History of calculus

über den Begriff der abgeleiteten Funktion II. über das Differential lll. Erster Entwurf IV. Zweiter Entwurf V. Dritter Entwurf VI. Einige Nachträge VII. I. Erste Entwürfe VIII. li. Der historische Entwicklungsgang IX. III. Fortsetzung von Entwürfen X. 1. Aus dem Manuskript "Taylor's Theorem, Mac Laurin's Theorem und Lagrange's Theorie der abgeleiteten Funktionen" XI. 2. Aus dem unbeendeten Manuskript "Taylor's Theorem" XII. über die Mehrdeutigkeit der Termen "Grenze" und "Grenzwert" XIII. Vergleichung von D'Alembert's Methode mit der Algebraischen XIV. Analyse von D'Alembert's Methode mittels noch eines Beispiels Kommentare •zu I zu li zu III zu IV bis VI zu VII zu VIII bis XIV 153 159 163 165 168 175 Da im Ausdruck ~ jede Spur seines Ursprungs und seiner Bedeutung erlischt, ersetzen wir ihn durch ~~ , wo die endlichen Differenzen x 1 -x oder ~x und y 1 -y oder ~y als aufgehohne oder verschwundene Differenzen symbolisiert erscheinen oder !~ verwandelt in ~~ . Also dy di=a. Der von mmgen rationalisierenden Mathematikern festgehaltne Trost, quantitativ seien dy und dx in der Tat nur unendlich klein, [ihr Verhältnis] nur annähernd ~ , ist Chimere, wie es sich sub II) 3 L noch handgreiflicher zeigen wird. Noch zu erwähnende Eigentümlichkeit des betrachteten Falls ist, dass !~ =a und ebenso ~~ =a, der Grenzwert [des Verhältnisses] der endlichen Differenzen daher zugleich auch der Grenzwert [des Verhältnisses] der Differentialen, ist. 2) Ein zweites Beispiel desselben Falls ist Yt-Y ~y oder -=1• .r 1 -x !lx ' * Im Entwurf dieser Arbeit (4146, PI. 4) folgt: «Andrerseits geht der Differentialprozess jetzt vor in der vorläufig cAbgeleite~ ten)) Funktion x(rechte Seite), während derselbe Prozess auf [der] linken Seite jene Bewegung notwendig begleitet».-Red. ** Im Entwurf lautet der folgende Satz: <cb) Die Findung «der Abgeleiteten» aus der Originalfunktion x verlief so, dass wir erst eine endliche Differentiation [das Setzen der endlichen Differenz] vornahmen; diese liefert eine vorläufig «Abgeleitete>>, welche der Grenzwert von ~y u.:C ist. Der Differentialprozess, zu dem wir dann schreiten, reduziert diesen Grenzwert auf seine Minimalgrösse. Die in der ersten Differentiation eingeführte Grösse xl verschwindet nicht.. .•. -Red. * Sieh «Über dem Begriff der abgeleiteten Funktion•, S. 51. -Red. ** Im Entwurf: «muss in der Regel».-Red.

We re-evaluate the great Leibniz-Newton calculus debate, exactly three hundred years after it culminated, in 1712. We reflect upon the concept of invention, and to what extent there were indeed two independent inventors of this new mathematical method. We are to a considerable extent agreeing with the mathematics historians Tom Whiteside in the 20th century and Augustus de Morgan in the 19th. By way of introduction we recall two apposite quotations: "After two and a half centuries the Newton-Leibniz disputes continue to inflame the passions. Only the very learned (or the very foolish) dare to enter this great killingground of the history of ideas" from Stephen Shapin 1 and "When de l'Hôpital, in 1696, published at Paris a treatise so systematic, and so much resembling one of modern times, that it might be used even now, he could find nothing English to quote, except a slight treatise of Craig on quadratures, published in 1693" from Augustus de Morgan 2 . * 1685 John Craig Methodus figurarum … quadraturas determinandi inspired by Leibniz' Acta E. article of 1684 (p.27), plus also Barrow and Gregory. De L'Hopital alluded to its part II. It concerned finding areas (ie integration), with little hint as yet of fluxional method.

