The year 1583 is fundamental for Galileo’s education, especially because he finally gets to know Maths, not as an abstract Platonic category, but rather as a concrete subject matter. However, if Maths seems to him more and more necessary in order to cultivate his interests in Natural Philosophy, his strong interest in “painting, perspective and music”—according to Vincenzio Viviani—pushes the young Medicine student to feel the need to know more about Maths and Geometry (Viviani 2001). Probably, the epistemological discussions about the relationship between Maths and Physics, to which both Buonamici and his father introduced Galileo, help him feel this need. Both Art and Natural Philosophy are inextricably intertwining in the intellectual life of the young student, towards the end of the Renaissance, when its spirit is still moving at the margins of the cultural world.

In any case, Galileo, while on holiday in Florence, without his father knowing, asks Ostilio Ricci, a family friend, who is mathematician at court, to be introduced to the study of Maths. Galileo, who is now 19, thus comes into contact with good Maths and Geometry, and falls in love with it. So much so, that he starts studying in depth Euclides’ Elementi on his own.

Ostilio Ricci from Fermo is a disciple of Nicolò Tartaglia. At the school of this master of Algebra, who has discovered the resolutive formula for the third-degree equations, Ricchi has learned Maths with an engineer’s approach: namely, as Maths applied to Architecture, military art and practical tasks in general. His formation is somewhat similar to that of an experimental mathematician. On the other hand, this experimental approach to Maths had induced Tartaglia to publish several works of Archimedes in Latin.

Ricci, just like his own master, has studied all ancient Mathematics, first of all the great Greeks, such as Euclides, of course. However, once again like his master, Ricci has a marked predilection for Archimedes, in whose works he finds the highest expression of experimental Maths, which he himself cultivates. Therefore he proposes this kind of Maths to his students in Florence, at the Accademia delle Arti del Disegno [Academy of Drawing Arts], established in 1563, where, over and above the fashionable subject of drawing, they teach theory of perspective, Astronomy, Mechanics, Architecture technique, and Anatomy.

Ricci is a progressive and eclectic thinker. He is interested in Hydraulic Engineering and Cosmology. In his opinion, Maths is not an abstract exercise, but rather a way of looking at the world and act in it. Mathematical principles, he says, can very well replace logic, even Aristotle’s logic, both in explaining the sky and the motion of planets, and on a battlefield.

Therefore Ricci teaches applied Maths, and gives his personal testimony of its public utility. He is particularly good in studying military fortifications, and is well paid to give his advice on the construction of the ramparts on the island of If, out at sea near Marseille. This island would become well-known later on, since Dumas chose it as a location for his novel The Count of Montecristo.

This scholar therefore introduces Galileo to the study of Euclides and Archimedes. Indeed, the young student reads and appreciates both Elementi of the former and De sphaera et cylindro of the latter. In this way, he comes into contact both with the purely geometrical thought of Euclides, and with the experimental mathematical thought of Archimedes. As Ludovico Geymonat remarks: “This love for Archimedes will be the most precious heritage which Ricci will hand him down” (Geymonat 1969) In Galileo, the passion for Maths will never be an end in itself. Rather, it will always be accompanied by his interest for sensuous experiences, for measure, for precise drawing, so that:

Maths will appear to him […] since the beginning, as a very powerful tool in order to get to know Nature, to catch its hidden secrets, to translate natural processes into precise, coherent and strictly verifiable speeches. (Geymonat 1969)

Therefore, if Galileo’s approach to the study of Nature will not be Platonic (as Alexandre Koyré states), but rather typical of Archimedes (as Ludovico Geymonat thinks), one should find the reason in this relationship with Ostilio Ricci and the Archimedes’ school of Tartaglia.

Moreover, Ricci feeds Galileo’s passion for drawing, a form of expression which he has learned and studied during his college years in Vallombrosa. He also encourages him to study engineering. The textbook adopted by Ostilio Ricci in order to explain the basis of drawing is Ludi rerum mathematicarum [Mathematical Games] by Leon Battista Alberti.

