At the beginning of the first episode of this series I wrote the following:
In popular histories of science in Europe the history of physics is all too often presented roughly as follows, in antiquity there was Aristotle, whose writings also dominated the Middle Ages, until Galileo came along and dethroned him, following which Newton created modern physics.
We have already seen that already beginning in the sixth century CE with John Philoponus, the impetus theory that would be taken up and developed by both Islamic and medieval European scholars offered a strong alternative to Aristotle’s theory of projectile motion. Philoponus, and many others, also questioned his theories of fall and as we have seen in the fourteenth century, the Oxford Calculatores and the Paris Physicists did quite a lot on the laws of fall that is usually credited to Galileo.
What is very often ignored in that Galileo was very much aware of substantial work done on both projectile motion and fall in the sixteenth century on which he built his own theories.
The first scholar to make an important contribution to the physics of motion during the sixteenth century was Niccolò known as Tartaglia (1499–1557). Although, often referred to as Niccolò Fontana, his actual surname is not known for certain. He came from simple circumstances and suffered much tragedy in his childhood. He was born in Brescia, in the Lombardy, the son of Michele a dispatch rider, who was murdered when he was just six years old. In 1512, French troops invaded Brescia and although his family sought refuge in the cathedral, the French troops entered the building and the young Niccolò was slashed across the face with a sabre slicing open his jaw and palate and leaving him for dead. His mother nursed him back to life but he was left with a speech impediment , which earned him the nickname Tartaglia, the stammerer. He grew a beard to cover his scars.
Largely self-taught, he moved to Verona around 1517 and then to Venice in 1534. He earned his living teaching practical mathematics in abbacus schools. A Maestro d’abaco or reckoning master Tartaglia was one of the first to transcend the world of practical mathematics that was common for the period and in which mathematicians were viewed not as scholars but as craftsmen, and in many senses became a mathematician in the modern meaning of the term. This transition of mathematicians from craftsmen to scholars was only truly completed a century later thanks largely to the contributions of Kepler and Galileo.
Tartaglia is, of course, best known as the second mathematician after Scipione del Ferro to discovery a general solution for some forms of the cubic equations, a solution wider ranging than that of Scipione. I wrote about this briefly in the last episode and more fully in two earlier posts, here and here, so I won’t repeat it here. It’s also not directly relevant to the topic of this episode.
As well as his work on the cubic equation, Tartaglia also wrote a typical reckoning mater guide to elementary mathematics his General trattato di numeri et misure, 6 pts. (Venice, 1556–1560).
In the second part of which he includes the triangle of binomial coefficients, known generally as Pascal’s Triangle, who first published it a hundred years later.
One should point out that Peter Apian (1495–1552) had already published it in his Ein newe und wolgegründete underweisung aller Kauffmanns Rechnung in dreyen Büchern, mit schönen Regeln und fragstücken begriffen, in 1527. It was earlier published by al-Karaji (953–1029), by Omar Khayyám (1048–1131). In Arabic it’s known as Kayyám’s Triangle. In China it was first published by Jia Xian (1010–1070) in the early eleventh century, and by Yang Hui (1238–1298) in the thirteenth century were it is known as Yang Hui’s Triangle.
In 1543, Tartaglia produced the first translation of the Elements of Euclid into Italian, which was also the first translation into the vernacular. There was a second edition in 1565 and a third in 1585. It appears that he translated from Latin not Greek and in his second edition he mentions the first translation by Campano, that is the Latin edition of Campanus of Novara ( c. 1220–1296), which was based on the translation of Robert of Chester (12th century) and which became the first printed edition, published by Erhard Ratdolt (1442–1528) in Venice in 1482. However, there is reason to believe that Tartaglia’s translation is actually based on the 1505 Latin translation direct from the Greek of Bartolomeo Zamberti (c.1473–after 1543) published in Venice.
