Post on 14-Jul-2020
LUCA PACIOLI’S ALPHABETO DIGNISSIMO ANTIQUO
A GEOMETRICAL RECONSTRUCTION
Paola Magnaghi-Delfino Tullia Norando
Laboratorio FDS
APLIMAT 2015
14th Conference on Applied Mathematics
Bratislava - February 3-5, 2015
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http://fds.mate.polimi.it
Formation, Didactics, Science Communication,
Experimental Teaching and Cultural Heritage
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http://www.policulturaexpo.it/world/
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2015, April 22th
Mathematics and Culture Seminars
Nuria Sanz
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Beware of the sorcery and the diabolical attractions of
geometry
Le Corbusier
But you have disposed all things by measure and number
and weight.
Holy Bible, The Book of Wisdom, 11 – 20
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6 Luca Pacioli
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De Divina Proportione (1496-1498)
• The first part, Compendio Divina Proportione, studies and
describes the Golden Ratio from a mathematical point of view
and studies polygons.
• The second part discusses the ideas of Vitruvius on the
application of Mathematics in Architecture.
• The third part, Libellus in tres partiales tractatus divisus, is
mainly an Italian translation of Piero della Francesca's Latin
writings De quinque corporibus regularibus
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9 Leonardo’s influence
Venice,1509 printed edition
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10 Pacioli’s Capital Letters
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Litterae Antiquae
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12 The first Alphabet Architects
Lorenzo Ghiberti - Tomb of Leonardo Dati
Masaccio - Trinity
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13 Felice Feliciano
Verona 1433 - 1480
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14 Felice Feliciano
Suole l’usanza antiqua cavare la littera di tondo e di
quadro
It was an old usage to form the letter from a circle and a square
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Del qual si cava il numero perfetto X e cossi vuol esser
la tua littera grossa la X a parte de l’altezza.
the ratio of the broad stroke to the total
height of the character
(like the right-hand side of the letter A)
is one to ten
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16 Leon Battista Alberti
Vitruvius says that the most
perfect number is a combination
of 10 and 6
6:1 7:1 10:1
Leon Battista Alberti contends
these proportions and proposes
7:1 8:1 9:1
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17 Leon Battista Alberti
Cappella Rucellai
St. Pancrazio Church Florence
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Luca Pacioli
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Borgo San Sepolcro
1445-1517
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1464 : tutor at Rompiasi’s family in Venice
1470 : in Rome living with Leon Battista Alberti
1475 : he became Franciscan friar
1489 : in San Sepolcro he wrote Summa de aritmetica,
geometria, proportioni et proportionalita
1496- 1499 : in Milan Luca met Leonardo da Vinci
1500- 1508 : he published De Divina Proportione in Venice
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Alphabeto Dignissimo Antiquo
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22 Chapter VI Pars Prima
Lordine del stilobata over pilastro overo basamento dela
colonna comme si facia
Construction of the piers and columns
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Felice Feliciano Luca Pacioli
Geoffroy Tory
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24 Calligraphic style
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25 The letterform’s competition
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Geoffroy Tory
Francesco Torniello
Felice Feliciano
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27 Geoffroy Tory
Le Champ Fleury 1529
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28 Geoffroy Tory – Lettera I
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33 Lettera R
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35 Alphabeto Dignissimo Antiquo
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Thank you for your attention
Paola Magnaghi – Delfino
Tullia Norando
Department of Mathematics
FDS Laboratory
Politecnico di Milano
www.mate.polimi.it
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Geoffroy Tory
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40 Geoffroy Tory - Alfabeto
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41 Geoffroy Tory – Lettera A
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42 Geoffroy Tory – Lettere O e Q
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44 Alphabeto Dignissimo Antiquo