi bien la vraie religion que la connaissance de la philosophie naturelle, l’animisme propre aux cosmologies des anciens peuples orientaux formant le pendant philosophique de l’astrolâtrie païenne. Il importait dès lors de désacraliser les éléments du cosmos afin de rétablir aussi bien le culte pur que la science véritable.Après avoir identifié les sources et décrit les principes exégétiques qui sous-tendent le traité des Origines, nous examinerons l’historiographie newtonienne des origines et de la diffusion de la physico-théologie païenne, depuis la naissance du culte des astres en Egypte ancienne jusqu’aux doctrines émanationnistes enseignées par les scolastiques. Nous montrerons ensuite en quoi le système du monde proposé par Newton se présentait comme une alternative désacralisée aux conceptions cosmologiques animistes des Anciens. Nous nous interrogerons finalement sur la provenance de l’animus iconoclaste qui caractérise les écrits théologiques et philosophiques de Newton. Il s’agira de discerner les sources d’influence qui marquèrent sa formation intellectuelle et religieuse au travers de l’examen des polémiques qui divisèrent le milieu réformé au sein duquel il grandit. Il en ressortira que l’auteur des Principes entendait bien désenchanter le cosmos afin de satisfaire les exigences d’un monothéisme austère et intransigeant
Isaac Newton stated in his conclusion to the Mathematical Principles of Natural Philosophy (1687) : “Idolaters imagined that the sun, moon, and stars, the souls of men, and other parts of the world were parts of the supreme God, and so were to be worshipped, but they were mistaken.” The famed mathematician correspondingly observed in the conclusion of his treatise on Opticks : “And no doubt, if the worship of false gods had not blinded the heathen, their moral philosophy would have gone farther than to the four cardinal virtues; and instead of teaching the transmigration of souls, and to worship the sun, and moon, and dead heroes, they would have taught us to worship our true Author and Benefactor.” The modern reader may ask : Why conclude two treatises that are fundamentally mathematical in nature with these theological considerations?Part of the answer lays in an uncompleted manuscript by Newton titled “The Philosophical Origins of Pagan Theology” (Theologiæ gentilis origines philosophicæ), a treatise on the history of religions comprising more than 130.000 words on about 200 folios. Newton’s claim therein is that the cosmology of the Ancients was in essence theological since it partly proceeded from the belief that the souls of the deified ancestors of mankind had been projected into elements of the cosmos. This catasterisation of early men was, in Newton’s eyes, the actual origin of stellar animism, star worship, and astrology. Thus, the original fall of man into idolatry corrupted both true religion and the right understanding of natural philosophy, as the intrinsic animism of oriental cosmologies was the philosophical counterpart of pagan astrolatry. Restoring pure worship and true science required, therefore, that elements of the cosmos be first desacralized.In this work, I will first identify the sources and characterize the exegetical principles behind the treatise on Origins. I will then examine the Newtonian historiography of the origins and dissemination of pagan physicotheology, from the beginning of star worship in ancient Egypt to the emanationist doctrines taught by Medieval schoolmen. I will then show how Newton’s own system of the world presented itself as a disenchanted alternative to the animistic cosmological beliefs of the Ancients. I will eventually trace the roots of Newtons’s iconoclastic ethos which characterizes much of his theological and philosophical writings. To this end, I will consider the sources of influence that bore upon Newton’s upbringing in relation to the religious contentions which divided the Reformed milieu he grew up in. I will eventually argue that the author of the Principia meant indeed to desacralize the cosmos to meet the demands of an austere and uncompromising monotheism

La question de la réalité, de la nature et du rôle de la relation science de l'univers - spiritualité dans l'œuvre de connaissance scientifique, plus généralement dans l'histoire de la pensée, motive le présent travail. Afin de traiter ce sujet, nous avons choisi d'étudier la pensée de deux savants spiritualistes : Isaac Newton et Georges Lemaître, qui façonnent deux moments majeurs de l'histoire des sciences, celui de la fondation de la mécanique céleste, creuset de la science moderne, et celui de la fondation de la cosmologie moderne, lieu d'une définition radicalement nouvelle de l'univers et de la place de l'homme en son sein. Ces deux moments, newtonien et lemaîtrîen, s'apparient l'un à l'autre, d'une part en raison de l'objet d'étude commun : le tout, et d'autre part en termes de succession et d'avancées dans l'histoire des sciences, puisqu'ils nous entraînent de la science du ciel en l'absolu newtonien, à la science du commencement et de l'évolution cosmologique en la relativité générale. La relation science de l'univers - spiritualité se révèle, sur la base de notre étude des deux pensées, comme une relation dynamique à double sens, une dimension cruciale de l'histoire conceptuelle et, au-delà, de l'histoire de la pensée. Elle permet de surcroît de procurer des éléments de synthèse et de comparaison de ces pensées, et d'asseoir plus largement, aux plans historique et philosophique, le choix du sujet. Notre idée première en ressort étayée et renforcée. Mais au-delà des termes mêmes de l'histoire de la pensée, notre démarche première, fondatrice, a consisté à comprendre des acteurs éminents de celle-ci, comprendre, à travers leur démarche de pensée, l'être, l'esprit, par la lettre de l'histoire
This research questions the existence, nature and role of the relationship between science and spirituality in the construction of scientific knowledge and, more generally, in the history of thought. To address this topic, we have chosen to examine the work of two spiritualist scholars: Isaac Newton and Georges Lemaître. These two figures set major landmarks in the history of science: the founding of celestial mechanics, the basis of modem science, and the founding of modem cosmology, which provided a radically new definition of the universe and of mankind's place within it. These two landmarks - one Newtonian and the other Lernaîtrian - go hand in hand, for one due to their shared subject: the whole, and also due to the subsequent succession and advancement in the history of science since they take us from the science of the sky, conceived as an absolute, to the science of the beginning and of cosmological evolution frorn general relativity. Our research into the two thinkers' philosophies shows that the relationship between science and spirituality is a dynamic, two-way relationship, a vital aspect of conceptual history, and more broadly of the history of thought. Moreover, it provides elements of synthesis and comparison between both scientists-philosophers and gives historical and philosophical rooting to the choice of subject. Our initial idea is thus supported and reinforced. Beyond the terms of the history of thought, our first approach consisted of understanding eminent actors in this history, understanding, through their ways of thinking, their being, their spirit, by their legacy in history

