From 3ea97b6b9a03d76e4a70836f7437c6963fc3b504 Mon Sep 17 00:00:00 2001 From: oskar Date: Sat, 25 Apr 2026 07:07:07 +0200 Subject: [PATCH] MacBookPro.lan 2026-4-25:7:7:7 --- ...tre XII et ses cercles non-concentriques.md | 20 ++- .../fiche_lecture.pdf | Bin 262921 -> 271784 bytes .../figures/mouvement_tube.tikz | 127 ++++++++++++++++++ .../figures/styles.tikzstyles | 1 + 4 files changed, 146 insertions(+), 2 deletions(-) create mode 100644 sources/0 - cours/LOGOS S2/le savoir en mathématiques/figures/mouvement_tube.tikz diff --git a/sources/0 - cours/LOGOS S2/le savoir en mathématiques/Fiche de lecture - La lettre XII et ses cercles non-concentriques.md b/sources/0 - cours/LOGOS S2/le savoir en mathématiques/Fiche de lecture - La lettre XII et ses cercles non-concentriques.md index 29607ffd..10bc4e0d 100644 --- a/sources/0 - cours/LOGOS S2/le savoir en mathématiques/Fiche de lecture - La lettre XII et ses cercles non-concentriques.md +++ b/sources/0 - cours/LOGOS S2/le savoir en mathématiques/Fiche de lecture - La lettre XII et ses cercles non-concentriques.md @@ -46,6 +46,7 @@ header-includes: | \usepackage{csquotes} \usepackage{figures/tikzit} + \input{figures/styles.tikzstyles} \newcommand{\figref}[1]{Figure\,\ref{#1}} --- \setlength{\parindent}{4ex} @@ -149,7 +150,6 @@ D'autres questions de traduction sont soulevées par Camerini. Que signifie \say - On pourrait inverser le sujet de la phrase pour parler d'\say{inégalités \emph{de} distances}. Ce qui serait infini ne serait plus, alors, les distance, mais les inégalités entre elles. - Une autre interprétation, à privilégier selon Camerini : Spinoza ne parlerait pas de longueurs ou de distances, mais de *variations de l'espace*. Pour justifier ce choix, Camerini se réfère à un passage des *Principes de la philosophie de Descartes*, où Spinoza propose un schéma similaire, et où il affirme que l'espace est partout égal pour des (demis-)cercles concentriques et partout inégal pour des (demis-)cercles non-concentriques[^ppc-cercles]. Ce lien semble pertinent étant donné la similitude des figures et d'autant plus si l'on se rappelle que la lettre est fort probablement une réponse à des questions de Meyer au sujet des *Principes de la philosophie de Descartes*. Nous verrons plus tard comment le lien entre ces deux figures s'inscrit dans une histoire plus large de la figure des cercles non-concentriques. -La formulation \say{Duolus circulis $AB$ et $CD$} pose également un problème de traduction. En effet, la notation \say{$AB$ et $CD$} n'est pas très claire. Il semble impossible que cette notation désigne les deux cercles (elle serait assez incompréhensible considérant la position des points, voir \figref{fig:cercles-non-concentriques}) ; cela exclut la traduction par \say{distances inégales comprises entre deux cercles $AB$ et $CD$}. Camerini examine d'autres traductions, mais conclus que la meilleure solution est celle proposée par @barbarasSpinozaScienceMathematique2007 : \begin{figure}[h] \center @@ -158,9 +158,15 @@ La formulation \say{Duolus circulis $AB$ et $CD$} pose également un problème d \label{fig:inaeq-spatii} \end{figure} +La formulation \say{Duolus circulis $AB$ et $CD$} pose également un problème de traduction. En effet, la notation \say{$AB$ et $CD$} n'est pas très claire. Il semble impossible que cette notation désigne les deux cercles (elle serait assez incompréhensible