Leon Battista Alberti is one of the most classical (and brilliant) examples of the Renaissance eclectic artist. He was born in Genova and lived in the fifteenth century, and has been a writer, a linguist, a music critic, a mathematician, an architect, and even a cryptographer (he invented the disco cifrante [cipher disk].

Leon Battista Alberti has also been a theoretician. We might call him a specialist in the relationship between Art and Science. In particular, between Art and Geometry. Indeed, in ad hoc works, he has tried to establish precise rules and canons for painting (De Pictura), sculpture (De Statua), and architecture (De re aedificatoria). In all of these works, there is a constant element: the presence of Geometry. The rules of perspective are proposed in De Pictura in such a rigorous manner that it can be considered the first scientific work on perspective.

As for Ludi rerum mathematicarum, there is a teaching intention in it. The book was written in 1450, but only printed in Venice in 1568, thanks to Cosimo Bartoli. Ostilio Ricci adopted it as a textbook because it contains, in an entertaining fashion, practical problems to be solved, such as calculating the height of a tower, or the depth of a pit, the width of a river, or the area of some ground. The proposed solution is an example of the rigorous use of Maths (mainly Geometry), and of hypothetical-deductive reasoning, which many consider unique in Europe.

This reasoning and usage are already familiar to Galileo—see his discovery of the pendulum’s isochronism. Now, however, he acquires them in a systematic way.

Ricci introduces his students not only to perspective, but also to the basics of Optics. Among the textbooks he uses, we may find Della prospettiva [About Perspective], attributed to Giovanni Fontana, which is one of the most updated books at the time.

With Ostilio Ricci, the young student learns also the first elements of military Engineering: from the techniques of fortifications to the method for calculating the trajectory of bullets.

Finally, thanks to Ricci, the young Galileo refines the practical art of drawing, both through the application of the strict rules of perspective, and with a more and more accurate technique of chiaroscuro. We can see a few examples of these geometrical and artistic skills of the young student in some manuscripts, which date back to 1584. At the margins of those manuscripts, we often find emblems, people, small landscapes, fantastic figures (Tongiorgi 2009a). It is just a series of quick sketches, and yet they show an artistic trait, as well as a deep knowledge of the theory of drawing and its interpreters.

Among so many drawings, analyzed in a monumental work, with over 700 illustrations, devoted to Galileo as a draftsman, the German art historian Horst Bredekamp draws attention to two portraits of women, made in 1584 and contained in a manuscript kept at the National Library in Florence, in which we can see similarities with the painter Luca Cambiaso and the sculptor Bartolomeo Ammannati, who are well-know in the city (Bredekamp 2009)

If the German historian is right, we have the proof that young Galileo bears comparison with the main theoretical and practical themes of contemporary figurative art: namely, the relationship with Geometry, florentine mannerism and scientific drawing.

In this task, he is helped—over and above the books and the ideas of Leon Battista Alberti—by the start of a long friendship with an artist, Ludovico Cardi called “il Cigoli”, whom Galileo meets at the classes of Ostilio Ricci.

Meeting Ludovico Cardi, Called “Il Cigoli”

Ludovico is five years older than Galileo: he was born in 1559 in Cigoli, near San Miniato al Tedesco. He is a painter, but also much more than that—as it was usual at the time, towards the end of the Renaissance. Indeed, he is also a draftsman, a sculptor, an architect, a choreographer, a poet and a musician. Cigoli is also an art critic, who is interested both in colour and perspective (he will publish essays on these topics) in figurative arts, and in the relationship between sculpture and painting. Ludovico also gives life to a movement which proposes a revolution—or at least a profound reformation—of the current style in figurative arts, both in Florence and elsewhere.