Trobarà el lector en aquestes planes una anàlisi, que desitgem prou sòlida, al voltant de la gènesi dels Philosophiae naturalis principia mathematica de Newton i de les conseqüències teològiques que van derivar-ne. L’objectiu d’aquesta anàlisi no és merament un estudi descriptiu, sinó un intent de resoldre què fou Newton des d’una perspectiva teològica i com hem d’entendre, en última instància, la seva relació amb la lògica interna del discurs científic. Dues tesis aquestes que l’autor ha procurat respondre aportant noves visions tot recolzant-se amb la documentació escaient i l’esforç de les investigacions que n’han brollat. En vista a la resolució d’aquestes tesis, és convenient entendre abans que res, en una primera part de l’obra, l’evolució genètica de les idees que van dur a la formulació gravitatòria. La revisió de les concepcions sobre l’estructura de l’univers anteriors a l’obra de Newton es fa imprescindible per a entendre el context en què va donar-se la seva revolució. A partir d’aquí, la deducció de la llei de l’invers del quadrat de la distància representa el bateig del trajecte excepcional que durà a l’aparició de la física newtoniana. Partint de la famosa trobada de Halley, Hooke i Wren al gener de 1684, la tesi aporta un seguiment de la gènesi de les idees de Newton, cosa que seria impensable sense entretenir-se en una anàlisi acurada del seu opuscle De motu corporum in gyrum de 1684. En aquesta obra apareix el fil conductor de gran part dels continguts posteriors que seran presents als Philosophiae naturalis principia mathematica. La segona part de l’obra haurà de considerar quins efectes va tenir sobre la teologia el descobriment de la llei de gravitació universal per part de Newton. Calen, d’entrada, una anàlisi de les coordenades teològiques del segle XVII i, sobretot, del corpus religiós que dominava la mentalitat de Newton. Quina visió tenia Newton de la divinitat, quina era la seva actitud en relació a l’oficialitat, i com hi relacionava l’exercici científic, són assumptes de cabdal rellevància. El veritable inici de la suma de les distintes conseqüències teològiques a què va dur la publicació dels Principia rau en les possibles respostes a la pregunta de quina hauria de ser la naturalesa de la gravetat mateixa. Haurem de veure, doncs, si rere el Déu que sentia Newton s’hi amagava realment una emmascarada visió deista de la realitat. Una anàlisi d’aquesta qüestió ha de fer veure la vertadera complexitat del Newton religiós: un teista heterodox i fragmentari que fins i tot va acabar flirtejant amb algunes imatges d’un panteisme prou inesperat i inconfessable. Es demostra, a més, que tant les exigències de la nova física de Newton com la presentació tan polièdrica de Déu i del fet religiós que s’enceta amb les seves críptiques concepcions van tenir unes conseqüències metafísiques i teològiques absolutament rellevants dins de certs cercles intel·lectuals propers al newtonianisme. Aquesta herència va constituir el fonament d’un grup de pensadors que es van erigir en «apòstols» del pensament newtonià i que van acabar esdevenint els teòrics de la nova «astroteologia». El lector té doncs a les mans una obra on s’entrecreuen gran part dels distints sabers humans essencials: la matemàtica, la física, la metafísica, la teologia i fins i tot, una reflexió antropològica implícita que no pot menysprear-se. Una cruïlla de sabers que ha de dur, després de realitzat un pregon estudi –o almenys aquesta ha estat la intenció-, a unes conclusions que, si bé estem molt lluny de titllar de sorprenents, aspirem que puguin ser útils tant al teòleg com a l’hermeneuta de la història i de la filosofia de la ciència.
In these pages, the reader will find an analysis, which we conceive sound enough, of the genesis of Newton’s Mathematical Principles of Natural Philosophy and the theological consequences that arose from it. The main purpose of such an analysis is not a mere descriptive study, but an attempt to solve what Newton was from a theological perspective and how we must understand ultimately his relation to the internal structure of the scientific discourse. The author has tried to enlighten both theses by making new crucial contributions based on the available documentation and many other studies. This work is divided in two parts. The first one tackles the scientific path towards the discovery of the universal law of gravity. After careful consideration to the great part of the prenewtonian physical visions –and from the relevant events that took place in January 1684- the author delves deep and thoroughly into the intricate facts which led Newton first to the publication of his De motu and then to the classic physical comprehension of nature in his Principia. An accurate explanation of some mathematical principles is not only developed therein, but also and most especially the winding way Newton was able to walk in order to overcome the challenges and adversities. The second part of the work focuses on the main theological consequences of such a discovery. The author aims to understand better Newton’s religious soul and how he tried to clarify the deepest intangible nature of gravity with regard to his religious concepts. The scientific requirements emerging from the Principia had an important influence in determining the new religious visions which sought to harmonize the «God’s work» and the »God’s Book». In this context, the author demonstrates that Newton was not a deist nor even strictly an orthodox theist, but he should be rather considered as a «formal panentheist» who laid the foundations of what will be known in the future as «astrotheology».

Resumo: Esta pesquisa apresenta um estudo sobre o conceito de força gravitacional na filosofia da natureza de Isaac Newton. O presente texto foi elaborado a partir dos argumentos desenvolvidos por Newton para defender esse conceito em sua obra mais importante, o Philosophiae Naturalis Principia Mathematica (1687). Será visto que, em tais argumentos, Newton restringe o conceito de força gravitacional a partir de um tratamento matemático, que ele próprio elaborou em sua obra. Por outro lado, Newton argumentava, como físico, sobre a necessidade de fornecer uma explicação adequada das leis e conceitos relacionados à experiência. Assim, o programa de Newton deve conter uma explicação de como os princípios matemáticos, dos dois primeiros livros, poderiam ser aplicados ao mundo dos fenômenos, tarefa a qual ele se edicou no Livro III do Principia Mathematica. Por último, é necessário dizer que o conceito de força gravitacional na filosofia da natureza de Newton só pode nos oferecer um resultado significativo quando analisado de um duplo ponto de vista, a saber, o da mecânica racional, isto é, sua “ciência do movimento”, e o da filosofia da natureza, isto é, do “sistema de mundo”.

