Leonardo & Luca Pacioli the Evidence


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If you lend some jewels or gold or silver table services to some friend for 8 or 15 days, particulars of same must not be put into the ledger, but must be recorded in a book of reminders, because in a few days they are to be returned. Thus also, if things of a similar kind were lent to you, they must not be placed in the ledger, but make a note of the matter in the reminders book, because you have to return them very soon.

At this time, a Venetian merchant was not just anyone, even when — after the taking of Byzantium Constantinople by the Turks in — relations with the Orient were inevitably modified. I have given in a previous article the list of goods shown in the ledger of Giacomo Badoer, a Venetian merchant circa In that inventory, very similar to the one given by Luca, one can however find an item which has, fortunately, disappeared in Summa.

In the middle of spices, skins and pelts, textiles and gems, and ginger, slaves appear — counted by heads like cattle. This business was so prosperous that it constituted a third of the turnover. As for the manner in which Badoer kept his ledger, it con-forms to those described by Giovanni Antonio Tagliente in his Luminario di Arithmetica of two years after the second edition of Summa , suppressing the memorial and the journal.

The transposition was made directly — with all desired details — in both accounts of the ledger, connecting one to the other. Certainly these accounts are by double-entry, but the absence of the journal leads to readjustments which would have shaken our friend Pacioli. Absence of biographical documents concerning Piero della Francesca leads historians to make suppositions which are al-most impossible to transform into certainty. Were Piero and Alberti well-known to each other? Did they even meet? One common point alone is certain between these two geniuses: Apart from that, nothing is sure.

Even at the period of the Renaissance, a man such as Alberti is rare. Descended from Florentine aristocracy, his scientific knowledge was immeasurable. Handsome as a young god, he excelled in all sports, while he took the classical studies with unbridled ardor. He did so much that, at 20, his health was affected.

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He had to rest. He did so by writing a comedy in the antique style, with such a pen that scholars for a long time believed it to be an original from Latin antiquity. Such a man most assuredly would not have associated himself with — and above all entertained at home — an ordinary student. It can be presumed that it was on the recommendation of Piero that Luca was allowed this honor. Surely he found great profit from it. It is at this time that Pacioli rejoins two of his brothers in the Order of Franciscans. And a little later circa we shall see him — as we have said — under the portrayal of St.

This is also the period when the University of Perugia appointed Pacioli to the Chair of Mathematics. That was the occasion for Luca to write a second work, dedicated to his new students. This text is that much more precious in that it is the only manuscript we have from Pacioli before Sumtna, this text provides, therefore, a direct approach to analyzing Summa. The book, the author says, discusses mathematics and particularly algebra, but in a way less elaborate than the manuscript of The work contains, however, pages which deal with rules of three and of companies, baratti or barter, false position, meriti or interest, business transactions and currency.

Without entering into details, the problems of companies are those in which several merchants participate in making a purchase, each of them taking shares in a more or less considerable part of the capital, in proportion to which the profit is to be divided. In the problems of barter, the merchant gives wool in exchange for cloth or spices, and the calculations of interest concern money invested or borrowed for a short or long time period, at a low and a high rate of interest.

He does not detour — as many others of his time did — to astronomy and still less to astrology. He preserves in his first research efforts and always extends them with the aim of being useful to all, rendering knowledge accessible to the greatest number of readers. One may be surprised to observe a monk, having taken a vow of poverty, preoccupied with business and commerce. That would be to misunderstand Pacioli badly. Assuredly, more than gold and silver, tor him the most enviable wealth consists in the knowledge of mathematics — the science without which nothing can exist.

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Luca Pacioli

It is with mathematics that the Great Architect created the universe, this world being represented by five regular bodies. This science is naturally indispensable, as much to philosophy as to fine arts, to the art of war as to commerce. I shall be the professor par excellence.


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He is accordingly writing in the common vernacular in order to be read by those whom the failure to understand Latin would have barred from the knowledge. That was not without disadvantages for his style, for which style purists have naturally reproached him. If it is true that fifteenth century Italy had a language, it is also true that dialects were numerous. Add to that the fact that he was writing, transposing, and translating from Latin texts, Pacioli was often obliged to forge his own words or to slip in terms since fallen into disuse.

Finally, and particularly, he is the master writing for his pupils, in the same matter that he spoke to them, with — alas — the same repetitions.


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Unceasingly, he announces his preoccupation of being brief, but incessantly his style marches from sentence to sentence, with the desire not to omit anything. As I have said, you shall diligently take note of all the things you have in belongings and estate, one by one, even if they number ten thousand, mentioning their condition and nature, if deposited in a bank, or if placed in loans.

