LUCA PACIOLI’S ALPHABETO DIGNISSIMO ANTIQUO A...

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

Paola Magnaghi Delfino - Tullia Norando

2

http://fds.mate.polimi.it

Formation, Didactics, Science Communication,

Experimental Teaching and Cultural Heritage

http://fds.mate.polimi.it/










3

http://www.policulturaexpo.it/world/

Bando_ENG_matemangiamo.pdf


4

2015, April 22th

Mathematics and Culture Seminars

Nuria Sanz


5

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


6 Luca Pacioli


7


8

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


9 Leonardo’s influence

Venice,1509 printed edition


10 Pacioli’s Capital Letters


Litterae Antiquae

11


12 The first Alphabet Architects

Lorenzo Ghiberti - Tomb of Leonardo Dati

Masaccio - Trinity


13 Felice Feliciano

Verona 1433 - 1480


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


15 Felice Feliciano

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


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


17 Leon Battista Alberti

Cappella Rucellai

St. Pancrazio Church Florence


Luca Pacioli

18

Borgo San Sepolcro

1445-1517


19

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


Alphabeto Dignissimo Antiquo

20


21


22 Chapter VI Pars Prima

Lordine del stilobata over pilastro overo basamento dela

colonna comme si facia

Construction of the piers and columns


23

Felice Feliciano Luca Pacioli

Geoffroy Tory

A_Pacioli_spiegata.ggb


24 Calligraphic style


25 The letterform’s competition


26

Geoffroy Tory

Francesco Torniello

Felice Feliciano


27 Geoffroy Tory

Le Champ Fleury 1529


28 Geoffroy Tory – Lettera I


29 Lettera I

Video_Lettere/Pacioli_I.avi


30 Lettera A

Video_Lettere/Pacioli_A.avi


31 Alphabeto Dignissimo Antiquo

Schema_Testa_spiegata.ggb


32 Lettera B

Video_Lettere/Pacioli_B.avi


33 Lettera R


34 Lettera O

Video_Lettere/Pacioli_O_new.avi


Thank you for your attention

Paola Magnaghi – Delfino

Tullia Norando

Department of Mathematics

FDS Laboratory

Politecnico di Milano

www.mate.polimi.it


Geoffroy Tory

39


40 Geoffroy Tory - Alfabeto


41 Geoffroy Tory – Lettera A


42 Geoffroy Tory – Lettere O e Q


43 Geoffroy Tory – Lettera O

O_Tory_finale.ggb

LUCA PACIOLI’S ALPHABETO DIGNISSIMO ANTIQUO A...

Documents

Transcript of LUCA PACIOLI’S ALPHABETO DIGNISSIMO ANTIQUO A...