Une théorie mathématique de la physique puise ses fondements aussi bien dans les mathématiques que dans la nature. N'étant ni une discipline des mathématiques ni une théorie considérant les mathématiques comme un simple outil, elle s'appuie conjointement sur des notions physiques et sur des notions purement mathématiques. Au cœur de sa genèse se situe ainsi la question de la relation entre conceptualisation et mathématisation. En étudiant la genèse de la mécanique rationnelle de Newton entre le premier " De motu " de 1684 et les " Principia " de 1687, nous avons ainsi mis en évidence leur caractère inséparable. Nous avons montré comment les notions physiques déterminent les solutions mathématiques aux problèmes de la mécanique et comment ces solutions à leur tour influencent l'élaboration du cadre conceptuel sur lequel la mécanique newtonienne se fonde. Dans ce cadre, par une étude approfondie et détaillée des manuscrits, nous avons cherché à comprendre comment les notions fondamentales naissent et évoluent dans cette période de gestation. Tout particulièrement, la récente datation du "De gravitatione" (à 1684-85 plutôt qu'à 1662-70) nous a permis de mieux saisir la genèse conceptuelle et de mieux appréhender comment la question de la mathématisation a été traitée par Newton lui-même. Nous avons ainsi pu donner un nouvel éclairage sur la formation de la mécanique newtonienne. Nous avons également démontré que l'idée de la quantité évanouissante sur lequel les démonstrations mathématiques des " Principià " s'appuient, est directement issue d'un problème de fondement de la théorie des fluxions, résolu par Newton en 1671-72. Par là-même, nous pouvons aujourd'hui soutenir que la mathématisation de la mécanique dépend conceptuellement de la méthode des fluxions. Enfin, en étudiant ce problème conjoint de la mathématisation et de la conceptualisation chez Leibniz, nous avons pu montrer la spécificité de l'approche de Newton
A mathematical theory of physics is founded in mathematics as well as in nature. Being neither a discipline of mathematics nor a theory considering mathematics as a plain instrument, it builds jointly upon concepts of physics and of pure mathematics. Regarding its genesis, this implies a question of the relation between conceptualisation and mathematisation. In our study of the genesis of the rational mechanics of Newton between the first "De motu" (1684) and the "Principia" (1687), we show that this relation is of an inseparable kind. Thus, we look at how the concepts of physics determine mathematical solutions of mechanical problems and how these solutions again influence the elaboration of the conceptual framework on which the Newtonian mechanics is founded. In this respect and by a deepened and detailed analysis of the manuscripts, we have sought a better understanding of how the fundamental notions are born and developed during this gestation period. In particular, the recent dating attributed to “De gravitation” (1684-85 instead of 1662-70) has made it possible to better grasp the conceptual genesis and identify how the question of mathematisation was resolved by Newton himself. Thus, we provide new insight, in the development of the Newtonian mechanics. Further, we demonstrate that the idea of vanishing quantities, essential to the mathematical demonstrations in the “Principia”, is a direct consequence of a foundation problem related to the method of fluxions, resolved by Newton in 1671-72. From this, we may claim today that the mathematisation of the mechanics is conceptually depending upon this method of fluxions. Considering at last the joint problem of mathematisation and conceptualisation in Leibniz' thought, we get a better knowledge of the specificity of Newton's approach

Orientador: Fatima Regina Rodrigues Evora
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas
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Resumo: Essa dissertação analisa o chamado "problema de Newton", isto é, o problema de conciliar conceitualmente a inatividade essencial da matéria com a evidente atividade na natureza representada pela força de gravitação universal. Num primeiro momento, temos por objetivo examinar a gênese desse problema e, num segundo momento, os argumentos que Newton desenvolve procurando rebatê-lo
Abstract: This thesis analyses the so-called "Newton's problem", that is, the problem of conceptually conciliating the essential inactivity of matter with the evident activity in nature represented by the universal gravitation force. In a first moment, we are intended to examine the origin of this problem and, in a second moment, the arguments Newton develop in order to solve it
Mestrado
Filosofia
Mestre em Filosofia

Orientador: Laymert Garcia dos Santos
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Educação
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Resumo: Nesta dissertação de mestrado o leitor encontrará os principais aspectos da obra de Newton,. vistos a partir das relações entre ciência e religião em seus escritos.o foco da análise é a lei da atração gravitacional, aqui utilizada como uma metáfora valiosa para o ensino de Segundo Grau, mais especificamente o ensino de Física. O resgate das origens do conceito de força à distância, baseado em autores como B. Dobbs, R. Westfall, A. Koyré e outros, mostra que no ceme do pensamento científico moderno é possível encontrar respostas para questões essenciais da Educação do nosso tempo
Mestrado
Mestre em Educação

Peut-on épistémologiquement prétendre que concept et image se forment sur deux pôles opposés de l’activité psychique ? En guise de réfutation de cette idée bachelardienne, la Mécanique de Newton est ici soumise à une sorte d’analyse « multivariée » qui évalue le poids respectif des variables philosophique, alchimique, théologique et géométrique dans l’essor du premier modèle de la science moderne. Une rapide ouverture souligne le mode flexible de réception analytique de la théorie de la gravitation universelle et indique combien la démarche newtonienne, où concourent mathématiques et thêmata, est loin d’être singulière : par-delà la notion de champ en relativité, celle d’acausalité – un «concept-symbole » à l’image de l’attraction – rend possible la construction de variables philosophique, socio-esthétique, mathématique et expérimentale dans l’élaboration de la physique quantique. En point d’orgue vient la problématique de la « mort » de Newton – liée à l’étude de phénomènes stochastiques et irréversibles – qui met en regard les implications du « chaos alchimique » et du « chaos mathématiques » pour notre conception de la rationalité, de la créativité et de l’objectivité scientifiques
Can one argue from the standpoint of history and philosophy of science that scientific rationality and imagination are antagonistic ? To refute this conception of Bachelard, the study focuses on Newton’s Mechanics, especially on the contribution of philosophy, alchemy, theology and geometry to the development of modern physical science. Final considerations touch very briefly on the flexible analytic reception of the theory of universal gravitation and the possibility the mathematics as combined with themata does not concern Newton’s science only : beyond the concept to field in relativity, an other one, that is acausality, coined by us “concept-symbol” like that of attraction, makes it possible to account for the rise of quantum mechanics in terms of convergence of philosophical, social, aesthetic, mathematical and experimental elements. Also succinct discussion of question raised by stochasticity and irreversibility tries to compare the implications of “alcheminal chaos” and “mathematical chaos” for our conception of scientific rationality, creativity and objectivity

A partir de l'étude des sources manuscrites (manuscrits théologiques d'Isaac Newton, correspondance de Samuel Clarke et de William Wjiston), ainsi que de sources imprimées rarement étudiées, on montre les failles de l'exploitation qui est faite de la science newtonienne à des fins idéologiques (politiques et religieuses pour l'essentiel). Afin de légitimer l'image que le nouvel ordre religieux et politique issu de 1688 cherche à donner de lui-même, la physique newtonienne est débarrassée par ses commentateurs des éléments qui permettraient une utilisation idéologique par les néo-républicains et les matérialistes. En outre, cette étude révèle les divergences proprement théologiques qui opposent les newtoniens les plus fidèles à l'Église d’Angleterre. Toute la deuxième partie est consacrée à l'étude du contenu des manuscrits théologiques de Newton, de manière à mettre en évidence ses concepts fondamentaux (idolâtrie, enthousiasme, fantaisie, métaphysique), qui décrivent essentiellement ce que la religion ne doit pas être. On insiste sur la dimension rationaliste et protestante de la pensée théologique de l'auteur des "principia", ce qui autorise un rapprochement frappant avec le courant déiste, lui-même étudié de manière à en faire saisir certaines dimensions habituellement négligées. La conclusion isole quelques schémas fondamentaux de la théorie newtonienne des religions et de leur histoire et montre que cette pensée constitue une transition entre Renaissance et Lumières
The study of both printed sources (rarely studied) and of manuscripts (Isaac Newton's theological writings, Samuel Clarke's and William Whiston's letters) shows the discrepancy between the ideological (i. E. Political and religious) exploitation of Newtonian science and the works of newton. In order to legitimate the settlement of 1688, the commentators of Newtonian physics divested it of any element allowing a radical interpretation in neo-republican or materialistic terms. Besides, this study reveals the properly theological discord between the inner circle of the Newtonians and the Church of England. The second part is about the contents of newton's theological manuscripts and reveals its fundamental notions (idolatry, enthusiasm, fantasy, metaphysics), which describe what religion is not about. The rationalist and protestant aspects of Newton's thought are emphasized, thus allowing a parallel with deist thought, here revisited in order to show its lesser-known aspects. The conclusion emphasizes some key concepts of Newton's theory of religion and of its history, thus relating it, ultimately, with the rise of enlightenment thought in England