Ludovico, who arrived in Florence when he was merely nine in order to study “human letters”, has immediately shown his artistic talent. In 1572, when he is thirteen, on the recommendation of Senator Iacopo Salvati, he starts attending the school of Alessandro Allori, a very well-known painter who is accredited at court. In 1574, when Cosimo I dies, the choreography for his solemn funerals is entrusted to Allori, with whom Cigoli already collaborates. We have the proof that Ludovico still works with his master Alessandro at the start of the 1580s in the decorations of the Uffizi Gallery. On the other hand, Allora is looking for a “understandable” style, a project he shares with Cigoli.

Florence has been the capital of the “modern manner”, the style which—towards the end of the sixteenth century—dominates painting all over Europe. This manner originates at the beginning of the century, as Florence was hosting at the same time three absolute geniuses of figurative arts, namely: Leonardo da Vinci, Michelangelo Buonarroti and Raffello Sanzio. The competition among these three artists, which goes on in the same topics with different interpretations, paves the ground for what Giorgio Vasari defines the “third manner” or the “modern manner” in his famous book Le vite dé più eccellenti pittori, scultori e architettori da Cimabue insino à tempi nostri [The Lives of the best painters, sculptors and architects from Cimabue to our Age], published in 1550 and reprinted in 1568 with the add-on delle vite dé vivi et dé morti dell’anno 1550 insino al 1567 [with the lives of dead or alive artists from 1550 until 1567].

Starting from Cimabue and Giotto, Vasari says, Italian art has developed three different “manners” in order to represent Nature more and more faithfully. With the third and last manner, Leonardo, Raffaello and above all Michelangelo have overcome any old-fashioned manner and Nature itself, thus reaching absolute perfection.

Now figurative arts should take a different route, which does no longer consist in merely representing Nature, since nothing can be added to the achievements of those three geniuses. Rather, figurative arts should become a formal research.

This is why several artists, by the half of the sixteenth century, are looking for an eclectic style, in the effort to reconcile the plasticity of Michelangelo’s figures with Leonardo’s nuances, according to the admirable balance achieved by Raffaello, in the attempt of copying them, through a formal research which, according to the critics, becomes more and more an end in itself.

The proposal of the new “manner” in Florence is welcomed by the restless, somewhat disturbing artists Jacopo Carrucci, called “Pontormo” and Giovanni Battista di Jacopo, called “Rosso Fiorentino”, who break with the past. However, the new “manner” is also represented by Vasari himself, as well as by the Flemish painter and sculptor Jean de Boulogne, called “Giambologna”, as well as Agnolo Bronzino, Francesco Salvati, Benvenuto Cellini, Giovanni Angelo Montorsoli, Baccio Bandinelli, Bartolomeo Ammannati, Bernardo Buontalenti. These artists all have access to the court.

These are doubtless excellent artists. However, some critics say that the new “manner”, which originated as the style of an insurgent faction after 1540, becomes a “regime” manner, which, with its formal exasperation, actually expresses the still image of the Medici’s absolute power (Zuffi 2005).

Perhaps, because of this closeness to power, the new “manner”—which from the Nineteenth century onwards will be called “mannerism”—achieves consensus at the French court too, and later spreads all over European courts. With its precious, aristocratic style, also because of its buyers, the new “manner” had become a cultured art for cultured people.

However, starting from the 1570s, a disciple of the mannerist artist Agnolo Bronzino, Alessandro Allori—Cigoli’s master—represents the best of the new “manner” at court.

Let us go back to Ludovico Carli, a.k.a. “il Cigoli”. Towards the end of the 1570s, he has a few health problems. Apparently, he has caught the so-called “falling sickness” [mal caduco], a form of depression, caused by the prolonged contact with corpses, who are often cut open at the workshop in order to improve their knowledge of anatomy. The empirical fever for direct observations spreads everywhere in Sixteenth century Italy, among the artists too. This happens even among those belonging to the new “manner”, since they do not despise imitating great artists, even in representing nature at its best. In any case, Ludovico must seek a cure, and leaves Florence for a couple of years.

