London, [for] William and John Innys, 1720
Newton's protégé. First edition, very rare in commerce, of Maclaurin's first book, dedicated to Newton and bearing his imprimatur as president of the Royal Society. Maclaurin is best known for his Treatise of Fluxions (1742), 'the earliest logical and systematic publication of the Newtonian methods. It stood as a model of rigor until the appearance of Cauchy's Cours d'Analyse in 1821' (DSB).
Maclaurin, who taught at Aberdeen, was brought to the attention of Newton's circle in London early in his career when he published two papers on the construction and mensuration of curves. 'He was admitted to membership in the Royal Society (1719), and often visited Newton, who encouraged him to publish the rest of his work on the description of curves. MacLaurin did so in his first major book, the Geometria organica, which was published under Newton's imprimatur in 1720. In its dedication and preface MacLaurin praises his patron Newton for having determined the proper relationship between mathematics and natural philosophy, and he defends and justifies the pursuit of pure geometry' (Oxford Dictionary of National Biography).
The Geometria organica 'treats curves from the point of view of their theoretical construction by means of abstract instruments. MacLaurin uses this method to generalize the Newtonian organic generation of conics to all orders of curves, and applies it to the classification of curves on the model of Newton's Enumeratio linearum tertii ordinis. Among other things in this treatise, he invents pedal curves, he states Cramer's paradox, thirty years before Cramer published it and attributed it to MacLaurin, he describes many of the particular curves thought to have been discovered in the nineteenth century, and he treats many applications to mechanics, including problems of centripetal forces and motion in resisting media. The influence of Geometria can be seen in the work of the later geometers Poncelet, Chasles, Steiner, Grassmann, and Salmon. Also in 1720, MacLaurin published De linearum geometricarum proprietatibus, in which he studies the curvature and harmonic properties of curves, and properties of their tangents and secant lines. Poncelet was to make extensive use of this work in his Traité des propriétés projectives des figures (1822) (ODNB).
First edition; 4to (23.1 x 18.2 cm); [10], 139, [1] pp., contains 12 folding engraved plates, woodcut initials, woodcut head- and tailpieces, plates browned, light spotting confined mostly to endpapers; Contemporary full vellum with gilt lettering to spine, red speckled edges, some soiling to boards, corners slightly rubbed. Overall, a very good, wide-margined copy.
Maclaurin, who taught at Aberdeen, was brought to the attention of Newton's circle in London early in his career when he published two papers on the construction and mensuration of curves. 'He was admitted to membership in the Royal Society (1719), and often visited Newton, who encouraged him to publish the rest of his work on the description of curves. MacLaurin did so in his first major book, the Geometria organica, which was published under Newton's imprimatur in 1720. In its dedication and preface MacLaurin praises his patron Newton for having determined the proper relationship between mathematics and natural philosophy, and he defends and justifies the pursuit of pure geometry' (Oxford Dictionary of National Biography).
The Geometria organica 'treats curves from the point of view of their theoretical construction by means of abstract instruments. MacLaurin uses this method to generalize the Newtonian organic generation of conics to all orders of curves, and applies it to the classification of curves on the model of Newton's Enumeratio linearum tertii ordinis. Among other things in this treatise, he invents pedal curves, he states Cramer's paradox, thirty years before Cramer published it and attributed it to MacLaurin, he describes many of the particular curves thought to have been discovered in the nineteenth century, and he treats many applications to mechanics, including problems of centripetal forces and motion in resisting media. The influence of Geometria can be seen in the work of the later geometers Poncelet, Chasles, Steiner, Grassmann, and Salmon. Also in 1720, MacLaurin published De linearum geometricarum proprietatibus, in which he studies the curvature and harmonic properties of curves, and properties of their tangents and secant lines. Poncelet was to make extensive use of this work in his Traité des propriétés projectives des figures (1822) (ODNB).
First edition; 4to (23.1 x 18.2 cm); [10], 139, [1] pp., contains 12 folding engraved plates, woodcut initials, woodcut head- and tailpieces, plates browned, light spotting confined mostly to endpapers; Contemporary full vellum with gilt lettering to spine, red speckled edges, some soiling to boards, corners slightly rubbed. Overall, a very good, wide-margined copy.
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