Informe de Seminario para optar al grado de Licenciado en Filosofía
El presente trabajo plantea como hipótesis que las matemáticas aplicadas a la formulación y desarrollo de los enunciados de ley en la física clásica realizan una contribución pragmática por medio de sus distintos roles metodológicos. Estos últimos son entendidos como aquellos roles que permiten establecer y determinar las relaciones inter- e intra-teóricas entre los distintos enunciados de ley. En este sentido, se plantea como objetivo general analizar críticamente la contribución de las matemáticas aplicadas para la construcción y desarrollo de las estructuras de las leyes fundamentales de la física clásica. Para abordar este objetivo, se plantean los siguientes tres objetivos específicos: (1) analizar la contribución de los roles metodológicos de las matemáticas aplicadas en la formulación de los enunciados de ley; (2) analizar la metodología aplicada en la práctica científica para la formulación de estos enunciados; y (3) analizar los puntos anteriores en un caso de estudio correspondiente a las leyes dinámicas de Newton presentadas en su Philosophiea naturalis principia mathematica (1687). Este trabajo se estructura en tres capítulos. En el primero se analiza la contribución del rol metodológico de las matemáticas aplicadas en la formulación y desarrollo de los enunciados de ley de la física clásica, en términos de su relación con otros roles, el carácter instrumental de las matemáticas, la versatilidad de aplicación de las mismas y la validez de estas por medio de la invariancia. En el segundo capítulo se analiza la metodología utilizada en las matemáticas y cómo se utiliza tal metodología en las ciencias, en particular cómo es utilizada en la práctica científica para la formulación de las leyes. En el tercer capítulo se analiza los resultados de los capítulos precedentes, teniendo a la vista la formulación de las leyes de Newton, en términos de la metodología utilizada, los fundamentos para establecer los conceptos físicos fundamentales y la formulación y desarrollo de las leyes dinámicas. Los resultados arrojan que, (i) dada las herramientas de razonamiento que ofrecen las matemáticas para formular estructuras, que permiten inferir las consecuencias de las leyes y descubrir las conexiones entre distintas estructuras matemáticas; y (ii) dada las herramientas formales de estas, las cuales proporcionan una amplia variedad de conceptos para representar y cuantificar entidades físicas, permiten inferir las conexiones entre leyes y otras estructuras matemáticas; permiten concluir que las matemáticas realizan una contribución de carácter pragmático, tanto en la formulación de los enunciados de ley en la física clásica como en la deducción de otras leyes. En efecto, la variedad de herramientas ofrecidas por las matemáticas se adecúa a diversos contextos de investigación en la práctica científica. Esta misma contribución, a su vez, permite realizar una jerarquización formal de las leyes en términos de la deducción de leyes (generando niveles), por medio de matemáticas complejas, y de la robustez de las mismas. Además, se muestra cómo el método axiomático de las matemáticas contribuye en la formulación de los enunciados de ley, puesto que la axiomatización semi-formal utilizado en la práctica científica permite formular de manera consistente los conceptos y axiomas físicos, establecer las relaciones pertinentes entre estos y deducir las consecuencias de estos axiomas. Esta contribución del método axiomático es pragmática debido a que la caracteriza como una axiomatización débil pragmática. La aplicación de estos resultados se puede apreciar en la formulación y desarrollo de las tres leyes dinámicas que formuló Newton en sus Principia. En efecto, Newton al formular estas leyes se guía por una metodología que le permite precisar sus dos conceptos físicos claves, a saber, la masa y la fuerza, y establecer correlaciones entre estos, y, en base a esto, generar distintas estructuras matemáticas. Además, se aprecia cómo el rol metodológico contribuye a demostrar cómo las tres leyes de Newton se relacionan con la ley de Galileo y las leyes de Kepler. En síntesis, los resultados de este trabajo permiten dar cuenta que las matemáticas aplicadas contribuyen de manera pragmática en la formulación y desarrollo de los enunciados de ley en la física clásica, puesto que el rol metodológico de estas es un rol de carácter pragmático.

Orientador: Fátima Regina Rodrigues Évora
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas
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Resumo: Essa Tese analisa a controvérsia entre Gottfried Wilhelm Leibniz e Isaac Newton acerca do estatuto adequado à gravitação universal newtoniana. Mais precisamente, ela procura esclarecer porque Leibniz critica a teoria newtoniana, acusando-a de postular um princípio milagroso ou uma qualidade oculta escolástica no domínio da filosofia natural, enquanto Newton, por sua vez, tentará defendê-la dessas críticas, afirmando ser a gravidade uma qualidade manifesta da matéria e o princípio que a expressa uma verdadeira lei da natureza. Para tanto, serão analisadas as cartas desses autores onde essas questões são pontualmente discutidas, quais sejam a Correspondência Leibniz-Clarke [1715-1716], a Correspondência Leibniz-Newton [1692-1693], a Carta de Leibniz a Hartsoeker [1711], a Carta de Newton ao editor das "Memoirs of Literature" [1712]; ademais, serão analisadas passagens importantes das três edições dos Princípios Matemáticos de Filosofia Natural [1687, 1713 e 1726], das cinco edições da Óptica [1704, 1706, 1717, 1721 e 1730 (edição póstuma)] e de alguns outros textos talvez menos conhecidos de Newton se comparados a estes dois, mas igualmente fundamentais para um bom entendimento das suas réplicas a Leibniz, a saber, a Carta de Newton a Bentley [1692], a Carta de Newton a Cotes [1713], a resenha que Newton publica anonimamente nas Philosophical Transactions da Royal Society sob o título de "An Account of the Book Entituled Commercium Epistolicum" [1714-1715] e uma "Conclusio" projetada por Newton para fazer parte da primeira edição dos Princípios Matemáticos de Filosofia Natural, a qual ele acabou não incluindo na versão final deste texto de 1687, mas que deu origem às considerações do famoso Escólio Geral, inserido na obra partir da sua segunda edição em 1713. Todo esse trabalho deverá, ainda, levar em conta os métodos e as entidades explicativas admitidos no panorama geral da ciência nos séculos XVI e XVII
Abstract: This Thesis analyzes the controversy between Gottfried Wilhelm Leibniz and Isaac Newton regarding the adequate statute to the Newtonian universal gravitation. More precisely, it tries to elucidate why Leibniz criticizes the Newtonian theory, accusing him of postulating a miraculous principle or a scholastic occult quality in the domain of Natural Philosophy, whereas Newton advocates his theory and protects it from such reviews claiming that gravity is a manifest quality of the matter and that the principle which expresses it is a true law of nature. To conduct this work, letters and texts written by these authors discussing such issues will be analyzed: The Leibniz-Clarke Correspondence [1715-1716]; The Leibniz-Newton Correspondence [1692-1693]; The Letter from Leibniz to Hartsoeker [1711]; and The Letter from Newton to the Editor of the "Memoirs of Literature" [1712]. Besides these letters, other important texts will be studied: passages from three editions of the Mathematical Principles of Natural Philosophy [1687, 1713 and 1726]; passages from five editions of the Optics [1704, 1706, 1717, 1721 and 1730 (a posthumous edition)]; and some other Newton¿s texts perhaps not as well-known as the other two, but equally fundamental for a good understanding of the author¿s replies addressed to Leibniz: The Letter from Newton to Bentley [1692], The Letter from Newton to Cotes [1713], the review Newton published anonymously in the Philosophical Transactions of the Royal Society under the title of "An Account of the Book Entituled Commercium Epistolicum" [1714-1715] and a "Conclusio" projected by Newton to be part of the first edition of the Mathematical Principles of Natural Philosophy, which he did not include in the final version of this text from 1687, but which was the origin to the considerations presented in the famous General Scholium, appended to his work since its second edition in 1713. It should also be mentioned that this Thesis will take into consideration the methods and the explanatory entities admitted in the general panorama of science of the XVI and XVII centuries
Doutorado
Filosofia
Doutor em Filosofia