When he comes back, around 1582, he studies with Bernardo Buontalenti, a sculptor and architect belonging to the “florentine mannerism”, as well-known and influential as Allori. In fact, Ludovico had already been a disciple of Buontalenti. They had even began an unfinished painting, S. Francesco di Paola, in the church of San Giuseppe. Now back to Florence, Cigoli can complete it.

Ludovico Cardi started attending the Academy of Drawing in 1578. The painting he made for his admission, Cain and Abele, has been judged the best one among all the paintings submitted. Cigoli is a professional painter, and his artistic production continues in the years he attends the Academy. So much so that, before meeting Galileo, the young student has painted the Vestizione di San Vincenzo Ferrer [Vincenzo Ferrer dressing] and the Cristo al Limbo [Christ in the Limbo], which have been placed in the large cloister of the church of Santa Maria Novella, and the Nascita della Vergine [Birth of the Virgin], in the church of SS. Concezione.

Ludovico is actually becoming popular among the “new” painters, who are opposed to the “manner”, by now considered—in turn—old-fashioned. Like his colleagues, Cigoli defends a very accurate, but growingly naturalistic style, based upon the study of both colour and drawing: that is why Ludovico studies with Santi di Tito, the well-known painter who criticizes mannerist culture and, answering the invitation of the Council of Trento to search for the truth, he proposes an accurate, simple and moderate style.

In looking for the truth and the essence of things, Ludovico is also interested in Anatomy (which he has studied with Allori) and Geometry. This is why he attends the classes of Ostilio Ricci, where he meets Galileo Galilei.

Ludovico’s search is at the same time active, practical and theoretical, and absorbs most of his time. Through this work, Ludovico will become one of the key players in the transition from “manner” to “baroque”. In the meantime, he establishes an independent academy with his friend Gregorio Pagani, in the study of Girolamo Macchietti, where they draw and use colours “from Nature”.

There follow a thousand discussions about the relationship among Art, Maths and Nature, in which Galileo, skilled craftsman and son of a musician, is soon involved.

As it often happens in discussions among friends, they talk about the whole Universe: in this case, they debate the Universe of Art. Ludovico Cardi, for example, is a knowledgeable Dante reader, and has also read works from other poets and novelists. Indeed, he encourages Galileo to follow him along this intellectual path (Chappell 2009). Both of them are also skilled, though amateur musicians. They certainly do not exclude from their discussions Vincenzio’s challenge to his master Zarlino, a challenge which is rather similar to Ludovico’s own challenge to his masters, when he preaches simplicity vs. ornate mannerism. They both want to banish artifice in favour of simplicity.

Both Ludovico and Galileo are interested in the “truth without passion”, namely in a determined, unconditional search for objective and universal truth, both in Natural Philosophy and in Art.

Scientific Drawing

There must have been several discussions between Galileo and Ludovico about scientific drawing, an element of figurative art which dominates this age. According to Giorgio Vasari, scientific drawing is worth the primacy, because it allows a precise formal search in terms of order, composition, perspective vision, balance and chiaroscuro (Tongiorgi 2009).

Drawing, as a technique, has always existed. It has constituted a relevant form of art, at least since the thirteenth century, not only in the field of Architecture. The projects of the facades of the Orvieto Cathedral (1310), and of the Siena Cathedral (1339) are particularly famous, because they represent an excellent architectural design. In the Fifteenth century, the florentine sculptor Vittorio Ghiberti says that “drawing is the basis and the theory of any art.” However, only in the Sixteenth century does drawing cease being a useful and humble servant, in order to become a master of all arts.

In fact, Giorgio Vasari defines drawing as “the father of three arts” rather than their master. In any case, in 1561, Vasari establishes the Accademia delle Arti del Disegno [Academy of Drawing Arts] with the grand duke’s approval. This is an unprecedented act of appreciation for drawing and draftsmen.