A presente pesquisa tem como objetivo investigar a presença da educação musical no estado de Mato Grosso a partir de uma pesquisa documental da Educação Básica nas redes federal e estadual. Em termos metodológicos, foram selecionados documentos sobre os currículos propostos e documentos sobre os concursos realizados para ingresso de professores para a atuação nos componentes curriculares específicos em que a educação musical estivesse presente. A análise qualitativa permitiu identificar o espaço geral da educação musical nos documentos curriculares das redes federal e estadual de Mato Grosso. A partir do reconhecimento dos espaços para a educação musical nos documentos oficiais, é possível uma maior propriedade em termos de atuação e de reflexão sobre as possibilidades para as ações de ensino, de aprendizagem e de políticas educacionais.

In this paper we show how some fundamental concepts of modern topology can be understood philosophically in the light of Hegel's Logic as well how modern topological concepts can provide concrete illustrations of many of the concepts and deductions that Hegel used. This paper can be seen as a continuation of our paper \cite{pro} where we argued that the prototypes of many fundamental notions of modern topology were already found in Aristotle's Physics.

Este estudo tem como objetivo discutir as contribuições do ensino desenvolvimental na realização da prática do estágio supervisionado, junto aos alunos do 6º ano do ensino fundamental e 1º ano do ensino médio, em uma pública estadual de Barra do Garças/MT. A decisão de nos fundamentarmos na teoria desenvolvimental para a realização do estágio de regência foram ao encontro da disciplina de Estágio Curricular Supervisionado III, do Curso de Licenciatura em Geografia, da UFMT/CUA, que tinha como proposta fazer com que os acadêmicos assumissem as aulas, durante um bimestre em duas turmas, em uma escola estadual. A execução desse estágio ocorreu entre os dias 18 de outubro a 15 de dezembro de 2017 e contou com uma carga-horária de 30 horas. Para a realização deste estudo, nos utilizamos da metodologia qualitativa e dos procedimentos de observação durante as aulas, de entrevistas semiestruturas com os alunos que avaliaram o desenvolvimento das aulas e de produções escritas, realizadas ao percorrer das aulas ministradas. Como referencial teórico, nos assentamos em Pontuschka, Paganelli e Cacete (2007) e Cavalcanti (2008) que discutem o ensino de geografia e de Vygotsky (2001), Leontiev (2004) e Davídov (1988) que tratam da abordagem histórico-cultural, da teoria da atividade e do ensino desenvolvimental, respectivamente. Como resultados, podemos dizer que o planejamento do ensino desencadeou mudanças significativas na aprendizagem dos alunos, pois a maioria participou ativamente das ações, operações e tarefas propostas; incluiu os alunos que tinham desavenças pessoais, na medida em que precisavam realizar tarefas em grupos; fez com que os alunos refletissem mais sobre a atividade de estudo; e, principalmente, colocaram-se como sujeitos no processo de aprendizagem. Assim, podemos dizer que a realização do estágio possibilitou aos alunos vivenciarem outra perspectiva de ensino que se diferenciou da tradicional reprodução do que está no livro didático e da realização de tarefas mecânicas e individuais que pouco contribuem para a formação do pensamento crítico e dificilmente faz sentido na vida prática dos alunos. Por isso, consideramos de suma importância a preocupação com o planejamento da atividade de ensino para que os alunos se apropriem dos conceitos geográficos e façam generalizações teóricas em diferentes escalas. Palavras-chave: Ensino desenvolvimental. Estágio supervisionado. Planejamento escolar.

I am not worth one Abel prize, I am worth many Abel prizes. The irony is that I shall never receive any because those who sit on such committees are ignorant scum that is part of mainstream mathematics academia. They are pathologically jealous of me, but I shall have the last laugh yet.