Orientadores: Marcia A. Gomes Ruggiero, Vera Lucia da Rocha Lopes
Tese (doutorado) - Universidade Estadual de Campinas. Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Neste trabalho, apresentamos um método de Newton inexato através da proposta de uma nova escolha para o termo forçante. O método obtido é globalizado através de uma busca linear robusta e suas propriedades de convergência são demonstradas. O passo de Newton inexato é obtido pela resolução do sistema linear através do método GMRES com recomeços, GMRES(m). Em testes computacionais observamos a ocorrência da estagnação em GMRES(m) e um acréscimo inaceitável na norma da função nas primeiras Iterações do método. Para contornar estas dificuldades são propostas estratégias de implementação computacional simples e que não exigem alterações internas no algoritmo do GMRES, possibilitando a interação com softwares já disponíveis. Exaustivos testes numéricos foram realizados, os quais nos permitiram concluir que a proposta para o termo for¸cante e as estratégias introduzidas foram bem sucedidas, resultando em um algoritmo robusto, com propriedade de convergência global e taxa superlinear de convergência
Abstract: In this work it is presented an inexact Newton method by a new choice for the forcing term. A globalization of the new method is done by introducing a robust line search strategy. Convergence properties are proved. The inexact Newton step is obtained through the restarted GMRES, GMRES (m), applied for solving the linear systems. Numerical experiments showed a stagnation of the GMRES (m) and also an occurrence of a great increase in the norm of the function at the initial iterations. Some strategies were proposed to avoid these drawbacks. These strategies are characterized by their simplicity of implementation and also by the fact that they do not need internal modifications of the GMRES algorithm. So, the interaction with available softwares are trivial. A bunch of numerical experiments were performed. With them it can be concluded that the new choice for the forcing term and the strategies incorporated in the algorithm were successfull. The resulting algorithm is then robust and has global convergence property with supelinear convergence rate
Doutorado
Doutor em Matemática Aplicada

Prises indépendamment, les conceptions newtonienne et leibnizienne de l'espace et du temps ont beaucoup attire l'attention des historiens et philosophes des sciences. Par contre, prises ensemble, elles n'ont fait l'objet que de rares et d'incomplètes études. Cette situation tient à plusieurs facteurs dont le plus important est le suivant : dès le 18eme siècle, Newton fut opposé à Leibniz comme le savant s'oppose au théologien ou comme le pur empiriste s'oppose au plus grand rationaliste. D'où le refus de toute possibilité d'une confrontation globale. Grace à la découverte d'un certain nombre de manuscrits, on a commencé, dès la fin du siècle dernier, à abandonner ce schéma simpliste et unilatéral. Aujourd'hui, il est établi que : bien qu'il fut un savant de métier, Newton fut aussi un grand théologien et vice-versa; bien qu'il fut un théologien déclaré, Leibniz fut aussi un excellent savant. Notre contribution s'inscrit ouvertement dans cette orientation. Pour Newton comme pour Leibniz, la discussion du problème de l'espace et du temps fut l'occasion privilégiée pour manifester ce double intérêt. L'examen de la controverse entre Newton et Leibniz sur l'espace et le temps nous a conduit à conclure que la controverse en question traduit et se traduit par une opposition tranchée aussi bien sur le plan théologique que sur le plan physique. Sur le premier plan, le problème de l'espace et du temps est suspendu aux problématiques théologiques les plus cruciales (la nature et les propriétés de dieu et du monde ainsi que leur rapport); il engage, de droit et de fait, le système théologique tout entier. A l'ensemble de ces questions, Newton et Leibniz ont apporté des réponses radicalement opposées. Sur le second plan, l'espace et le temps sont indissociables des problèmes de la matière et du mouvement sur lesquels nos auteurs se faisaient des conceptions fort différentes. Outre ces deux aspects, la controverse Newton Leibniz sur l'espace et le temps engage aussi leur épistémologie. En effet, confrontes a des problèmes cruciaux poses par la substitution de la science nouvelle à celle des anciens et des médiévaux, newton et Leibniz ont adopté deux attitudes différentes conditionnant leur conception de l'espace et du temps.

