Pacioli’s Summa proved to be one of the most consequential books of alltime.

In 1540 a Venetianprinter named Domenico Manzoni excerpted them, without attribution(Pacioli himself had acknowledged most, but not all, of his sources) butusefully adding hundreds of worked examples which illustrated Pacioli’spoints. Tellingly, Manzoni retitled the work Quaderno Doppio, ‘the doubleledger’. Selling even better than Maestro Luca’s original, it went throughsix or seven editions and prompted a wave of adaptations and translations.

of the six hundred pagesof the Summa, only twenty-seven covered bookkeeping.

Pacioli completed another equally playful book at about the same time:De Viribus Quantitatis (‘On the powers of numbers’), which compilesnumber games, card tricks, riddles and reasoning problems. It makesfrequent mention of Leonardo, and much of the content overlaps withpuzzles that can be found in the notebooks.

In February 1498, Maestro Lucacompleted De Divina Proportione, which was illustrated by ‘the graciousleft hand’ of his new friend, as Leonardo showed off his mastery ofperspective and geometry with a set of precise, fenestrated illustrations ofthe six Platonic solids, from the four-faced tetrahedron to the twenty-sidedicosahedron.

Pacioli’s reader, in whose company he would spend most of thefollowing decade, was Leonardo da Vinci.

Pacioli was granted copyright inthe work by the Venetian authorities, protecting his work from piracy.

Paganino de Paganini

In short: Book ix of the Summawas the nearest thing to an MBA textbook that the fifteenth century had tooffer. And one of the first lessons that its aspirational readers digested wasthat every business needed at least four blank books – the memoriale, orday book, the giornale, or journal, the quaderno, or general ledger, and abook for correspondence – and maybe even a fifth, the squartofoglia, or

He supplemented the commercial arithmetic with instruction in goodpractice in letter-writing, record-keeping, filing – and even that staple of theworkplace notebook, the things-to-do list

And buried deep inside,Book ix of the Summa presents a concise and surprisingly readable coursein double-entry bookkeeping, spelling out exactly how a business should berun – and why the Florentine-Venetian system of double entry was the bestway to do it. ‘Without double entry, businessmen would not sleep easily atnight’, he writes. ‘Their minds would keep them awake with worry.’

An ambitious synthesis of all the mathematical knowledge he could find,Pacioli’s Summa de arithmetica, geometria, proportioni et proportionalitais a baggy monster of a book. Six hundred and fifteen pages long, nearlyhalf a million words, full folio in size, closely printed on fine paper, itcomprehensively sums up the state of European mathematical knowledge,and was intended for a wide audience – Fra Luca wrote informally, inTuscan, not Latin, making it accessible to anyone with a basic education.The book combines a general treatise on theoretical and practical arithmetic– including the Liber Abaci of the then little-known Fibonacci, whichPacioli had discovered on a monastery bookshelf – with an introduction toalgebra, currency conversions, multiplication tables, weights and measuresof the Italian states, a summary of Euclidean geometry, and accounts ofArchimedes, Euclid and Piero della Francesca.

At one point he was forced to move on, when in 1491 he wasforbidden from teaching young men in Sansepolcro, presumably for somekind of sexual impropriety.

Luca Pacioli