considérant la position des points, voir \figref{fig:cercles-non-concentriques}) ; cela exclut la traduction par \say{distances inégales comprises entre deux cercles $AB$ et $CD$}. Camerini examine d'autres traductions, mais conclus que la meilleure solution est celle proposée par @barbarasSpinozaScienceMathematique2007 : \say{$AB$ et $CD$} serait une notation pour parler de l'espace entre les limites $AB$ et $CD$, à l'intérieur des deux cercles. +Une dernière question de traduction se pose : par \say{\emph{quantumvis parvam ejus portionem capiamus}}, Spinoza veut-il dire \say{Si petit que nous le supposions [l'espace]} ou bien \say{si petite que nous prenions la portion de cet espace} ? Camerini adopte la seconde option en suivant Barbaras. Cela est encore cohérent avec les *Principes de la philosophie de Descartes*, lorsque Spinoza clarifie la définition VIII[^ppc-parties]. +Ainsi, Camerini obtient la traduction suivante : +\begin{displayquote} + Ainsi, par exemple, dépassent tout nombre toutes les inégalités de ­ l’espace placé entre deux cercles, et toutes les variations que la matière mue dans celui-ci doit subir. Et cela ne se déduit pas de ­ l’excessive grandeur de ­ l’espace interposé : car si petite que soit la portion que nous en prenions, les inégalités de cette petite portion dépasseront tout nombre. Et cela ne se déduit pas non plus, ­ comme il arrive en ­ d’autres cas, de ce que nous ­ n’ayons pas leur maximum et minimum : dans cet exemple-ci, en effet, nous avons les deux, à savoir exactement le maximum AB et le minimum CD. Plutôt, cela se déduit seulement de ce que la nature de ­ l’espace placé entre deux cercles ayant des centres différents ne peut rien subir de tel. Et pour cette raison celui qui voudrait déterminer par quelque nombre toutes ces inégalités devrait en même temps faire en sorte que le cercle ne soit pas cercle. +\end{displayquote} [^3]: [@camerini-lettre12, p.8] [^imagination-perception]: C'est ce qu'affirment Russ Leo et Giovanni Liacata : \say{Quant au concept d’*imaginatio*, il faut toujours garder à l’esprit qu’il est ici synonyme de perception sensible, et qu’il ne s’agit donc pas seulement de la manière dont l’esprit projette une image relative à quelque chose qui n’est pas présent à nos sens : l’imagination ne correspond pas au sens contemporain de fantaisie. Il est donc légitime de dire que toute sensation est une imagination.} [@ethique-rovere, p.246 note 225] @@ -170,11 +176,21 @@ La formulation \say{Duolus circulis $AB$ et $CD$} pose également un problème d [^camerini-trad-spatii]: [@camerini-lettre12 p.9] [^ppc-cercles]: [Principes de la philosophie de Descartes, @spinoza-pleiade p.141 proposition 9] [^correspondance-rovere]: [@spinoza-correspondance-rovere] - +[^ppc-parties]: \say{par partie de la matière il [Descartes] entend tout ce qui est transporté ensemble, même si cela peut être à son tour constitué de multiples parties} [Principes de la philosohpie de Descartes, Partie II, Définition VIII @spinoza-pleiade p.226] $$*\,*\,*$$ +Après avoir analysé philosophiquement le texte pour en produire une traduction la plus fidèle possible (travail qu'il appelle exégétique), Camerini passe à une approche plus historique, qui va inscrire la figure des cercles non-concentrique dans une lignée de figures et de réflexions au sujet de l'infini actuel. + +La figure des deux cercles est déjà