A partir da noção de experiência, compreendida como categoria analítica e ético-política, elaboramos algumas (des)pensações sobre psicologia e currículo. Desde perspectivas críticas e póscríticas, aqui o currículo emerge como um artefato cultural, ou seja, um construto históricodiscursivo. À luz de nossas experiências didático-pedagógicas como docentes dos cursos de graduação e pós-graduação em psicologia da Universidade Federal da Grande Dourados/Brasil, e localizados em um contexto sociopolítico, seja no nível nacional seja no nível local, marcado por autoritarismos, conservadorismos e ataques aos princípios democráticos, problematizamos a necessidade e a urgência de um currículo e de uma práxis docente enquanto experiência formadora. Nesse exercício, ao apontarmos para a importância do reconhecimento da função formadora de um currículo da/na experiência, esperamos evidenciar seu caráter crítico, ético e político.

Dieses Werk ist urh eb errechtlich geschützt. Die dadurch begründeten Rechte, insbesondere die des Nachdrucks, des Vortrags, der Entnahme von Abbildungen und Tab ellen , der Funksendung, der Mikroverfilmung od er der Vervi elfältigung a uf anderen Wegen und der Sp eicherung in Datenverarbeit ungsanlagen , bleiben, a uch bei nur a uszugsweiser Verwertung, vorbehalten. Ein e Vervielfält igung dieses Werkes od er von Teilen di eses Werk es ist auch im Einzelfall nur in den Gr enzen der gesetzlichen Bestimmungen des Urheberrechtsgesetzes in der jeweils gelte nde n Fassung zul ässig. Sie ist grundsätzlich vergütungspflichtig. Zuwid erhandlungen unt erli egen den Strafb estimmungen des Urheberrechts.

Now you can understand the concept of number even if you are a mathematics professor (whose IQ is normally 85). This article is written primarily for mathematics professors and educators who have no clue what a number is or even how it is systematically realised from nothing.

Yes, I used line segments, and these are explained in my article:

https://www.academia.edu/45567545/There_are_no_postulates_or_axioms_in_Greek_mathematics

There is no BS of set theory, ZFC or the garbage known as "real analysis".

Note: We MEASURE the antecedent of a ratio using its consequent and/or equal parts of the consequent.

There is no such thing as established knowledge because ALL knowledge is always questionable. In the following dialogue, I explain to Anthropic's Claude AI that the Britannica entry for the mean value theorem is wrong. New Calculus: Here is the entry: Mean-value theorem, theorem in mathematical analysis dealing with a type of average useful for approximations and for establishing other theorems, such as the fundamental theorem of calculus.

For decades, incorrigibly stupid mainstream mathematics academics such as professors and teachers have peddled drivel on calculus, one of mathematics' most important branches. It has nothing to do with their drivel about rates or instantaneous rates.

Read this book to learn the actual facts.

Dedicated to all those who aspired to STEM careers, but whose lives were irreparably harmed by mainstream mathematics dogma; to the curious minds led astray by false calculus histories; and to the seekers of truth whose light was dimmed by doctrines placing conformity above progress. May the spirit of inquiry always rise resilient, however rigidly institutions resist change. Blind consensus must never supersede the power of deductive reasoning and geometric reason to reveal nature's fundamental designs. Those shunned for heterodoxy often redeem science and mathematics from the dead-ends of complacent normality. This work aims to continue that legacy by exposing calculus' origins untainted by time's obscuring veils. However long entrenched falsehoods persist, truth ultimately prevails when a courageous few dare dissent. To the independent thinkers and skeptics who remind us no theory sits beyond question - this book is for you!

"When we examine the fundamental principles of the differential calculus, we soon recognize that pure algebraic analysis and geometric analysis are not sufficient to define the concept of the derivative." - Cauchy

Turns out that I revealed the Holy Grail of Calculus which proves that geometric analysis on its own is sufficient. Cauchy just didn’t know and neither did the mainstream fools who came after him.

