Regular readers of this blog will know that I challenge the big names, big events version of the history of science going into battle for the less well-known figures, who often made highly significant contributions to the progress of science. I often argue that many of these figures should be pulled out from under the shadows of the giants of #histsci and be much better known than they are. If I had to choose a figure in the history of physics in the Early Modern Period, who I thought most deserved to be much better known than he is, then that choice might well fall on the Italian mathematician, Giambattista Benedetti (1530–1590), who formulated much of the theory of falling bodies attributed to Galileo fifty years before Galileo did so.
Very little is known about Benedetti’s origins. He appears to have been born into a wealthy family in Venice. The Italian astrologer and astronomer, Luca Gaurico (1475–1558), famous for his negative horoscope of Martin Luther, said that Benedetti’s father was a Spaniard, philosopher, and physicus, probably meaning student of nature but also possibly meaning physician. According to Gaurico he was mainly educated by his father, who made him a philosopher, musician and mathematician by the time he was eighteen.
In one of the few autobiographical records that we have, he stated that he had received no formal education beyond the age of seven, except that he studied the first four books of Euclid under Niccolò Tartaglia (c. 1499–1557), probably about 1546–1548. The don’t appear to have been close as Tartaglia makes no mention of him as a pupil; Benedetti only mentioning him in 1553 “to give him his due.” In later years Benedetti would severely criticise Tartaglia’s writings.
In 1558, Benedetti became court mathematicus to Ottavio Farnese (1524–1586), Duke of Parma, where he remained for about eight years, serving as court astrologer and engineer. He also made astronomical observations and constructed sundials. In the winter of 1559/60, he lectured in Rome on the science of Aristotle creating a good impression.
In 1567, he became court mathematicus to Emanuele Filiberto (1528–1580) Duke of Savoy, in Turin. Here he taught mathematics and science, and advised the Duke on appointments to the university, although he was never appointed to a professorship himself.
He remained in Turin until his death, as in Parma undertaking engineering projects and constructing sundials. In 1574, he published a treatise on the construction of sundials his De gnomonum umbrarumque solarium usu Liber, the most comprehensive volume on the topic at that time. He also published his De temporum emendatione on the correction of calendars in 1578 but it is his work on the laws of fall that interests us here.
Benedetti’s first excursion into the world of anti-Aristotelian mechanics was surprisingly in a book on Euclidian geometry, his Resolutio omnium Euclidis problematum published in 1553, when he was just twenty-two years old.
This was the book that contained his grudging acknowledgement of Tartaglia. The Resolutio concerns the general solution of all problems in Euclid’s Elements using only a compass of fixed opening. His book displayed his mathematical talent and was superior to similar volumes by Tartaglia and Ludovico Ferrari (1522–1565), a pupil of Cardano. Included in this book was a letter of dedication addressed to the Spanish, Dominican priest, Gabriel de Guzman with whom he had conversed in Venice in 1552. Guzman was interested in Benedetti’s theory of free fall and asked him to publish it. Apparently to avoid his idea being stolen Benedetti now outlined it in the dedicatory letter, although it had nothing to do with Euclidian geometry.
Seemingly based on Archimedes’ work on hydrostatics, On Floating Bodies, which almost certainly came to his attention through Tartaglia’s translation published in Venice in 1551, Benedetti held that bodies of the same material, regardless of weight, would fall through a given medium at the same speed. This contradicted Aristotle’s theory that they would fall at speeds proportional to their weights.
Benedetti asks his reader to imagine two spheres of the same material, one of which has four times the volume of the other. He then says they should reconstitute the material of larger sphere as four smaller spheres each one equal in volume to the small sphere but joined together by a fine wire. The four joined together spheres would fall at the same rate as the single small sphere, end of argument. Astute readers will recognise this is the same argument as the famous thought experiment that Galileo published in his Discorsi in 1638, as a part of the dialog on the First Day:
Salviati. If then we take two bodies whose natural speeds are different, it is clear that on uniting the two, the more rapid one will be partly retarded by the slower, and the slower will be somewhat hastened by the swifter. Do you not agree with me in this opinion?
Simplicio. You are unquestionably right.
Salviati. But if this is true, and if a large stone moves with a speed of, say, eight while a smaller moves with a speed of four, then when they are united, the system will move with a speed less than eight; but the two stones when tied together make a stone larger than that which before moved with a speed of eight. Hence the heavier body moves with less speed than the lighter; an effect which is contrary to your supposition. Thus you see how, from your assumption that the heavier body moves more rapidly than the lighter one, I infer that the heavier body moves more slowly.
This is universally hailed as a sign of Galileo’s scientific genius and very often presented as the prime example of a thought experiment. Wikipedia also describes it as “a significant step forward in the history of modern science.” Galileo first published it, as already noted, in 1638 that’s eighty-five years after Benedetti had published it. To be fair Galileo probably first formulated it around 1590 when he was composing his unpublished manuscript De motu, to which we will return later, but that was still almost forty years later than Benedetti. However, you almost never hear of Benedetti’s formulation let alone hear him being praised for having taken “a significant step forward in the history of modern science.”