présente dans les *Principia Philosophiae* de Descartes de 1644. Elle s'inscrit dans le cadre de la physique de Descartes, dont il est utile de présenter quelques principes. Pour Descartes, la matière n'est pas composée d'atomes ; le vide n'existe pas ; le mouvement est pensé à travers la notion de *mouvement local*, c'est-à-dire que l'on considère une portion de matière qui se transporte ensemble, à une même vitesse[^ppc-parties] ; la matière est potentiellement infiniment divisible, mais n'est *actuellement divisée* qu'en tant qu'elle se concoit en parties ayant des mouvement distincts, autrement dit des vitesses distinctes. C'est alors qu'intervient la figure des cercles : on imagine que ces cercles représentent la coupe d'un tube de diamètre variable, à l'intérieur duquel se trouve un fluide parfait. Dans le cas de cercles concentriques (c'est-à-dire pour un diamètre constant) on peut diviser la matière en parties finies et expliquer ainsi un mouvement circulaire du fluide (voir \figref{fig:mvt-tube}, à gauche). La vitesse de chaque partie de matière sera la même, l'espace étant homogène, et chaque partie suivra un déplacement le long du tube (représenté par les flèches de la \figref{fig:mvt-tube}) (la matière agissant comme un tout de vitesse uniforme, il n'est en fait pas nécessaire de la diviser pour expliquer son mouvement. Mais dans le cas de deux cercles non-concentriques (si le diamètre varie) (voir \figref{fig:mvt-tube}) il faudra que, en même temps qu'une certaine quantité de fluide passe par $AB$, une même quantité passe par $CD$. Les diamètres $AB$ et $CD$ étant inégaux, il faudra que la matière aille plus vite lorsqu'elle passe par $CD$ que lorsqu'elle passe en $AB$ : l'espace non-homogène entraine des vitesse non-homogènes. Plus encore, la matière située entre $AB$ et $CD$ dans le tube (par exemple, située en $E$) aura une vitesse distincte de celle située en $AB$ et de celle située en $CD$. + +\begin{figure}[h] + \center + \resizebox{!}{4cm}{\input{figures/mouvement_tube.tikz}} + \caption{mouvement des parties de la matière} + \label{fig:mvt-tube} +\end{figure} # Critique diff --git a/sources/0 - cours/LOGOS S2/le savoir en mathématiques/fiche_lecture.pdf b/sources/0 - cours/LOGOS S2/le savoir en mathématiques/fiche_lecture.pdf index 499b832bd53c9525b4b0a5dd947ae5bc00d50db5..a729feac4c52947fe3613f515259d78d1ea24b1c 100644 GIT binary patch delta 108755 zcmZs?Q*fYN7p)sR9ox3iNjkP|bZpyslXQ$u(y?vZwr$(C_xGQwed=7CyESXfo4IOT zJT=B#;UUN+ndy%*6IaR&cz$a7?nMcIGY?#H^g$oXIHOU^IZ1O#FHaO4oGt z%wz^F>`)}cDZX-Tr#waCaM4A^karG+7ZhVe+OF|ZdpG~)36wtBsQ0MY0ABRf&@z#> zlXG`mdiR#(SJ$V@{o5ZJPU%QeHMjfIb8%Q2441L!HT2+_F`EpjV4Atf;{7AW(+}T$ z0U6`+^~_nuSNg`*%~D{3ysI=Tr0&UgRfE9oNa|VhX-nlNLWAnt{dj7&T-lW)Bc{h) 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+ \draw [style=fleche] (68.center) to (67.center); + \end{pgfonlayer} +\end{tikzpicture} diff --git a/sources/0 - cours/LOGOS S2/le savoir en mathématiques/figures/styles.tikzstyles b/sources/0 - cours/LOGOS S2/le savoir en mathématiques/figures/styles.tikzstyles index 1d19bfb9..f3d73556 100644 --- a/sources/0 - cours/LOGOS S2/le savoir en mathématiques/figures/styles.tikzstyles +++ b/sources/0 - cours/LOGOS S2/le savoir en mathématiques/figures/styles.tikzstyles @@ -8,3 +8,4 @@ % Edge styles \tikzstyle{fill}=[-, fill={rgb,255: red,76; green,76; blue,76}, draw=none] +\tikzstyle{fleche}=[->]