In 1543,Tartaglia also produced a seventy-one page edition of the Latin translation of the works of Archimedes by William of Moerbeke ( between 1215 & 1235–c. 1286), Opera Archimedis Syracusani philosophi et mathematici ingeniosissimi containing Archimedes’ works on the parabola, the circle, centres of gravity, and floating bodies. In 1551, he published an Italian translation of parts of the Archimedes text, part of Book I of De insidentibus aquae. His active interest in Archimedes would have an influence on his one time pupil Giambattista Benedetti (1530–1590), as we will see in a later episode.
Tartaglia’ contribution to the laws of motion were not made in what we would recognise as a work of physics but in what was the first ever mathematical treatise on gunnery or ballistics, which of course is the study of projectile motion. The earliest known mention of gunpowder in European literature is by Roger Bacon in his Opus Major in 1267. Depiction of guns begin to appear in the early fourteenth century. The use of cannons in warfare, particularly during sieges, developed over the fourteenth and fifteenth century. The invention of the gun carriage at the end of the fifteenth century saw the introduction of field artillery and the need for a science of gunnery or ballistics. A need that Tartaglia became the first to fulfil.
Tartaglia’s first published book Nova Scientia (Venice,1537), a tome on ballistics, was in the words of historian Matteo Valleriani:
In 1537, a mathematician from Brescia, Nicolò Tartaglia (1500–1557) published a work entitled Nova scientia. It is this work that established the modern science of ballistics, as characterized by the search for a mathematical understanding of the trajectory of projectiles. Tartaglia’s intentions were to create a science based on axioms and more geometrico, fundamental to the entire subject of mechanics, starting from a limited number of principles and arriving at a series of propositions through a process of rigid deduction. The methodological model Tartaglia intended to follow was the one he was able to extrapolate from works like Euclid’s Elements.
[…]
However, from a wider perspective, more specifically from the perspective of the entire history of the development of mechanics during the Renaissance, Tartaglia’s most important achievement is having demonstrated in 1537 that an exact science of ballistics was possible, based on the application of mathematical and geometrical methods. Challenged by the knowledge and experience of the bombardier, Tartaglia made an enormous contribution to the field of mathematical physics.[1]
The book was very successful and very widely read. There was a second edition published in 1550 with reprints in 1551 and 1558. Further reprints were made in 1562, 1583, and 1606. There were translations into French and English.
Tartaglia wrote a second more widely ranging book including the topic of artillery his Quesiti et Inventioni Diversi published in 1554.
In this work Tartaglia dealt with algebraic and geometric material (including the solution of the cubic equation), and such varied subjects as the firing of artillery, cannonballs, gunpowder, the disposition of infantry, topographical surveying, equilibrium in balances, and statics.[2]
Galileo was influenced by the works of Tartaglia and owned a richly annotated copies of his works on ballistics. These contained the first statement of the theorem that
…the maximum range, for any given value of the initial speed of the projectile, is obtained with a firing elevation of 45°. The latter result was obtained through an erroneous argument, but the proposition is correct (in a vacuum) and might well be called Tartaglia’s theorem. In ballistics Tartaglia also proposed new ideas, methods, and instruments, important among which are “firing tables.”[3]
Although he rejected the theories of Aristotle, Tartaglia’s work was informed by the impetus theory and his projectiles did not fly along parabolic trajectories. Tartaglia’s trajectories were in three segments, first a straight line upwards, then a curve, and finally a fall straight down to earth when the impetus was exhausted and gravity took over.
Through his work on ballistics Tartaglia had a major impact on the physics of projectile motion in the first half of the sixteenth century. It continued to be a major influence in the practical field of gunnery well into the eighteenth century.
Addendum:
Jacopo Bertolotti, Associated Professor of Physics at the University of Exeter posted the following on social media inspired by this post:
If you ever studied any Physics in school you probably know that the trajectory of an object in a uniform gravitational field will be a parabola. But if the drag is not negligible, the trajectory will be much more skewed, and it will fall almost vertically.
[1] Matteo Valleriani, Metallurgy, Ballistics and Epistemic Instruments: The Nova Scientia of Nicolò Tartaglia, Berlin, 2013.
[2] Arnaldo Masotti, DSB
[3] Arnaldo Masotti, DSB