The Mathematical Practices Of John Staticus, By George Pitcairne

The evidence for assuming the dispute as a debate of theories and methodologies and not only as a debate of therapies is in the by-products emerged as consequence of the dispute. After Pitcairne’s publication of his answer to Brown, a brief anonymous manuscript appeared, entitled Apollo mathematicus –which Cunningham attributes to Eizat-. In it, the author criticizes the mathematical approach developed in physics and physiology. By contrast, he praised the value of the Aristotelian qualitative explanations, which he relates to a Galenic medicine and a Sydenhamnian empiricism. As a response for this manuscript, Pitcairne publishes his Apollo staticus (1695), a translation of his lecture in Leyden about fevers, where he extends the demonstration
One of the most interesting and revealing is the one of George Cheyne, appeared in his book A new theory of continual fevers in 1701. Interestingly, Cheyne advanced Pitcairne’s ideas in a more mathematical fashion, developing a strong iatromathematical position founded on the use of Newton’s forces and his methodology. Since the preface of his work, Cheyne reveals the mechanical character of his physiology and its mathematical implications. For him, the human body is nothing but a set of ‘branching and winding’ canals, through which different liquors are flowing constantly. As Cheyne explains, a disease is the consequence of a malfunctioning of the mechanical system of the body and, because of this, any treatment should be gathered from the experimental data provided by the anatomical studies and the mathematical analysis that the physiologist
Explained in a geometrical way, Cheyne begins establishing a couple of Postulata and Lemma, deducing from them a general proposition, where he explains the cause of the fevers. In the Postulata I, Cheyne defines the body as ‘nothing but a congeries of canals, the greatest (at least considerable) part of which is Glands, properly so called, design’d for the separation of some fluid’ (Cheyne, 1701: 1). The evidence of this postulata is intuitive and it is based on the observation of the swelled parts of the body and Leuwenhoek’s and Malpighi’s microscopic observations. The Postulata II establishes the mechanical character of Cheyne’s analysis by means of the use of the metaphor of the machine: ‘That when a machine is disordered, if we should see it righted by adjusting such a particular part, we might without scruple affirm, that it was some injury done to that part, which had dissorder’d the machine’ (Cheyne, 1701: 2). By comparing the body to a machine, Cheyne provides a holistic conception of the body, where every part is intimately related to each other. Wherefore, the malfunctioning of a part may produce the malfunctioning of the entire body. In this conception of the body, the determination of the specific place of the disease is possible for the healing process. From the Postulata, Cheyne