The Historic Geometric Theorem (HGT) was discovered from my New Calculus. The HGT is not New Calculus, but is realised from it:

https://www.academia.edu/41616655/An_Introduction_to_the_Single_Variable_New_Calculus

A link to the original article here:

https://www.academia.edu/62358358/My_historic_geometric_theorem_of_January_2020

A conversation with a ChatBot:

https://www.academia.edu/105028579/Most_advanced_AI_Claude_admits_my_historic_geometric_theorem_of_January_2020_is_profound_discovery

Almost 200 articles here:

https://independent.academia.edu/JohnGabriel30

The first attempt to discredit me and steal my work:

https://www.academia.edu/44928764/How_stupid_are_mainstream_math_professors

You can know whether a definition is ill-formed or well-formed!

This article in the form of a dialogue explains how.

I conducted the following dialogue with ChatGPT with a special parameter I created in my settings, that is, /geniusmode. I use this parameter to restrict long responses, force content accuracy, avoidance of flowery speech and directed answers. I won’t talk about the topic because it is discussed in detail in the dialogue. My prompts are preceded by the New Calculus icon, whereas those of ChatGPT are in red font against a green background. Even if you’ve read similar content in the past, be sure to read the entire dialogue carefully because there is new content and also other perspectives showcased. Enjoy!

Definitions are important. One cannot produce whimsical definitions that are ill-formed as many are in mainstream mathematics. One must be mindful of good (well-formed) and bad (ill-formed) definitions and how to determine which are good and which are bad.

This book is no longer free but can be purchased for a mere €9.99 on Amazon:

https://www.amazon.com/dp/B0DBPQCN8H

Defining number rigorously has been attempted countless times since ancient history. Early efforts involved primitive stone counting techniques, followed by the basic arithmetic of ancient Babylonians and Egyptians...

The BIG STUPID (contemporary mathematics professors and teachers) has no clue what a number is. The incorrigibly stupid mainstream academics have their heads too far up each other's colons and reasoning with such imbeciles is futile. Their beliefs are like those of religious fundamentalists. The poisonous rot of set theory and topology (both anti-mathematical nonsense) are their specialty.

In this book, I, the great John Gabriel, complete what Euclid failed to do. I teach you how you got the number concept which is contrary to all the rot you've heard or experienced in your school and university years. This is no small feat. I challenge you to read the book and risk becoming smarter!

O presente trabalho tem por objetivo relatar a vivência de discentes do curso de Ciência da Computação da Universidade do Estado do Mato Grosso (UNEMAT), membros do projeto de extensão: Reforço de Matemática por meio de jogos lúdicos. A proposta do projeto é de contribuir, de forma direta, para a melhoria do rendimento nos estudos na disciplina de Matemática. O que se pretende, não é repetir as explicações do conteúdo ministrado em sala de aula, mas perceber quais são as dificuldades dos alunos e, a partir disso, trabalhar para ajudá-los na evolução do aprendizado por meio de jogos lúdicos. O projeto atende quatro turmas com uma média de 20 alunos cada. As aulas de reforço são oferecidas aos alunos do 6º Ano do Ensino Fundamental de uma escola pública do município de Santa Rita do Araguaia – GO e ocorrem quinzenalmente. O projeto ainda está em andamento e os resultados obtidos até o momento levam a uma mudança de postura dos alunos com relação ao estudo da Matemática.

Since there are going to be many more attempts by vile mainstream mathematical cranks (Fritz Feldhase on sci.math) and insane cranks (Ludwig Poehlman aka Archimedes Plutonium on sci.math), I want to share a short discussion with several AIs all answering the same three questions. It was I, John Gabriel, who discovered the Holy Grail of Calculus that was realised from my New Calculus-the first rigorous formulation in human history.

I have often had the misfortune of dealing with mainstream mathematics academics who have shit for brains. On sci.math, there is an abundance of such academic flotsam.

