De subtilitate. Libri XXI. Ad illustriss. Principem Ferrandum Gonzagam, Mediolanensis provinciae Praefectum.

Nuremberg: Johann Petreius, 1550.

First edition of Cardano’s encyclopaedic survey of the sciences. This “was the most advanced presentation of physical knowledge up to its time. It contains many remarkable observations and ideas, including Cardano’s distinction between the attractive powers of rubbed amber (electric) and the lodestone (magnetic), his pre- evolutionary belief in creation as progressive development, and the premise that natural law was unified and could be known through observation and experiment” (Norman catalogue). This work, “written in an elliptical and often obscure Latin, contains a little of everything: from cosmology to the construction of machines; from the usefulness of natural sciences to the evil influence of demons; from the laws of mechanics to cryptology. It is a mine of facts, both real and imaginary; of notes on the state of the sciences; of superstition, technology, alchemy, and various branches of the occult. The similarities between the scientific opinions expressed by Cardano … and those of Leonardo da Vinci, at that time unpublished, have led some historians, particularly Pierre Duhem, to suppose that Cardano had used Leonardo’s manuscript notes … Be that as it may, Cardano must always be credited with having introduced new ideas that inspired new investigations” (DSB). Cardano defines metals as solids that can be melted and, once melted, will harden upon cooling. He distinguishes two sorts of air, “one being destructive of inanimate objects and supportive of animate ones, and the second being destructive of animate objects and supportive of inanimate ones” (Parkinson). “In mechanics, Cardano was a fervent admirer of Archimedes. He studied the lever and inclined plane in new ways and described many mechanical devices, among them ‘Cardano’s suspension’ … Cardano followed a middle road between the partisans of the theory of impetus and the supporters of the Aristotelian theory, who attributed the movement of projectiles to pushing by the air … Notable is his observation that the trajectory described by a projectile is not rectilinear at the center, but is a line "which imitates the form of a parabola”. Cardano’s chief claim to fame, however, was his affirmation of the impossibility of perpetual motion, except in heavenly bodies. “Cardano’s contributions to hydrodynamics are important: counter to contemporary belief, he observed that in a conduit of running water, the water does not rise to the level from which it started, but to a lower level that becomes lower as the length of the conduit increases. He also refuted the Aristotelian ‘abhorrence of a vacuum’, holding that the phenomena attributed to this abhorrence can be explained by the force of rarefaction. Cardano investigated the measurement of the capacity of streams and stated that the capacity is proportional to the area of the cross section and the velocity” (DSB). ABPC/RBH list only two copies in the last 40 years, both with significant condition issues (including the Norman copy, in a modern binding and with significant paper restoration). The Honeyman copy, in a 19th century binding, made £3,000 in 1979.

Cardano’s De subtilitate came to him in a recurrent dream in 1547; it is one of two works (the Dialectica, conceived in 1559-60, being the other) which sets out to be a comprehensive (if allusive) account of a whole field of knowledge … The De subtilitate is part of a series of four works (together with the De fato of 1533, the Arcana aeternitatis of 1538 and the De rerum varietate of 1552-3), all written not for a popular audience but for the learned. Together they constitute Cardano’s comprehensive account of all of nature, cosmology, and human activity. These are not texts which rely on auctoritates, although they recognize the virtues of past thinkers: in the case of Galen, his method (that of the Ars parva), various of his precepts, and his mode of argumentation, and in the case of Aristotle his ‘experimenta’ and to some degree his logic. From the outset, Cardano makes a clear distinction between Aristotle the student (but not the theorist) of nature and Aristotelians, who elevate him to the status of authority, and who are described as intellectually incompetent. Cardano insists from the beginning on the priority of res over verba, of experience over theory, and on the correct trajectory from experiment to ‘rationes’, demonstration, and finally ‘declaration’ (the substantive doctrine proposed in the De subtilitate). He contrasts this work with his Contradicentia medica of 1548, where he claims still to use ancient writings as authorities. He certainly refers to authorities in the De subtilitate, using the formulae ‘teste Galeno,Aristotele, authoritas Hippocratis’, but what he is referring to is their record of ‘experientia’, not their theories. For him, reliance on the word of any master is both pusillanimous and misguided: the practice of extracting meaning about the world from authoritative texts through commentary, he claims, has blighted 2000 years of natural philosophical enquiry: ‘for as peripatetic philosophy has been with us for 2000 years and has been celebrated by so many commentaries, but, on the other hand, the piety with which it has been treated has in truth been only damaging, and it has produced so little fruit in the investigation of nature and the arts in comparison with our discoveries, that it is now agreed to be false about nature or to have interpreted it wrongly.’

“The novel doctrine of the De subtilitate is still recognizably a revision of Aristotelian physics, even if the number of elements and qualities has changed. There is a clear commitment to Galen’s functionalist approach to nature and human physiology, but it is not unreflecting: Cardano is aware of the Epicurean arguments about chance and nature, which he explicitly rejects. Because of the global compass of the De subtilitate, Cardano has to negotiate an awkward frontier with theology. He seriously mismanaged this in the first edition of the De subtilitate in his discussion about religions, by suggesting at one point that they were all equipollent. That sentiment (‘his arbitrio victoriae relictis’) caused outrage, and was duly eliminated from the second edition of 1554, which contained many other revisions and corrections” (Maclean).