Orientador: Maria Jose Pereira Monteiro de Almeida
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Educação
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Resumo: Neste trabalho, a partir de um estudo realizado em uma escola pública da cidade de Jundiaí - SP, buscou-se aliar o ensino da Física à prática de leitura de um livro de divulgação científica, em alunos da primeira série do ensino médio, procurando-se verificar o funcionamento da leitura das leis de Newton, como apresentadas no livro: Isaac Newton e sua maçã, com a mediação da pesquisadora. Tendo em vista atingir esse objetivo, propusemo-nos a responder a seguinte questão: Como são produzidos os significados a partir da leitura do texto citado sobre Isaac Newton, considerando as condições de produção do estudo e as mediações ocorridas durante o desenvolvimento das aulas assumidas pela pesquisadora (autora deste trabalho)? O suporte se encontra na linha francesa da análise de discurso, principalmente em trabalhos de Michel Pêcheux e Eni Orlandi. Nesses autores encontra-se sustentação para admitir a relevância de se compreender o funcionamento dos discursos escolares. Verificamos que os processos de produção de sentidos, a partir de atividades de leitura em sala de aula, como as que foram realizadas, ocorreram de maneira específica para cada aluno, e, como esperávamos, confirmamos que os mesmos processos dependem das condições de produção e das histórias de vida dos estudantes
Abstract: In this present work carried out in a public high school placed at Jundiaí - SP, a Brazilian country city, we tried to put together the physics teaching methodology with the reading of a scientifc disclosure book, on high-school-students of the first school year, aiming to verify how works the reading of Newton's laws presented in the book: Isaac Newton and his apple. With the research mediation. Attempting to reach this goal, we propose ourselves to answer the follow question: How does the meaning are produced from the reading of Isaac Newton's texts, taking into account the condiction of the study' s output and the mediations happened through the developing of the classes assumed by myself? We have found out the support into the French line of the speech analysis, mainly on the authors Michel Pêcheux and Eni Orlandi. On these ones we got the sustentation in order to let in the relevance on the scholar speech understanding. We also have verified that the sense-prductions proceedings, from the reading activities applied into the classrooms, second those ones by us carried out, to come out in a specific way to each student, how we hoped, sustaining that the same process depend on the production's condictions and the private-history-life
Mestrado
Ensino, Avaliação e Formação de Professores
Mestre em Educação

Orientador: Zeljko Loparic
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas
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Resumo: Não informado
Abstract: Not informed.
Mestrado
Mestre em Filosofia

En opposition à une opinion assez, répandue, selon laquelle. Newton a fondé la mécanique rationnelle en s'appuyant sur les travaux de Kepler, Galilée et Huygens, puis en rejetant la « physique cartésienne », cette thèse apporte un nouvel éclairage sur la construction de la mécanique classique. En effet, nous nous intéressons dans ce travail, aux obstacles épistémologiques que tes savants des XVIème et XVIIème siècles rencontrèrent lors de l'élaboration des concepts et principes fondateurs de ia physique. Ceux-ci, serviront à la fin du XVIIème, à bâtir l’axiomatique de la mécanique newtonienne. Ainsi, nous démontrons, à partir d'une lecture historique et critique, que les fondements théoriques de la mécanique moderne s'élaborent, en définitive, au cours de la controverse conceptuelle opposant Descartes à Newton à propos du mouvement circulaire. À la suite de cela, le savant anglais introduit son concept d'espace « absolu ». Comme garant du « principe de l'inertie ». A partir de cet axiome l'ensemble des concepts essentiels de sa théorie s'organisent. II s'agit essentiellement du concept de « force » et de la notion de « masse », cette dernière étant indispensable dans ia quantification des « forces ». Qui sont au cœur de la théorie newtonienne. Au-delà des difficultés d'ordre mathématique et physique, propre à la théorisation newtonienne, notre travail a permis de mettre en évidence le caractère non nécessaire de l'espace « absolu >>, de la « force d'inertie », et de la « force centrifuge », démontrant ainsi le paradoxe qui existe entre la dimension opérationnelle d'une théorie et le statut ontologique des concepts qu'elle utilise
In opposition to a. Widespread opinion that considere Newton to have founded rational mechanics by leaning on the works of Galileo. Kepler and Huygens, and then rejecting "Cartesian physics", this thesis sheds new light on the construction, of classic mechanics. Indeed. In this work we are interested in the epistemological obstacles that scholars of the XVIth and XVIIth centuries met during the elaboration of the concepts and the key principles of physics. These will serve at the end of the XVIIth century to build the axioms of Newtonian mechanics. We demonstrate, from a historical and critical reading, that the theoretical foundations of modem mechanics are elaborated during the conceptual controversy pitting Descartes against Newton on the issue of circular movement, From this content, the great English scientist introduces his notion of '"absolute" space as that which guarantees the "|aw of inertia". From this axiom, Newton can organize all the essential concepts of his theory. This concerns essentially the concept of "force" and the notion of "mass". The latter being essential to the quantification of "forces", which are the heart of Newtonian theory. Beyond the difficulties of a mathematical and physical order that are proper to Newtonian theory, our work allows us to bring to light the inessential character of "absolute" space, ''inertia" and "centrifugal force", thus demonstrating the paradox between the operational dimension of a theory and the ontological status of concepts it uses

Le livre : Principia Mathematica Philosophiae Naturalis (1687) de Isaac Newton constitue pour la science moderne un texte fondateur. Le corps de cet ouvrage est constitué de trois parties principales appelées livres. Parmi ces trois livres, les livres I et III consacrés principalement à l'étude du cosmos ont fait l'objet de nombreuses études. Le livre II consacré à l'étude de la résistance au mouvement des milieux fluides a été quelque peu délaissé et même dévalorisé par l'historiographie. Dans le livre II Newton détourne son regard du ciel et le porte sur terre. L'étude de cette partie des Principia nous permet de : revisiter et d'approfondir le concept newtonien de force, de découvrir l'usage de la notion de pression, de préciser le rôle de la géométrie euclidienne. Pour la géométrie nous avons été particulièrement attentif aux différentes fonctions des figures. Nous avons travaillé à partir de plusieurs traductions, principalement celle de la marquise du Châtelet de 1759 et de celle plus récente de Cohen et Whitman. Nos référents essentiels sont : Blay, Cohen, De Gand, Janiak, Koyré, McMullin, Smith et Westfall
Book : Isaac Newton's Principia Mathematica Philosophiae Naturalis (1687) represents a fundamental text for modern science. The body of that work is in three major parts called books. Among these three books, I and III are primarily dedicated to the study of the cosmos and have been the objects of numerous studies. Book II is dedicated to the study of resistance to movement of fluid environments and has been somewhat ignored and even devalued by historiography. In book II Newton turns away from the sky and looks down at earth. The study of that part of Principia allows us to revisit and deepen our knowledge of the newtonian concept of force, to discover and learn how to use the concept of pressure, and to clarify the role of euclidean geometry. As for geometry, we have paid special attention to the different functions of figures. We have worked with several translations, primarily Marquise du Chatelet 1759's translation, and the more recent one by Cohen and Whitman. Our essential references are Blay, Cohen, De Gand, Janiak, Koyre, McMullin, Smith and Westfall