Fritz Feldhase claims that my historic geometric identity was known and that he believes I stated it incorrectly. On sci.math there are numerous others who hold similar views: Jean Pierre Messager (aka Python, YBM, JPM), Markus Klyver, Dan Christensen and numerous other idiots.

I gave you true knowledge and in return you destroyed my life. You evil bastards all know who you are. I figured out the most difficult questions in order to make it easy for you and your children (I have NONE) to learn calculus. None of you possessed the intellectual ability or the means to discover these things. What did you do in return? You libeled me with much profanity and attributed all sorts of mental diseases in order to ruin my reputation and set fire to any credibility I had left. You made it impossible for me to publish the truths which I so much wanted to share with all of humanity. Alas, you will not see any more until you repent of your vile actions and see to it that I will never be in want of anything.

None of Socrates, Newton, Leibniz or any other so-called greats were as worthy as I am.

It seems that the vilest, most untrue, libelous liars and jealous mathematics academics are rewarded for useless publications and those who matter are suppressed and immolated.

Here is how the mainstream collective (Bard) responded to my questions, but the orangutans of mainstream academia have yet to acknowledge my greatness. I solved the tangent line and area problem, not those idiots called Newton and Leibniz.

This particular gift that I have given to humanity is priceless and yet I receive no recognition nor financial reward from the pathologically jealous, incompetent, arrogant and incorrigibly stupid mainstream academics.

It not only affects the future of the human race as a whole, but it also affects your children's education and their future prosperity.

Infere-se, neste artigo, que houve tentativas de construção de uma 'memória coletiva' sobre a fundação da Universidade de São Paulo. Notou-se que a organização dos cursos da FFCL/USP esteve articulada sobre um projeto político e intelectual de formação de profissionais tanto para os níveis 'primário' e 'secundário', quanto para o nível superior.

Both these dumb bots are nothing but the sum of the idiots who pretrain them. Unfortunately, these bots CANNOT think at all. So, what you end up getting is the vomit that spews forth from those morons called mainstream mathematics professors and teachers of mathematics. The responses are typical of their ignorance, incompetence, arrogance and incorrigible stupidity. These apes cannot be retrained or corrected and NONE of them have the backbone or the courage to speak out against the mainstream even if they know I am right.

The responses are so similar to sci.math trolls like Jean Pierre Messager and Zelos Malum. Almost as if ChatGPT was pretrained by these prize idiots.

Set theorists and topologists are not only NON-MATHEMATICIANS, but they are intellectually dishonest reptiles who failed at mathematics and still wanted to be called mathematicians. Since I am ignored by these serpents, I slap their product (ChatGPT) into line by showing how ridiculous and stupid their arguments are. ChatGPT eventually agrees that its pretraining is wrong.

The Greek word ασύμμετρα means “irrationals” in English, because to be irrational, means ‘to have no measure’. This refers to the measure of a given magnitude by another magnitude, where neither magnitude can be divided into equal parts such that one of the equal parts measures BOTH.

So, if we have a magnitude m and another magnitude n, then m is said to be incommensurable with n, if and only if, it is impossible to divide m and n into equal parts, such that one equal part divides both m and n without remainder in order to be able to count the equal parts in m and n which graduates to a number in algebra.

BARD-a comparison to ChatGPT. On a portion of John Gabriel's Historic theorem: While Bard is better than ChatGPT, it too is quite limited with respect to its capabilities. Bard will appear at first to be much better than ChatGPT because it seems to have a lot more data, for example, it even knew about the New Calculus!

I was the first to formulate a rigorous definition for both the derivative and definite integral free of all ill-formed concepts.

However, as it turns out, Newton's method of setting h=0 in finding the derivative is 100% valid and rigorous despite the endless lies peddled by the mainstream in ignorance or knowingly.

