Download MacLaurin's Physical Dissertations by Ian Tweddle PDF

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By Ian Tweddle

The Scottish mathematician Colin MacLaurin (1698-1746) is healthier identified for constructing and increasing Newton's paintings in calculus, geometry and gravitation; his 2-volume paintings "Treatise of Fluxions" (1742) was once the 1st systematic exposition of Newton's equipment. it truly is popular that MacLaurin used to be provided prizes through the Royal Academy of Sciences, Paris, for his previous paintings at the collision of our bodies (1724) and the tides (1740); despite the fact that, the contents of those essays are much less primary - even if many of the fabric is mentioned within the Treatise of Fluxions - and the essays themselves usually difficult to acquire. This booklet offers those vital works in translation for the 1st time, preceded by means of a translation of MacLaurin's MA dissertation on gravity (Glasgow, 1713) which gives proof of his early learn of Newtonian principles.In his primarily descriptive dialogue of gravity MacLaurin levels over planetary orbits, vortices and theology. His dialogue of collisions features a disputatious account of what could be understood by way of the strength of a relocating physique, a contentious subject on the time. The essay at the tides has the unique model of his celebrated theorem at the equilibrium of a spheroidal fluid mass and employs a awesome blend of geometry and calculus to figure out forces of attraction.The goal is to make this fabric extra often obtainable to researchers and scholars in arithmetic and physics, and certainly to someone with an curiosity within the ancient improvement of those topics. A common advent places the works in context and provides an summary of MacLaurin's occupation. every one translation is then followed through an advent and a sequence of notes and appendicesin which person effects are analysed, either in sleek phrases and from a old perspective. historical past fabric can be supplied.

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Translation of MacLaurin’s Essay DEMONSTRATION OF THE LAWS OF THE COLLISION OF BODIES. 69) SECTION I. Where we present the Axioms and Principles which are in no way disputed concerning the motion of bodies. I. Every body at rest remains in this state until some extraneous cause sets it in motion; and every body in motion continues to move in a straight line, without changing its velocity, as long as no extraneous cause acts on this body. II. The change of force, that is to say, its increase or decrease, is always proportional to the applied force, and takes place in the direction of this force.

We note in particular that Wren had dealt with perfectly elastic collisions, his results being in agreement with corresponding results of Huygens, who also gave equation (vi). In fact, Huygens had already completed a treatise on motion and collision in 1656, although it was only published posthumously in 1703 (see [57]); the rules which he presented in [59] were also published about the same time in [58]. 25 The study of collisions was at the centre of a major controversy over what should be understood as the force of a moving body.

It was read before the Royal Society in March or April, 1741, and had been printed in the Philosophical Transactions, had I not desired the contrary. Certainly, Simpson’s methods, based on clever manipulations of infinite series, are quite different from MacLaurin’s geometrical approach. However, as noted by Todhunter [103, Article 247], the gist of MacLaurin’s work, in particular his Fundamental Theorem on the equilibrium of fluid bodies, had already appeared in his prize essay, predating the Treatise of Fluxions [69], to which Simpson alludes.

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