En recherchant la loi de force centripète inscrite dans les Principes Mathématiques de la Philosophie Naturelle, Newton donna au temps un statut de grandeur privilégiée de la philosophie naturelle. Cependant, celui-ci apparaît de façon ambiguë, tantôt grandeur discrète, tantôt grandeur continue. Sa manipulation mathématique, qui repose essentiellement sur la Méthode des premières et dernières raison et sur la loi des aires, laisse, en outre, apparaître un temps de nature géométrique. Confronté, dans la proposition X du livre II, à la résolution du mouvement d'un mobile qui éprouve une résistance en raison du carré de sa vitesse, Newton ne parvient pas à résoudre cette proposition au moyen de la géométrie. Il est contraint de reprendre son raisonnement et de recourir à une méthode algébrique pour énoncer de manière juste, dans l'édition de 1713, la solution de cette proposition, dans laquelle le temps apparaît alors sous une forme algébrisée, représenté par une lettre. Ainsi, d'un temps géométrisé, figuré par un élément d'espace dans l'édition de 1687, Newton en fit un être per se représenté par une lettre dans la proposition X de l'édition de 1713. Cependant, c'est à Varignon, qui aborda les propositions des Principia de Newton à l'aide du calcul différentiel, que l'on doit la fin de la mathématisation et la finalisation du concept de temps mathématique
By looking for the law of centripetal force registered in the Mathematical Principles of the Natural Philosophy, Newton gave to time a status of privileged magnitude of natural philosophy. However, this one appears in a ambiguous way, sometimes discrete magnitude, sometimes continuous magnitude. Its mathematical manipulation, which rests essentially on the Method of first and last ratios and on the law of areas, lets appear a time of geometrical nature. Confronted, in the proposal x of the book II, with the resolution of the movement of a mobile which tests a resistance which is proportional in the square of its speed, Newton does not succeed in solving this proposal by means of the geometry. It is forced to resume its reasoning and to resort to an algebraic method in order to express in a just way the solution of this proposal, in which the time appears then under an algébraic shape, represented by a letter. So, from a geometrical time, represented by an element of space in the edition of 1687, Newton made an entity per se represented by a letter in proposal x of the 1713 edition. But it is to Varignon, who approached the proposals of the Principia by means of the differential calculus, that we owe the end of the "mathematization" and the finalization of the concept of mathematical time

Acompanha: Raciocinal e empírico: caderno pedagógico
Este trabalho trata de uma pesquisa qualitativa sobre a mediação de roteiros no ensino-aprendizagem do experimento da segunda lei de Newton. Iniciamos a pesquisa com uma análise documental sobre a demanda histórica, procurando diagnosticar a produção de roteiros da segunda lei nos últimos 50 anos, baseados nos arquivos históricos do Colégio Estadual do Paraná, os resultados da investigação bibliográfica mostraram que não existiu evolução didático-metodológica em relação as orientações para a execução das práticas experimentais em torno da segunda lei de Newton. Mesmo com a evolução tecnológica e instrumental dos laboratórios já interfaceados com fotogates e computadores, os roteiros ainda privilegiam uma concepção de ensino tradicional de ciência altamente reprodutivista. Concluímos que desde os projetos como o PSSC (MIT), o de Harvard e outros que tinham uma base tecnicista e que propunham o aprendizado de Física tornando os estudantes pequenos cientistas, e que proporcionou aos estudantes muita habilidade motora e uma aprendizagem automatizada e, acabou negligenciando a parte cognitiva presente no processo entre observações e fatos, ao nosso ver isso corrobora com uma concepção de ensino de divulgação de ciência no estilo panfleto. Para nos auxiliar neste problema buscamos principalmente os estudos de Gaston Bachelard, Paulo Freire, Thomas S. Kuhn, Ian Hacking, Neill Postman e Kim Vicente. Problema delimitado propomos uma possível modificação do roteiro da segunda lei de Newton com uma sequência de atividades experimentais com plano de fundo de uma lei ou teoria associado à ciência normal no sentido de Kuhn, no qual os estudantes são provocados em resolver quebra-cabeças, propostos na problematização do roteiro promovendo uma possibilidade de entrelaçamento entre teoria e a prática, valorizando aspectos racionais e empíricos, de forma de aproximação, de tensão conciliadora e de retroalimentação. No método experimental artesanal e tecnológico associado a contextos e problematizações, apostamos na especulação complexa do aparelho experimental e das entidades da física relacionadas com a lei fundamental dos movimentos, com a intencionalidade da especialização na utilização dos aparelhos e do aumento do realismo científico das entidades manipuladas pelos estudantes. Como principais resultados que verificamos pela comparação de representações dos estudantes em questionários aplicados antes e depois da sequência de atividades, apontamos aspectos de uma evolução em maior ou menor grau do gênero de raciocínio associado à cultura do laboratório, com indícios de uma possível evolução do perfil epistemológico dos estudantes em relação as entidades da física manipuladas, através do aparelho experimental e dos elementos articuladores, entre eles o cálculo, no manuseio da linguagem físico matemática.
This assignment is a qualitative research on mediation scripts in the teaching- learning experiment of Newton's second law. We started the research with documentary analysis of the historical demand, looking diagnose the production of script about second law on last fifty years, based on the historical archives of the Colégio Estadual do Paraná. The results of the literature search showed that there was not didactic-methodological, development in relation the guidelines for execution of experimental practices around Newton's second law. Even with the technological and instrumental development of laboratories already interfaced with photogates and computers, the scripts still prefer a traditional school design highly reproductivist science. We conclude from since the projects as the PSSC (MIT), of the Harvard and others, who had a technical basis and that the proposed Physical learning becoming the students in little scientists. And which provided students with a lot of motor skills and an automated learning and, finishes up neglecting the cognitive part of this process between observations and facts, in our view this confirms a science of dissemination of teaching design in the pamphlet style. To help us in this problem we sought studies of Gaston Bachelard, Paulo Freire, Thomas S. Kuhn, Ian Hacking, Neill Postman and Kim Vicente. With the delimited problem, we propose a possible modification of the script of Newton's second law, with a series of experimental activities with the background plan of a law or theory associated with normal science in Kuhn's sense, in which students are challenged to solve puzzles. Problematized in script with a chance of entanglement between theory and practice, valuing rational and empirical aspects, promoting his approach, tension and feedback. In experimental method associated with contexts and problematizations, handmade and with technology, we bet on complex speculation, of the experimental apparatus and of the physical entities related to the fundamental law of motion, with the intentionality of the specialization in the use of equipment and the increase of the realism scientific of the manipulated entities by students. The main results that we see by comparing representations of students in questionnaires before and after the sequence of activities. We point out aspects of an evolution to a greater or lesser degree, gender of reasoning associated with the laboratory culture, with indications of a possible evolution of the profile epistemological of students regarding the physical entities manipulated by the experimental apparatus and the joint by calculation with the handling of physical mathematical language.