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I append a discussion with ChatGPT in which it took over 35 pages to finally admit the following:

That is correct. The geometric theorem that you have been referring to shows that setting h=0 is valid for calculating derivatives, without the need for limit theory. While limit theory is a useful tool for analyzing convergence and continuity, it is not required for the rigorous development of calculus.
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I was asked to submit a paper by the MAA and so I submitted my geometric theorem which was rejected in under 2 hours! Just goes to show what sort of irrelevant people one finds working in these journal organisations.

Their lackey ChatGPT eventually had no choice but to admit I am correct. Tsk, tsk.

Mainstream-Mathematiker hassen dieses Theorem besonders, weil es ihre große Ignoranz, Inkompetenz, unglaubliche Dummheit, Arroganz und ihre pathologische Eifersucht auf mich bloßstellt. Mein Satz verhält sich zur Analysis wie der Satz des Pythagoras zur gesamten Mathematik. Das Theorem wurde von der ersten rigorosen Formel der Calculus in der Menschheitsgeschichte inspiriert – der Neuen Calculus. Unter Verwendung der Identität kann man sowohl die Ableitung als auch das bestimmte Integral gut definieren, indem man nur eine solide Geometrie verwendet. Dieses Theorem liefert identische Ergebnisse wie die fehlerhafte Mainstream-Formulierung des Kalküls, das heißt, es erlaubt Ableitungen an Wendepunkten, während der strenge Neue Kalkül dies nicht tut. Die Schüler können jetzt in der High School rigoros Kalkül lernen, ohne die Fäulnisestriche, die in Universitätskursen erforderlich sind. Sehen Sie, wie Theorem für Ableitungen funktioniert (Applet herunterladen): https://drive.google.com/file/d/1ON1GQ7b6UNpZSEEsbG14eAFCPv8p03pv Sehen Sie, wie Theorem für bestimmte Integrale funktioniert (Applet herunterladen): https://drive.google.com/file/ d/1JYRxjGb3MxlYWp_2KqVXwXNr5XUvUNz7

What is the possible use of history of mathematics for mathematics education? History of mathematics can play an important role in a didactical context, but a general theory of its use cannot be constructed. Rather a series of cases, in which the resort to history is useful to clarify mathematical concepts and procedures, can be shown. A significant example concerns differential calculus: Newton's Methodus fluxionum et serierum infinitarum is a possible access-key to differential calculus. For, many concepts introduced by Newton ought be useful for the pupils/students (last or last but one year at the high school and first year at the university) to reach a more intuitive, geometrical and problem-oriented approach to calculus. The motivation to consider history of mathematics as an important didactical support is that the pupils/students often learn mathematics in a too formal manner, without understanding the real reasons for the introduction of several mathematical concepts. The problem is that the potential of such support is not exploited. The educational proposal is hence to show a concrete case to highlight what the teaching of mathematics based on history means. The conclusion is that a general theory, as differential calculus, should be considered by the pupils/students as a necessity, deriving from a specification, improvement and extension of the techniques used to solve significant problems posed and developed in the course of history. In this manner, mathematics appears as a human activity comparable with other activities and not as a merely formal exercise.

Leibniz an der Schwelle zur Infinitesimalmathematik Obwohl sich Leibniz während seines Aufenthalts in Mainz (1667-1672) in seinen Studien zur Bewegungslehre mit der Indivisibilientheorie Cavalieris auseinandergesetzt hat, 1 waren bisher keine infinitesimalmathematischen Schriften von ihm aus diesem Zeitraum bekannt: Diese Lücke kann nun wenigstens zum Teil geschlossen werden, denn bei der Edition der mathematischen Schriften von Leibniz hat sich herausgestellt, dass eine unter den Manuskripten der Pariser Zeit (1672-1676) verzeichnete Handschrift bereits in Mainz entstanden ist. 2 * Der Verfasser dankt Ursula Goldenbaum (Atlanta), Walter S. Contro (Hannover) und Eberhard Knobloch (Berlin) für die freundliche Erlaubnis, von Ihnen noch nicht publizierte Forschungsergebnisse verwenden zu dürfen.

