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To the most Distinguished and Worthy gentleman and most Skilled Mathematician, Dr William Oughtred Rector of the church of Aldbury in the county of Surrey

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The Arithmetic of Infinitesimals

Abstract

Here for you at last (most distinguished gentleman) is now the whole of that work of which I gave hope in that proposition on circle measurement that I gave you in its stead in print last Easter (see Figure 1). For since, by custom, when one puts something out in public, it ought to be dedicated to someone, I thought to seek not only a great gentleman but a great mathematician to whom I might offer it. And therefore I saw that to none other greater than you can that easily be done, who is among mathematicians most deserving, and also by whose writings I readily confess that I have profited: who indeed in your Clavis mathematicae, though not a large work, have there taught both briefly and clearly, what we seek in vain in the large volumes of others.1

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References

  1. William Oughtred, Arithmeticae… quasi clavis est, London 1631.

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  2. Wallis himself translated the title as ‘Arithmetick of Infinites; for discussion of the title and its translation see Introduction p. xvii.

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  3. Bonaventura Cavalieri, Geometria indivisibilibus continuorum nova quadam ratione promota, Bologna 1635;

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  4. Evangelista Torricelli, Opera geometrica, Florence 1644.

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  5. Wallis did not know Roberval’s ‘Traite des Indivisibles’, which was not published until 1693. See Introduction p. xiv and note 15.

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  6. Fermat had done this, but Wallis was ignorant of it, see Introduction p. xiv and note 15.

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  7. Grégoire De Saint-Vincent, Opus geometricum quadraturae circuli et sectionum coni, Antwerp 1647.

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  8. Christiaan Huygens, Theoremata de quadratura hyperbolae, ellipsis et circuli... Quibus subjuncta est Exetasis cyclometriae G. a S. vincentio, Leiden 1651. Wallis’s copy of Huygens’ Theoremata de quadratura and of his De circuli magnitudine inventa of 1654 are both bound in Bodleian Library Savile G.26.

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  9. Thomas Hobbes, Elementorum philosophiae; sectio primo de corpore, London 1655.

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  10. John Wallis, Elenchus geometria Hobbianae… refutatio, Oxford 1655.

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Wallis, J. (2004). To the most Distinguished and Worthy gentleman and most Skilled Mathematician, Dr William Oughtred Rector of the church of Aldbury in the county of Surrey. In: The Arithmetic of Infinitesimals. Sources and Studies in the History of Mathematics and Physical Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4312-8_1

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  • DOI: https://doi.org/10.1007/978-1-4757-4312-8_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-1922-9

  • Online ISBN: 978-1-4757-4312-8

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