O papel dos indivisiveis para a explicação da velocidade nos Discorsi de Galileu

Abstract

Resumo: Na discussão sobre a causa da coesão entre as partes mínimas da matéria, exposta nos Discorsi (1638), Galileu alude à tese aristotélica conhecida tradicionalmente como horror vacui. Aparentemente, a orientação de Galileu é atribuir a coesão entre as pequeníssimas partes que compõem os sólidos à presença de vácuos intersticiais inextensos. Valendo-se disso e da concepção de que a natureza é constituída e acessada pela linguagem matemática, Galileu estende as propriedades geométricas do ponto aos átomos, considerados as unidades últimas da matéria. Depois, ao tratar das regras do movimento local, tema da terceira jornada dos Discorsi, Galileu usa figuras geométricas para analisar o movimento uniformemente acelerado em termos de proporcionalidade entre espaço, tempo e velocidade, sendo esta última diretamente proporcional ao tempo nos seguintes termos: "a intensificação da velocidade se produz de acordo com a extensão do tempo". Enquanto espaço e tempo são quantidades contínuas medidas de acordo com sua extensão, a velocidade varia em grau ou segundo sua intensidade e, por isso, foi considerada pela tradição que chega até Galileu não como quantidade, mas como qualidade ou quantidade intensiva. A finalidade deste trabalho é utilizar a explicação geométrica da linha composta por infinitos indivisíveis para tratar da representação geométrica da velocidade na terceira jornada dos Discorsi. Esta opção é uma tentativa de compreender como a concepção de velocidade na explicação geométrica do mo imento acelerado seria fundamentada nas relações entre contínuo & descontínuo, divisível & indivisível, por fim, extenso & intenso da primeira jornada.

Abstract: In the discussion on the cause of cohesion between the minimum parts of the matter, exposed in the first journey of Discorsi (1638), Galileo mentions the thesis by Aristotle traditionally known as horror vacui or dislike of nature by vacuum. Apparently, the orientation of Galileo is to allocate cohesion between the very small parts which make up the solids to the presence of interstitial vacuum. Considering this and the idea that nature is lodged and accessed by mathematical language, Galileo extend the geometric properties from the point of atoms, considered the units of last sensitive matter. In spite of continuous, the geometrical dimensions involve indivisible points. Dividing repeatedly a line in increasingly smaller parts, will never be possible to reach its last indivisible unit, which is the point. In fact, the complex of points constituting the lines are continuous totalities, so that, between any two points, it will always be possible to create a line and sign in it another point. On the other hand, since the lines may be higher or lower and both the largest and the minors are composed of infinite points, in a greater one are not included more points which in a smaller, nor the number of them is the same. For Galileo, the relations of higher, lower and equal cannot be established between endless quantities, but only among the finite. In sequence, to deal with the rules of the local movement, theme of the third journey of Discorsi, Galileo makes use of the geometrical figures to analyze the movement uniformly accelerated in terms of proportionality between space, time and speed, the latter being directly proportional to the time in the following terms: "the intensification of speed produces in accordance with the extension of time". While space and time are continuous quantities measured in accordance with its extension, the speed varies degree or according to their intensity and, therefore, it was considered by tradition that reaches Galileo not as quantity, but as quality or intensive quantity. Thus, the different grades of speed in an accelerated movement speed may be represented by means of two areas composed of parallel endless lines, drawn from each point of the line that represents the time. But, if the areas are different, it is not possible to identify the number of lines of an area with the number of lines of the other, since they are drawn from infinite points or points of the amount of which we cannot preach any relationship of equality. Thus, Galileo faced with a kind of paradox concerning the composition of the line and its employment for the representation of the accelerated movement; allocate equality between two infinite quantities. The purpose of this work is to use the geometric explanation of the line composed of infinite indivisible to deal with the geometric representation of the speed in the third journey of Discorsi, in order to understand how speed geometric explanation of the accelerated movement would be based on relations between continuous & discontinuous, divisible & indivisible and lastly, extensive & intense of the first journey.