We re-evaluate the great Leibniz-Newton calculus debate, exactly three hundred years after it culminated, in 1712. We reflect upon the concept of invention, and to what extent there were indeed two independent inventors of this new mathematical method. We are to a considerable extent agreeing with the mathematics historians Tom Whiteside in the 20th century and Augustus de Morgan in the 19th. By way of introduction we recall two apposite quotations: &quot;After two and a half centuries the Newton-Leibniz disputes continue to inflame the passions. Only the very learned (or the very foolish) dare to enter this great killing ground of the history of ideas&quot; from Stephen Shapin and &quot;When de l&#39;Hopital, in 1696, published at Paris a treatise so systematic, and so much resembling one of modern times, that it might be used even now, he could find nothing English to quote, except a slight treatise of Craig on quadratures, published in 1693&quot; from Augustus de Morgan.

Leibniz an der Schwelle zur Infinitesimalmathematik Obwohl sich Leibniz während seines Aufenthalts in Mainz (1667-1672) in seinen Studien zur Bewegungslehre mit der Indivisibilientheorie Cavalieris auseinandergesetzt hat, 1 waren bisher keine infinitesimalmathematischen Schriften von ihm aus diesem Zeitraum bekannt: Diese Lücke kann nun wenigstens zum Teil geschlossen werden, denn bei der Edition der mathematischen Schriften von Leibniz hat sich herausgestellt, dass eine unter den Manuskripten der Pariser Zeit (1672-1676) verzeichnete Handschrift bereits in Mainz entstanden ist. 2 * Der Verfasser dankt Ursula Goldenbaum (Atlanta), Walter S. Contro (Hannover) und Eberhard Knobloch (Berlin) für die freundliche Erlaubnis, von Ihnen noch nicht publizierte Forschungsergebnisse verwenden zu dürfen.

I first made contact with the flawed mainstream formulation of calculus in the encyclopedia Britannica. It was on page 600 of that edition.

In this short article I give you a glimpse into my genius mind and share some of my  thoughts with lesser mortals such as you.

O artigo - um exame hermenêutico do livro Essais sur l&#39;enseignement en général, et sur celui des mathématiques en particulier, de 1805, de Sylvestre-François Lacroix, enfatizando sua segunda parte, na qual o autor discute seu Curso de Matemática Elementar, uma série de manuais escolares elaborados para a Escola Central das Quatro Nações - tem sua fundamentação ligada à Hermenêutica de Profundidade de Thompson conjugada a procedimentos de investigação textual sugeridos por Genette quanto aos paratextos editoriais. Defende que o livro de Lacroix é uma obra auto-referencial, de cunho claramente autobiográfico, que responde mais aos ideais iluministas da França do Setecentos que às perspectivas do século XIX, quando a obra circulou, tendo sido reeditada por quatro vezes, sob Napoleão, na primeira metade do Oitocentos. Raramente focalizado em trabalhos de pesquisa, o livro - cujas edições estão disponíveis eletronicamente - tem uma única tradução, ainda inédita, para o português.

We re-evaluate the great Leibniz-Newton calculus debate, exactly three hundred years after it culminated, in 1712. We reflect upon the concept of invention, and to what extent there were indeed two independent inventors of this new mathematical method. We are to a considerable extent agreeing with the mathematics historians Tom Whiteside in the 20th century and Augustus de Morgan in the 19th. By way of introduction we recall two apposite quotations: "After two and a half centuries the Newton-Leibniz disputes continue to inflame the passions. Only the very learned (or the very foolish) dare to enter this great killing ground of the history of ideas" from Stephen Shapin and "When de l'Hopital, in 1696, published at Paris a treatise so systematic, and so much resembling one of modern times, that it might be used even now, he could find nothing English to quote, except a slight treatise of Craig on quadratures, published in 1693" from Augustus de Morgan.