All must be named in good order in the inventory, giving all the marks, name, surname, as detailed as possible, because things can never be too clear to a merchant on account of the quantity of cases that might occur in business, as he who daily works in business knows. The proverb is right when it says that more points are required to make a good merchant than a Doctor in Laws.

Who can enumerate the cases in which the merchant must intervene, at sea, on land, in time of peace and plenty, in time of war and famine, in time of comfort and in time of loss? In those circumstances, he must know what path to take in the markets and at fairs, which are held in one place, or in another. For these reasons, it is correct to say that the perfect merchant must resemble a cock, which is the most watchful creature in existence and keeps its nocturnal vigils in winter or in summer, never resting. It is said of the nightingale that it sings all through the night, but this can be verified only in summer during hot weather, and not in winter, as experience is ready to show.

It is also said the head of the merchant must have a hundred eyes, yet these are not enough to give him fair warning of what he must say or do. Witness the emphatic evidence of the great math-ematician, Cardan, insisting that without Pacioli, his own work would not be what it was. Thanks are due, therefore, to this remarkable teacher who was at the true take-off of the math-ematical revival in Italy and surrounding countries.

It is worth noting the care he took to precede his works with a detailed table of contents, which facilitated searching in his abstruse discourse, permitting the reader to arrive easily at the desired chapter. The table of distinctio 9 of the treatise alone requires a good two pages. If there are some who find that longish, it is, for Pacioli, only work done conscientiously.

Leaving Perugia for Zara about , he wrote in that town a third manuscript, the loss of which is particularly unfortunate. Speaking of this work in his Summa, he tells us, in fact, that the work of Zara is composed of difficult problems requiring deep comprehension.

History of Science - 15th-Century Science - 9.3 Science and Art

This seems to be the case in the Libellus, the text printed in at the end of the Divina Proportione, which is the cause of the most serious accusations made against Luca Pacioli. The fact that some persist — even without proof — in declaring this text about bookkeeping not to be original is of little importance, since the author himself does not claim it as an original work, but only one of compilation.

On the other hand, the text of the Libellus is, in the vernacular, exactly the same as that of the Quinque corporibus regularibus written, or rather translated, into Latin, and offered by Piero della Francesca, after , to the young Duke of Urbino. This text is a group of geometrical problems, solved mostly by algebra and calling for very difficult calculations because they are so complicated.

An example will give you an idea: When one sees that those roots require 9 or 10 numbers, followed by fractions which count the same quantity of numbers of the de-nominator and of the numerator, because at that time, one could not use decimals, much less calculating machines, finding the solution is baffling. One is especially amazed at the man who was capable of devising such a treatise. To credit a painter, even a great painter, who says of himself that he is aged and in poor health with this sort of exercise is, to say the least, incredible.

He gave a text to the Duke of Urbino, who is placed prominently in the picture, which was neither dedicated nor signed. It was astonishing because it avoided color in favor of geometry. It was written in the common vernacular, but the figures were very well finished, as you would expect from the hand of a great painter. Seven years later, the Duke of Urbino, protector of Piero, died when his so a and heir was 10 years old. It was to this child that Piero offered a text written in Latin with a dedication, so that everyone would know the author, though the first half of this dedication was an exact copy of the introduction to chapter III of Vitruvius.

In the second half, Piero asserts as his own the Prospectiva Pingendi given to the young Duke. It is on that work that Vasary — and others after him — founded their opinion that Luca had appropriated the work of his great elder, taking advantage of ease of access he would have at the Urbino library, where he could have purely and simply copied it. Was not the opposite more plausible? Indeed, where and from whom could Piero, at this time, acquire the necessary knowl-edge for the composition of a text bristling with difficulties?

How can one reconcile the work required to effect interminable calculations with the fact that the painter said himself he was weakened with age? How, above all, could the master painter of perspective, Piero, only succeed in illustrating his manuscript with false figures, constructed crookedly?

On the other hand, the drawing of both regular and irregular bodies was for Luca Pacioli a problem more difficult than calculations.


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This is evident in Summa. Beforehand, since , Luca had himself constructed his solid bodies, and Leonardo probably drew from those models. Nevertheless, the accusation brought against Pacioli, dis-seminated by Vasary in the sixteenth century, and by others too, particularly by Mancini in the twentieth century, do not agree with the most elementary logic.

These humorless detractors think they know better. To be fair, Luca has also happily found reliable defenders. The limit of absurdity in the calumnies came from an anonymous and undated Abaco, assigned by Mancini to Piero, because there are in it problems from the Libellus and also the whole of the problems which end Summa. This Abaco, if it is not signed is, however, presented like this I translate word for word:.