In his dedicatory letter to Guzman, Benedetti wrote that he was in the process of writing a book on the topic that he intends to publish soon. In fact, said book, his Demonstratio proportionum motuum localium contra Aristotilem et omes philosophos was published to the beginning of 1554. Benedetti mentions in his dedicatory letter to this book that there was talk of Rome of his work and that as Aristotle could not err his theory must be false. These discussions might explain why another statement on freefall , Giovanni Battista Bellaso of Brescia, question why a ball of iron and one of wood will fall to the ground at the same time, in his II vero modo di scrivere in cifra, mentioned in the previous post in this series, was also published in 1553.
The Demonstratio repeats the arguments made in the dedicatory letter to his Resolutio going into more detail, above all he elucidated the passages in the works of Aristotle that he was contradicting. In the Demonstratio, he also stated that objects in a vacuum would all fall at the same speed, thus contradicting Aristotle’s claim that they would accelerate to an infinite speed. Once again Benedetti is anticipating Galileo by decades with a statement for which Galileo gets praised to the heavens. Spectacular modern demonstrations of this fact in vacuum chambers or on the Moon are always accompanied by the commentary, “look, just like Galileo predicted!”
In 1562, the Wallonian musician, mathematician and astrologer Jean Taisnier (1508–1562) plagiarised the 1stedition of Benedetti’s Demonstratio together with the Epistola de magnete Petrus Peregrinus de Maricourt in his Opusculum perpetua memoria dignissimum, De Natura Magnetis et ejus effectibus, Item De Motu Continuo (“A little work worthy of preservation, On the Nature of the Magnet and its Effects, and another On Perpetual Motion.” He makes no mention of either author and in the dedication talks of “hoc meum parvulum opusculum” – this my little work.
Benedetti drew attention to the plagiarism in the Ad lectorem to his 1574 De gnomonum:
“…ut fecit impurissimus omnium Iohannes Taisnerus Hannonius. Qui opusculum nostrum… ita integrum sibi desumpsit, ut nihil praeter authoris nomen immutaverit; quid enim mutavisset, qui nec percipere poterat quae in ea disputatione continerentur? Homo vanus ab omni mathematica facultate alienus, qui merito propter crassissimam ignorantiam verebatur, ne vel aliqua Syllaba sublata aut addita totius tractationis inficeretur substantia. Credidit (ut opinor) me iam vita functum qui furti nunquam argui posse confidit…” (“as John Taisnier Hannonius did, the most unwholesome of all of them. Who so completely took for himself our little work, that he altered nothing except the name of the author – for what could he have changed, this vain man devoid of all mathematical capability, who was not able to grasp the things contained in that discourse? who justly feared, on account of his very gross ignorance, that by the addition or removal of a single syllable he might undo the meaning of the entire argument. I think he believed that I was already dead, and trusted that I would never be able to denounce his theft…”) Wikipedia
Ironically the Taisnier plagiarism became better known that the Benedetti original. It was even translated into English by the alchemist and cosmographer, Ricard Eden (c. 1520–1577), which was published posthumously in 1579. Simon Stevin quotes and criticises Benedetti on the laws of fall from the Taisnier plagiarism, in the appendix to his book on statics, De Beghinselen der Weeghconst ( “The Principles of the Art of Weighing”) in 1586, where is describes his own experimental confirmation of the laws of fall.
Interestingly, Benedetti published a second modified edition of the Demonstratio on Valentine’s Day, on 14 February 1554. The biggest change in this second edition is that whereas Benedetti had stated in the first edition that different sized bodies fall at the same rate both in a medium and in a vacuum, he now states that this is only valid for a vacuum. This is exactly the point that Stevin, only having read the first edition in the plagiarism by Taisnier, would criticise in 1586. Benedetti who replaced the Archimedean buoyancy with the term resistance also discussed how shape and surface area affected the rate of fall.
Benedetti’s final contribution on the topic took place in his collected work Diversarum speculationum mathematicarum, et physicarum, liber published in Turin in 1585 then reissued as Speculationum mathematiucarum, et physicarum, fertilissimus, pariterque utilissimus tractatus... in Venice a year later. It was published a third time, posthumously as Speculationum liber: in quo mira subtilitate haec tractata continentur... in Venice in 1599. Here he discusses the acceleration of falling bodies in terms of increments of impetus.
For all his inventiveness in contradicting Aristotle and anticipating Galileo, it should be noted that Benedetti’s work on the laws of fall was purely philosophical. He is not known to have carried out any experiments and he makes no mathematical analysis of the topic. However, he very much deserves to be better known and to be given more credit than has been the case in the majority of writings on the topic.