In the Sixteenth century, the artists start coming out of their workshops and enter Academies, as a proof of their changed social and intellectual status. The establishment of an Academy which is entirely devoted to drawing, in Florence, a city which is considered as the queen of arts, proves that the primacy of this art form is not only an abstraction.

In the evolution of the role of drawing within the arts, Leonardo da Vinci (1452–1519) has had a leading role, inasmuch as he has used drawing as a tool of scientific research on man, on the natural world and on machines. Leonardo has planned an illustrated anatomy essay in which, through his drawings, he has shown the human body as it really is, rather than as the classic canons of the “ideal body” would have it. Drawing, anatomy and scientific research merge also in the masterpieces of the German artist Albrecht Dürer (1471–1528). The peak of this merging is realized in De humani corporis fabrica [About the human body machine], which was published by Andrea Vesalio in 1543.

This book, illustrated by the tables of the German artist Johann Stephan Calcar, with whom probably Titian also collaborated, gives a definitive contribution to the popularity of scientific drawing—within the primacy of drawing in general. This scientific drawing, apart from Anatomy, is also related to Botanic, Zoology, and, in Tuscany, the Engineering of military fortifications, in which Ostilio Ricci is a master.

Starting from 1577, Jacopo Ligozzi from Verona, called by Francesco I in Florence, is assigned the task—among others—to realize an illustrated atlas of plants and animals. The painter makes a series of such beautiful drawing, pastels and watercolours, that he not only wins the Grand Duke’s gratitude, but also the admiration of several connoisseurs, such as Cardinal Francesco Maria del Monte and the scholar Ulisse Aldrovandi, who is preparing a “Theatre of Nature” in Bologna with 18,000 “different natural creatures”, among which at least 7000 plants. Both the cardinal and the scholar ask Ligozzi faithful copies of the tables he has made for the Grand Duke.

All these events, related to scientific drawing, with all their technical and theoretical implications, touch both Galileo and Cigoli. Not only do they hear of them by attending the Academy of Drawing and meeting Ostilio Ricci. Indeed Galileo also studies them in Pisa, while probably going to the “artistic workshop” near the Giardino dei Semplici, where one of his teachers, namely Andrea Cesalpino, a doctor and botanist, often holds classes. As for Ludovico Cardi, he is a disciple of Alessandro Allori, who dissects corpses in order to obtain realistic models for his anatomical drawings.

Let us leave space to the words of Vincenzo Viviani:

They entertained themselves in drawing with pleasure and admirable results; he was so talented that he used to tell his friends that, if he had been older, he might have chosen painting as a profession. Indeed, he maintained a flair for drawing, and he acquired such a good taste, that his opinion about paintings and drawing was preferred to the one of a professor. Artists such as Cigoli, Bronzino, Passignano, Empoli, who were his friends, often asked for his opinion in developing their stories, placing the various characters, choosing perspectives. They appreciated Galileo’s a perfect taste and an almost supernatural grace in painting, such as they could never find in other professional artists. The well-known Cigoli, who was considered by Galileo as the first painter of their age, attributed most of his good paintings to Galileo’s advice, and said that he had been his own master, as far as perspectives were concerned.

Therefore Galileo does not only try his hand at general drawing and scientific drawing, but also at art criticism (Viviani 2001).

As Galileo writes in a letter addressed to Marco Walser in the month of August 1612, good painting should be expressed through “concept”, “colour” and “drawing”, whereas one should condemn “inlaid painting”, which reminds us of an inlay—namely “small pieces of wood of different colours fitted together […], and yet crudely separate”, like those anamorphic, strained paintings, made by “whimsical painters”, who offer a”confused, disorderly medley of lines and colours” [XI, 308]. In this case, Galileo attacks painters such as Giuseppe Arcimboldo, whose paintings have been realized “through a motley collection of agricultural tools, fruits or flowers of this or that season” [XI, 308]. Summing up, at the school of Ostilio Ricci, Galileo studies drawing, with the remarkable results he will show later on. He also meets Ludovico Cardi and a group of “new painters”, who criticize the excessive formalism of the “manner”. These young painters are looking for a sober style, a balance between “idea” and “nature”. With them, Galileo discusses art and shows a “perfect” taste and an evident “supernatural grace”, so much so that he becomes their theoretical reference point: a teacher of teachers.