Beyond the fact that there is no mention of geometry, can you imagine merchants asking a painter to instruct them in the necessary mathematics for their trade! With great seriousness, but without an ounce of good sense, Margaret Daly Davis has, again in our time, defended this undefensible supposition. The contemporaries of Pacioli were fortunately more per-spicacious. This Summa, which well merits its name, contains Distinctio 9 Treatise, a chapter on bookkeeping, but the author warns that before studying this section it is necessary to have learned, thanks to preceding chapters, to be a fast calculator.

For anyone who has not assimilated them, it will be useless to study what follows. But if the reader must make some effort, the author too will have taken great trouble to relate in detail the entries in the Memorial, the Journal and the Ledger, with multiple examples. As this text is today available in most languages, no difficulty will be encountered.

I will, for my part, merely recall the sentence which comes nearly at the end of the chapter on bookkeeping: With attentive and devoted study, make the effort to become a good bookkeeper. I have amply shown you in this excellent work how to become one. I have given you all the rules, and the places where you can easily find them are indicated in the table of contents which is given at the beginning of this treatise. And think to pray to God for me, so that I can, for His praise and glory, continue to work to the best of my ability.

These prayers were probably heard, since, two years after the appearance of Summa, Pacioli was called by Ludovico Sforza to the court of Milan, as a commentator on Euclid. It is there that he met Leonardo da Vinci. These two men, outwardly so opposite, were in fact admirably complementary. The arrival of French armies in Italy drove both our friends to Mantua. It is a hand sketched draft of hundreds of complicated chess studies that Luca Pacioli must have been collecting over a long span of time.

Luca Pacioli - Wikipedia

Now, perusing the booklet something catches your attention and the more you look at it the more it becomes evident. While the writing is Pacioli's, two hands instead had been there penning in the chess pieces, the first with scholarly diligence the second with artistic swiftness. Luca was set to prepare another yet of his popularising textbooks and Leonardo had lent to his friend his "incomparable left hand" once again. Obviously the possible implication of Leonardo da Vinci in the drafting of the manuscript could not, not to be taken into consideration.

And it was rejected. Rightly, at times like ours, adept to Dan Brown's like flights of fancy, doubt is a virtue and suspicion should be "de rigueur" which means that a lasting grudge must not be held to the "expert" who, possibly startled by the news, not having been warned or seen the manuscript, quipped, "the silly season on Leo never closes".

In reality the discovery of Luca Pacioli's lost manuscript heralds, without doubt, that the "a la rabiosa" problems therein reported are of Leonardo's hand and we well know that Leonardo penned between and a rebus "I a roccha ro'" I shall castle confirming his perfect knowledge of the games new rules.

These can be traced back to the coronation of queen Isabella of Spain in the year and to her crowning are dated the new powers attributed to the Bishop and the Queen whose status of most powerful piece on the chessboard justified the new rules nickname of "mad queen" or "a la rabiosa". Yet nothing is said at that time about castling, that important move absolutely necessary in modern chess to counterbalance the overpowering new status of the Queen.

Evidence & study

Nothing, from until Leonardo's rebus of Time flies; while the excitement due to the discovery of Luca Pacioli's lost work is ineluctably subsiding, so the focus on this other of Leonardo's prodigious accomplishment is quietly worming its way into the cosy corners of expert knowledge and world oblivion.

Read more Read less. Customers who viewed this item also viewed. Page 1 of 1 Start over Page 1 of 1. Franco Rocco reveals that 49 of the 96 pages of the manuscript on the game of chess by famed renaissance mathematician Luca Customers who bought this item also bought. The Rules of Double-Entry Bookkeeping: Particularis de computis et scripturis.

Here's how restrictions apply. I'd like to read this book on Kindle Don't have a Kindle? Share your thoughts with other customers. Write a customer review. Showing of 5 reviews. Top Reviews Most recent Top Reviews. There was a problem filtering reviews right now. Please try again later. Ronnie Gonzalez Top Contributor: Ever since I read Jane Gleeson-White's book on Luca Pacioli called "Double-Entry", I've been consumed by studying everything about the man, his life, his influence, and his friends.

I'm delighted by this book because it's like discovering the mythical city of Atlantis -- who would've thought that none other than Leonardo Da Vinci and especially his good friend Luca Pacioli were behind not only the "rabiosa" rules of modern chess, whereby three of the pieces can move an infinite distance in any direction, but Da Vinci was probably behind the use of the lathe to achieve the standard look of the pawn and most of the rotational symmetry of the other pieces?

I'm not even through reading this book and though its layout and design definitely needs some refinement, I highly recommend it to "redpill" readers everywhere. Kindle Edition Verified Purchase. Great book, excellent graphics. Prompt delivery in excellent condition. Franco Rocco's book, Leonardo's Opening, is masterfully written and wonderfully illustrated.

In it he explores the here-to-for unknown and unheralded contributions of Leonardo da Vinci to modern chess.

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