THOMAZ, ALVARO

(also known as Alvaro Tómas or Alvarus Thomas

(b. Lisbon, second half of the fifteenth century; place and date of death unknown)

physics, mathematics.

Biographical data on Thomaz are lacking, save that he was regent of the Collège de Coqueret at Paris on 11 February 1509, as indicated in the colophon of his principal work, and that he is mentioned in the archives of the University of Paris as a master of arts at the same college in 1513. Thomaz is noteworthy for his Liber de triplici motu proportionibus annexis . . . philosophicas suiseth calculationes ex parte declarans (“Book on the Three [Kinds of] Movement, With Ratios Added, Explaining in Part Swineshead’s Philosophical [i.e., Physical] Calculations”), printed at Paris in 1509. This work shows Thomaz to be a mathematician and physicist of considerable ability who understood and organized the teachings of fourteenth-century English calculators and Parisian terminists, such as Oresme, making them available to a wide audience of European scholars in the sixteenth century.

Thomaz’ work is divided into three parts, the first and second of which are compact expositions of ratios and proportions respectively, while the third is a lengthy application to problems concerning motion. This last part treats, in turn, local motion, augmentation, and alteration. Although designed as a guide to the thought of Richard Swineshead, Thomaz’ treatise is not patterned after Swineshead’s Liber calculationum (“Book of Calculations”), but follows instead an ordering suggested jointly by Thomas Bradwardine’s Tractatus de proportionibus (“Treatise on Ratios”) and by William Heytesbury’s Tractatus de tribus praedicamentis (“Treatise on the Three Categories”). The first two parts seem to have been inspired by the inferior work of a certain Bassanus Politus, Tractatus proportionum introductorius ad calculationes Suisset (“Treatise on Ratios, an Introduction to Swineshead’s Calculations”), printed in Venice in 1505, a work that Thomaz effectively castigated as worthless.

Thomaz’ citation of authorities was extensive. His mathematics was drawn mainly from Nicomachus, Boethius, Johannes Campanus, and Jordanus de Nemore, while for Euclid he cited “the new translation of Bartholomeus Zambertus.” Among the Schoolmen he referred to Thomas Aquinas (and his commentator, Capreolus), Robert Holkot, Duns Scotus, Albert of Saxony, Marsilius of Inghen, Gregory of Rimini, and John Maior. He knew too of the work of Paul of Venice, James of Forli, Cajetan of Thiene, John de Casali, Andrew de Novo Castro, Peter of Mantua, and a writer whom he identified as the Conciliator (Pietro d’Abano). Above all he was conversant with the complex details of Bradwardine’s, Heytesbury’s, and Swineshead’s writings, and also with the little-un-derstood De proportionibus proportionum (“On the Ratios of Ratios”) of Oresme. Edwrd Grant states in his edition of the lattÉr work: “Alvarus is the only author known to me who shows an extensive acquaintance with, and understanding of, Oresme’s treatise” (p. 71).

Thomaz manifested some originality and considerable independence of judgment, as witness his rejection and reformulation of many of Swineshead’s and Oresme’s propositions. His treatment of falling bodies was highly imaginative in terms of the types of motive forces and resistive media discussed, but unfortunately was diffuse and inconclusive; contrary to what some scholars have suggested, it contains no explicit adumbration of Galileo’s law of uniform acceleration. Thomaz showed facility in the summation of series, generally indicating when they converge and when they do not and, in cases where he cannot determine a precise value, providing limits between which this value must lie.

The influence of Thomaz’ work is difficult to assess. Through his colleague at Coqueret, Juan de Celaya, he seems to have assisted in the formation of Celaya’s late disciple. Domingo de Soto, who was the first to apply unequivocally the Mertonian “mean-speed theorem” to the case of falling bodies. Thomaz’ treatise was cited by many Spaniards, fovorable by the Salamancan masters Pedro Margallo and Pedro de Espinosa and by the Dominican Diego de Astudillo, and unfavorably by the Augustinian Alonso de la Veracruz, who blames Thomaz’ “calculatory sophisms” for much wasted time (and midnight oil) on the part of students in arts. At Paris, however, there can be little doubt that Thomaz was the calculator par excellence at the beginning of the sixteenth century, and the principal stimulus for the revival of interest there in the Mertonian approach to mathematical physics.

BIBLIOGRAPHY

I. Original Work. Thomaz’ Liber de triplici motu. . ., is unavailable in translation; a copy of the original is in the library of the University of Michigan.

II. Secondary Literature. For discussions of Thomaz and his work, see Pierre Duhem, Études sur LÉonard de Vinci, III (Paris, 1913), 531–555, 557, 561; J. Rey Pastor, Los matemáticos españoles del siglo XVI. Biblioteca scientia no. 2 (Toledo, 1926), 82–89; Edward Grant, ed. and trans., Nicole Oresme: De proportionibus proportionum and Ad pauca respicientes (Madison, 1966), index; and William A. Wallace, “The ‘Calculatores’ in Early Sixteenth-century Physics”, in British Journal for the History of Science, 4 (1969), 221–232.

William A. Wallace, O.P.