One of these painters, perhaps Domenico Cresti, also known as Passignano, paints an unfinished portrait of young Galileo. Another painter, Santi di Tito, paints him at forty “with an authoritative attitude”, in a painting which was unfortunately lost, but reproduced in a later engraving (Tongiorgi 2009a).

Therefore in these months, Galileo shows yet another aspect of his Renaissance eclecticism, namely amateur painter and art critic, as Erwin Panofsky will define him with a deep critical insight (Panofsky 1956).

This eclectism will not prevent Galileo from becoming a pioneer of the “New Science”. Quite the opposite. Indeed, as we shall try to show, this will help him “break the seas” of history, according to the metaphor of Ernst Cassirer (Cassirer 1963).

Return to Florence

Let us not forget Ostilio Ricci and his role in Galileo’s life. The court mathematician, indeed, has a long-range cultural influence on Galileo and his view of the world. Moreover, he affects him in his immediate, concrete life. Indeed, Ostilio Ricci is so struck by Galileo’s enthusiasm for Maths, that he decides to talk about it with his father, so the he can continue to attend his classes. Vincenzio approves, as long as these classes are not too frequent and intense that they distract the student from his Medicine studies.

In the meantime in Pisa, they notice Galileo’s absence from the classes. The University management, for opposite reasons with regard to Ricci, decide to contact his father. This is probably one of the moments of major tension between Vincenzio and Galileo. It is time to decide the young man’s future. Galileo has clearer ideas about this in comparison with his father. In any case, he is much more determined than him. The point is that Galileo manages to convince Ostilio Ricci to talk with his father and let him leave the study of Medicine in Pisa, and devote himself to the study of Maths under his guide.

In 1584, Vincenzio is going to publish a new work in Florence, Tenore dé contrappunti a due voci di Vincenzio Galilei nobile fiorentino [Tenor of two-voice counterpoints by Vincenzio Galilei, a nobleman from Florence]; he does not feel like resisting his son’s will, or perhaps he just does not want to do that.

Galileo’s first biographers believed in the idea of a “thwarted vocation” of the boy who wanted to study Physics and was forced to follow Medicine classes instead. However, this is typical of some romanticized biographers of the time. The biographer of Benvenuto Cellini has described a boy forced to study music by his father; the biographers of Carlo Goldoni described a boy who was forced by his father to study philosophy. Things are rather different for Galileo. His father doubtless pushed him to enrol to the Faculty of Medicine. But it is also certain that he does not resist his son’s decision to go back home without a degree.

The point is that Vincenzio has easily been convinced by Ricci, as Ricci himself has easily been convinced by Galileo, whose arguments are based upon his learning progress and usage of Maths—Geometry in particular—which are as deep as quick.

As a consequence, for about one year, Galileo stays in Florence in a sort of limbo: officially, he is still enrolled at the University of Pisa; in fact, he only attends Ricci’s private classes, from the ancient Euclides and Archimedes down to the modern Leon Battista Alberti. Galileo devours all maths topics, from pure geometry to the theories of perspective and measuring techniques. He studies with intensity and passion, and gives excellent results. After a while, he manages to study the topics in depth on his own. In front of his progress, his father surrenders, and lets him leave the university without a degree, in order to devote himself entirely to his beloved studies.

Therefore in 1585, Galileo asks his father “not to divert him from his purposes, since he feels driven by his inclination”. Therefore Vincenzio Galilei , who has never been diverted by anyone from his inclination, once ascertained that his son is “born for Maths”, accepts that he officially leaves Pisa without either completing his studies or getting a degree (Viviani 2001).