Cardano organized his text along the same principle used in the arrangement of the writings of Aristotle, dividing the work into four parts and twenty-one books. In the first part, composed of 7 books, specific problems of natural philosophy are analysed; this provides the background to what is to come in the following books, which will study nature in its basic elements:

Book I: Principles, matter, form, vacuum, opposition of bodies, natural motion and place;

Book II: Elements, their motions and actions;

Book III: The heavens;

Book IV: Light (natural and artificial)

Book V: Mixing and the imperfect or metallic mixed [bodies]

Book VI: Metals

Book VII: Stones

In Books I and II, “Cardan makes what seem some rather exaggerated statements for his time concerning artillery. Having discussed the great force contained in thunderbolts, he asserts that they have been thrown into the shade by recent cannon which can down an entire tower at one blow and throw sixty pounds of iron five thousand paces. Indeed, but for the danger of fracture, nothing would prevent shooting from the Germanies to India” (Thorndike V, p. 567).

In Books VI and VII, “Cardano shows a modified Aristotelian idea of the physical world by omitting fire and accepting only three elements: earth, air and water. Repeating the facts and fantasies of the ancients, Cardano believed bodies found with in the earth were divided into four genera: earths, juices, stones and metals. Various actions of heat on mixtures of these substances gave rise to all stones, minerals and metals. Thus, clay and minum are grouped in the earths and diamonds, onyx, marble, jasper and quartz are considered stones. The seven metals grow in the earth from seed and are thought to have life. They are also each associated with one or more planets. Cardano also attempts without much success to represent the hexagonal form of quartz by close packing of spherical particles” (Schuh).

The books in part two cover problems to do with living beings (plants, animals, men):

Book VIII: Plants

Book IX: Animals generated from putrefaction

Book X: Perfect animals

Book XI: Needs and form of man

Book XII: Man’s nature and temperament

Book XIII: The senses, sensations and pleasure

Book XIV: Soul and intellect

In Book XI, Cardano included a dialogue in which the positive and negative points of Christianity are discussed in comparison with those of other religions. But instead of including a determining statement that Christianity is obviously the one true religion Cardano noted at the end that fate will decide the winner, leading to charges of atheism.

The books in the third part specify situations, methods and disciplines (the organisation of knowledge), giving space to issues that arise in the process of teaching:

Book XV: Useless or uncertain subtleties

Book XVI: Science

Book XVII: Arts and artificial things

In Book XV, Cardano gives a brief presentation of the work carried out with his pupil, Ludovico Ferrari, on the first four book of the Elements of Euclid, covering many propositions regarding the circle. Book XVI opens with certain general considerations relating to geometry, highlighting the relationship between the line and the circle and other curves, as well as issues to do with cones and their creation. These pages summarise the theory of conic sections, as set out in Apollinius’s Conics. Cardano, then moves on to discuss other geometrical shapes: spirals, rectangles, triangles, squares, pentagons, hexagons, heptagons, spheres, cones, spheroids, cylinders. Of particular interest here is Cardano’s solution of the problem to constructing a regular heptagon, which he shows reduces to the solution of a cubic equation, the formula for solving which he had given in his Ars magna (1545).

In the fourth part we find a reflection on ‘extraordinary’ situations: from the presence of devils and angels to that of God in relation to the universe:

Book XVIII: The extraordinary situations and the way to treat various matters outside the faith

Book XIX: Demons

Book XX: Angels and intelligent beings

Book XXI: God and the universe

In Book XX, Cardano discusses demons and witchcraft. While Cardano did believe in malevolent spirits and witches, he believed that many of the phenomena perceived as supernatural were in fact the result of exposure to natural, ambient phenomena (changes in atmosphere, temperature, altitude, light and darkness), ingesting certain foods and liquids, and the bodily application of unguents and salves. As an example, Cardano discusses the substance known as ‘witches’ grease’, an unguent made by witches from the fat of small children (stolen from fresh graves) mixed with parsley and aconite (wolf’s bane). Cardano argues that the mixture has a soporific effect on the “witches” and causes them to have vivid, fantastic dreams involving all manner of spectacular visions: theaters, giants, dances, young men and women having sex, kings and magistrates, prisons, solitary places, and torments.

Cardano’s De subtilitate inspired Julius Caesar Scaliger’s Exotericarum exercitationum (Paris 1557), “the most savage book review in the bitter annals of literary invective. Julius Caesar Scaliger, another vain and articulate natural philosopher of Italian origins, devoted more than 900 quarto pages to refuting one of Cardano’s books, ‘On Subtlety’, and promised to return to the subject at still greater length. Though Scaliger died without producing more than a fragment of this promised polemic, his Exercitationes became a standard work in university curriculums; perhaps the only book review ever known to undergo transformation into a textbook” (Grafton, Cardano’s Cosmos, p. 4).

BM/STC German p. 182; Dibner, Heralds of Science 139 note; Norman 402; Parkinson pp. 41-42.



Folio (315 x 208 mm), pp. [xxxvi, including one blank leaf], 371, [1, blank]. Roman type, italic marginalia. Woodcut printer’s device on title, woodcut portrait of the author on title verso, numerous woodcut illustrations and illustrations in text (some light browning). Contemporary limp vellum, spine lettered in manuscript (some brown spots, ink shelf number and remains of paper label on spine). A fine copy.

Item #5129

Price: $35,000.00