page_title: Niccolò Fontana Tartaglia
section_title: General Trattato di Numeri et Misure
hierarchical_section_title: Niccolò Fontana Tartaglia / General Trattato di Numeri et Misure
caption_attribution_description: Italiano: La prima parte del general trattato di numeri, et misure di Nicolo Tartaglia, nella quale in diecisette libri si dichiara tutti gli atti operatiui, pratiche, et regole necessarie non solamente in tutta l'arte negotiaria, &amp; mercantile, ma anchor in ogni altra arte, scientia, ouer disciplina, doue interuenghi il calculo. - In Vinegia&#160;: per Curtio Troiano de i Nauò, 1556. - [6], 277, [1] c.&#160;: ill. .
context_page_description: Niccolò Fontana Tartaglia was an Italian mathematician, engineer, a surveyor and a bookkeeper from the then-Republic of Venice. He published many books, including the first Italian translations of Archimedes and Euclid, and an acclaimed compilation of mathematics. Tartaglia was the first to apply mathematics to the investigation of the paths of cannonballs, known as ballistics, in his Nova Scientia; his work was later partially validated and partially superseded by Galileo's studies on falling bodies. He also published a treatise on retrieving sunken ships.
context_section_description: Tartaglia exemplified and eventually transcended the abacco tradition that had flourished in Italy since the twelfth century, a tradition of concrete commercial mathematics taught at abacus schools maintained by communities of merchants. Maestros d'abaco like Tartaglia taught not with the abacus but with paper-and-pen, inculcating algorithms of the type found in grade schools today.
  Tartaglia's masterpiece was the General Trattato di Numeri et Misure (General Treatise on Number and Measure), a 1500-page encyclopedia in six parts written in the Venetian dialect, the first three coming out in 1556 about the time of Tartaglia's death and the last three published posthumously by his literary executor and publisher Curtio Troiano in 1560. David Eugene Smith wrote of the General Trattato that it was:
  the best treatise on arithmetic that appeared in Italy in his century, containing a very full discussion of the numerical operations and the commercial rules of the Italian arithmeticians. The life of the people, the customs of the merchants, and the efforts at improving arithmetic in the 16th century are all set forth in this remarkable work.
  Part I is 554 pages long and constitutes essentially a commercial arithmetic, taking up such topics as basic operations with the complex currencies of the day (ducats, soldi, pizolli, and so on), exchanging currencies, calculating interest, and dividing profits in joint companies. The book is replete with worked examples with much emphasis on methods and rules (that is, algorithms), all ready to use virtually as is.
  Part II takes up more general arithmetic problems, including progressions, powers, binomial expansions, Tartaglia's triangle (also known as "Pascal's triangle"), calculations with roots, and proportions / fractions.
  Part IV concerns triangles, regular polygons, the Platonic solids, and Archimedean topics like the quadrature of the circle and circumscribing a cylinder around a sphere.
caption: General trattato di numeri et misure, 1556
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