Geocentro Magazine - Fondazione Geometri

Ai vari trattati di geometria pratica, sorti nei precedenti
decenni sulla scia della tradizione euclidea, si aggiunge
già sul finire del Quattrocento un nuovo genere di
opere, dedicato alla cosiddetta arte militare. Sulle orme
del vecchio trattato di Roberto Valturio, dal titolo De re
militari del 1472, che per primo raccoglie una descrizione
delle tecniche e degli strumenti di rilevamento ereditate
dalla tradizione medievale come bagaglio indispensabile
dell’uomo d’arma, nuovi sforzi si compiono da parte di
illustri matematici come Niccolò Fontana, maggiormente
noto come il Tartaglia, per il perfezionamento delle
pratiche topografiche in campo militare.
È quindi in funzione delle specifiche esigenze dell’artiglieria
che la carta geometrica comincia a dare risposte concrete
ai bisogni militari, consentendo di progettare opere di
fortificazione, bastioni, gallerie, trincee, diversivi, falsi scopi.
Non mancano poi in questo quadro sofisticati apparati
di “spionaggio topografico”, come il singolarissimo
distanziometro di Baldassarre Lanci, strumento ideato nel
1557 per rilevare il territorio con soli procedimenti grafici,
senza cioè l’esecuzione di calcoli, e per ricavare la pianta di
una fortezza da lontano, senza essere visti dal nemico.
Mentre alla scala urbana è principalmente ai topografi
rinascimentali che si deve dunque il merito di aver
codificato le regole per la realizzazione delle nuove carte
geometriche e di aver dettato i principi per la costruzione di
nuovi strumenti, con rare eccezioni come nel caso di Marco
Antonio Pasi e di Cristoforo Sorte, alla scala territoriale,
Therefore, we have to credit to the Renaissance topographers
the creation of a code for the realisation of new geometric maps
and the definition of the rules for the manufacturing of new
instruments. With the exception of Marco Antonio Pasi and
Cristoforo Sorte, the understanding of the Ptolemaic lesson
(how to draw a spherical surface on a plane, still maintaining
the abovementioned “proportio cuiusque partis ad universale”)
has to be credited to astronomers and mathematicians.
In Italy, the XVI century ends with important cartographical
documents, both in chorography and topography, masterpieces
of famous artists, such as Egnazio Danti (1536-1586) and
Giovanni Antonio Magini (1555-1617). This latter put an
end to the era of pre-geodetic cartography and drew the first
homogeneous map of Italy in 61 sheets. This map was elaborated
thanks to the data already collected in the course of the century
by other cartographers, Italian and not, reviewed thanks to
the new position of many sites that he himself calculated and
posthumous published by his son Fabio in 1620.
Therefore, we can say that geometric cartography had become a
reality as for the urban scale. Nevertheless, the awareness of the
necessity of topographical maps for the whole territory (and not
only for those landmarks represented by military structures such
as fortresses and parade-grounds) was still lacking. In order to
take this step forward, two things were still missing: on one
hand, a deepest scientific knowledge, particularly in the study
of the shape and the dimensions of our planet; on the other
hand, a good motivation to activate the great amount of money
that was necessary to sustain the long and expensive surveys and
the delicate phases of the cartographical restitution.
As for the first aspect, the scientific one, the XVII century
introduced a new method for the calculation of the landmark
position on the earth surface and a new general theory of reference
that allowed the discipline to progress towards a new era.
We are talking about the spreading of the new procedures
experimented in 1615 by Willebrord Snel van Royen (1580-
1626), also called Snellius. He suggested a way to transfer in
other sites, through a triangulation, the absolute coordinates of a
place obtained through astronomic measurement, even if, at the
beginning, the results of this method weren’t so convincing, due
to gross blunders in the calculations. Nevertheless, they opened
the way to the new operational geodesy and were confirmed as
the best method both for the length measurement of the grade,
and for the geometrical setting of all the topographical maps of
the world in the following centuries.
On the other hand, a new and sensational theory was spreading
all around Europe, although not yet confirmed by experimental
data. According to it, the Earth shape is more like an oblate
spheroid, than like a sphere. That was the idea of Isaac Newton in
his Philosophiae naturalis principia mathematica (Propositions
III, 19 and III, 20), published in London, in 1687.
While the European scientist were trying to confirm or to
refute such a theory, after 31 years from this publication,
Jacques Cassini (1677-1756) announced the results of geodetic
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