Tese de mestrado, Estudos Clássicos, Universidade de Lisboa, Faculdade de Letras, 2011
O presente trabalho consiste na tradução dos fundamentos dos Philosophiae Naturalis Principia Mathematica de Newton, ou seja, da parte axiomática, e no seu estudo, dando principal relevância ao estudo da Primeira Lei de Newton, ou lei da inércia. Na tentativa de compreender a importância que a Primeira Lei de Newton assume na história da ciência, é impreterível que se recue a Aristóteles, e aos primórdios dos estudos sobre o movimento e que, a partir de aí, se acompanhem as contribuições que autores posteriores tiveram no desenvolvimento desta ciência, para uma melhor percepção das alterações que esta física sofreu até ao tempo de Newton. Dada a extensão do objecto em estudo, cingimo-nos aos autores principais, Aristóteles, Kepler, Galileu, Descartes, Huygens, visto terem sido estes os autores que mais contribuíram para o desenvolvimento da lei consagrada por Newton. No entanto, não é um objectivo deste trabalho fazer um resumo da história da ciência, mas sim fazer uma síntese da génese e evolução do conceito de inércia, que culmina na Primeira Lei de Newton, para que se compreenda em que contexto surgiu e que condições proporcionaram o seu aperfeiçoamento. Assim sendo, analisámos e comparámos os textos dos referidos autores que mais importância tiveram nas alterações que o conceito de inércia experimentou até assumir a sua forma final nos Principia. Como grande parte da nossa atenção incide sobre a história do conceito em Newton, faz todo o sentido o debruçar sobre o texto original dos Principia, mais concretamente sobre a terceira e última edição, tentando entender a importância do termo na obra que o consagrou. Assim sendo, é indispensável a sua versão para a nossa língua, permitindo uma maior aproximação ao texto original. Em termos gerais, conclui-se que os predecessores de Newton foram essenciais, e as suas contribuições bastante significativas para que Newton chegasse onde chegou, no entanto, não podemos esquecer o mérito pessoal do autor.
Abstract: This work consists of translating the fundamentals of Newton‘s Philosophiae Naturalis Principia Mathematica, that is, from axiomatic, and in his study, giving primary importance to the study of Newton‘s First Law, or the law of inertia. In an attempt to understand the importance that Newton‘s First Law takes in the History of Science, it is imperative to go back to Aristotle, and early studies on movement and, from there, undesrstand the contributions that later authors have given to the development of this science. Given the extent of the object under study, we tried to focus on the main authors, like, Aristotle, Kepler, Galileo, Descartes, Huygens. These authors contributed the most to the development of the law laid down by Newton. The main goal of this study is to review the evolution of the concept of inertia, which culminated in Newton‘s First Law. In orther to understand the context in which they arose and the conditions provided its improvement. Therefore, we analyzed and compared the texts of those authors who had the most important changes that the concept of inertia tried to take it a final shape in the Principia. Our attention focused on the history of the concept in Newton, it makes sense to look into the original text of the Principia, more specifically on the third and last edition, and trying to understand the importance of the term in the work that made him famous. Therefore, it is indispensable to our language version, allowing closer to the original text. Overall, we conclude that Newton‘s predecessors were essential, and their very significant contributions to Newton where he arrived, however, we can not forget the value of the discovery of the author.

A presente dissertação tem como objetivo analisar tematicamente a polémica de 1715/16 entre Leibniz e Clarke, não apenas, como é usual, no âmbito das conceções do espaço e do tempo, mas no conjunto dos seus temas metafísicos, teológicos, gnosiológicos e físicos. Na estruturação da dissertação, adquiriu um papel central o confronto dos autores em torno da noção de liberdade, cuja importância é evidente na utilização do princípio da razão suficiente e seus corolários, na distinção entre verdades de razão e verdades de facto, entre os diversos tipos de necessidade, nas conceções alternativas de espaço e de tempo, na alternativa entre átomos e mónadas, na questão dos limites do universo, na relação entre a alma e o corpo, nas teses relativas à providência divina, na forma como se concebe a relação de Deus com a sua máquina, na noção de milagre e nas próprias noções de força e de movimento, pelo menos no que respeita à sua relação com Deus, isto sem desprezar a abordagem direta da própria noção de liberdade. Com este enquadramento, pretende-se mostrar, através de um eloquente exemplo histórico, que as teorias científicas naturais se podem alicerçar em teorias metafísicas e que esses alicerces não têm que se esgotar, mesmo no seio da metafísica, nas questões estritamente cosmológicas, isto para lá de poderem existir influências nunca menosprezáveis de domínios não filosóficos, como é o caso da teologia dogmática. Apesar disto ser evidente na abordagem dos textos, existe uma sistemática menorização contemporânea desta determinação, como se fosse uma idiossincrasia da época ou uma deferência que a ciência tinha de ter numa época ainda obscurecida pela autoridade das igrejas e pela especulação filosófica. Esta abordagem pretende compreender todos os aspetos do pensamento expresso pelos autores na polémica, na sua integralidade, sem reservas de qualquer tipo.
The present dissertation has as purpose to analyse thematically the 1715/16 controversy between Leibniz and Clarke, not only, as usual, within space and time conceptions' scope, but in the set of his metaphysical, theological, gnosiological and physical thematics. In the dissertation's structuration, it has acquired a central role the authors' confrontation about the liberty's notion, whose importance is evident in the use of the principle of sufficient reason and its corollaries, in the distinction between truths of reason and truths of fact, between necessity's various types, in the space and time's alternative conceptions, in the alternative between atoms and monades, in the universe's limits' problem, in the relation between soul and body, in the theses relative to the divine providence, in the way God's relation with his machine is conceived, in the notion of miracle and even in force and movement notions, at least in what regards its relationship with God, this without neglecting the direct approach to the very notion of liberty. With this framework, it intends to show, through an eloquent historic example, that the natural scientific theories may be founded in metaphysical theories and that these foundations don't have to be exhausted, even within metaphysics, in strictly cosmological questions, this beyond the possibility of never underestimable influences of non-philosophical domains, as is the case of dogmatic theology. Although this is evident in the texts' reading, there is a systematic contemporary lessening of this determination, as if it was an idiosyncrasy of the age or a deference that science had to have in a time still obscured by the authority of the churches and the philosophical speculation. This approach intends to understand all of the thinking's aspects expressed by the authors in the controversy, in its entirety, without reservations of any kind.

ABSTRACT The aim of this study was to investigate the effect of an active learning approach (ALA) on the achievement of 11 th grade learners in Newton’s laws of motion, The case study was done in one school by comparing the achievement of learners in Newton’s laws of motion through an Active Learning Approach (ALA) with that of learners taught through Traditional Direct I nstruction (TDI) and to determine whether learners taught with ALA retained the material better than those taught with TDI. Two grade 11 classes in one school in the Queenstown District of the Eastern Cape were selected on their performance in two differen t tests and used as case study . The Force Concept Inventory was used to determine the achievements and retention of knowledge of the two groups. The effect of the active lear ning approach on the treatment group was also measured by ask ing each learner in t he group to complete a learner assessment of instruction form. The treatment group was also subjected to a classroom group interview. T he following information emerged from the study: i) Learners taught using the ALA achieved significantly better in FCI pos t - test than those taught with traditional direct instruction. ii) In the retention of knowledge test, the mean score of the learners taught using the ALA was 4.8% higher than those taught with TDI although insignificant. iii) Learners subjected to the ALA liked the instructional approach and as such put in extra time to learn. The findings suggest that the active learning approach had positive effect on the achievement of the Grade 11 learners and thus, can be adapted to enhance learning in the classroom.
Physics