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| Richard Swineshead |
Richard Swineshead (Swyneshed; on the Continent, more commonly Suiseth) is the name now commonly ascribed to the author of the Book of Calculations (Liber Calculationum) although in various manuscripts and printed editions he is also given the first names John, Raymund, Roger, and William, among others.
Based on the work of James A. Weisheipl, a different person with the name Roger Swyneshed, who was a Benedictine monk at Glastonbury, is now credited with writing a work that is in some ways similar, titled Descriptions of Motions or On Natural Motions (Descriptiones motuum or De motibus naturalibus) dated to the mid-1330s and found in Erfurt manuscript Amplonian F 135, ff. 25va–47rb.
This same Roger Swyneshed is credited with logical works On Insolubles and On Obligations (De insolubilibus and De obligationibus) connected to standard academic exercises within medieval universities. If the same person wrote all of these works, then his views must have matured and changed considerably between the writing of the various works.
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| James A. Weisheipl |
The following entry will be limited to a discussion of the author of the Book of Calculations. Those interested in the history of logic should turn first to the articles, listed below, by Paul Spade on Roger Swyneshed’s works.
Documentary evidence indicates that Swineshead was a fellow of Merton College, Oxford, probably in 1340—certainly in 1344—and again in 1355.Manuscript copies of the Book of Calculations are often incomplete and arranged differently from the printed editions.
The work shows clear influence of Thomas Bradwardine’s On the Proportions of Velocities in Motions (1961 [1328]) and of William Heytesbury’s Rules for Solving Sophisms (1494 [1335]). Influence of the Book of Calculations begins to show up in Paris before 1350.
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| Roger Swyneshed |
Through the early sixteenth century, the work was widely studied on the Continent, in Italy and Spain as well as France, leading to various propedeutic works explaining its methods to potential readers. G. W. Leibniz several times recommended that the book be reprinted, both as a gem of the early history of printing and because the author was among the first to introduce mathematics into natural philosophy or metaphysics.
To that end Leibniz went so far as hire someone to copy the Venice, 1520, printed edition by hand in preparation for the reprinting. Although Leibniz’s project never came to fruition, the hand copy still exists in the Niedersächsische Landesbibliothek in Hannover, Germany.
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| G. W. Leibniz |
In the printed versions of the Book of Calculations there are sixteen treatises, which cover:
I. Intension and remission of forms.
II. (Measures of) difform qualities.
III. Intensity of elemental bodies having two unequally intense qualities.
IV. Intensity of mixed bodies.
V. Rarity and density.
VI. Augmentation.
VII. Reaction.
VIII. Powers of things.
IX. Difficulty of action.
X. Maxima and minima.
XI. Place of an element.
XII. Light sources.
XIII. Action of light sources.
XIV. Local motion.
XV. Motion in nonresisting media (in media with varying resistances).
XVI. Induction of the maximum degree.
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| William of Ockham |
What these treatises have in common is an effort to attach quantitative measures to physical entities. Swineshead first tries to establish scales of measure for static magnitudes, such as intensities of heat and cold. He then attempts to measure speeds of change in the three categories in which medieval Aristotelians believed motion to occur, namely place, quality, and quantity.
Treatise XIV, on dynamics, assumes the truth of Bradwardine’s rule stating that the velocities in motions depend on the ratios of forces to resistances, using a special sense of the variation of ratios connected with the notion of compounding ratios used in Euclid’s Elements (Book VI, proposition 23).
The Book of Calculations represents a stage in medieval intellectual development in which logic (including the theory of supposition) together with mathematics begin to move physics from the matrix of natural philosophy to the status of an exact science.
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| Edith Sylla |
Most of the treatises of the Book of Calculations follow the standard scholastic format in which arguments are given for and against competing opinions before Swineshead settles on and argues for the theory he believes to be more correct.
Like Heytesbury’s Rules for Solving Sophisms, the Book of Calculations seems to have been composed to provide university undergraduates with the analytical tools they needed to participate in disputations. As such, it is a good text to use for learning about the concepts and tools of fourteenth-century natural philosophy, including mathematics.
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| Richard Kilvington |
Although the book does not expound its natural philosophical, let alone its metaphysical, foundations in detail, Swineshead appears to have agreed with the other Oxford Calculators, who (with the exception of Walter Burley) adopted the Scotistic addition theory of qualitative change and favored the ontological parsimony usually associated with William of Ockham.
For more detail on the logical tools assumed by Swineshead, one should look to the work of Heytesbury, and for the natural philosophical background, to John Dumbleton’s Summa logicae et philosophiae naturalis, as described in the work of Edith Sylla (1991b). A final fourteenth-century Oxford scholar whose work is related to that of Swineshead is Richard Kilvington, on whom there is significant recent scholarly work.
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| Oxford Calculators |
