I do not suppose a "teleogical" evolution towads this form, but the fact is , that this specific 78 structure finally became dominant : see the Rules of 1637 (probably 1585) and the following different TDM.
All are unambiguously structured as a 78 deck.
Now, from where did this typical structure originate?
"That is the questin, n'est-pas?"
I have an opinion : the structure came from the neo-pythagorean knowledge via Byzantium.
Hi Huck,
This oipinion is mine as you know and hasn't the approval of other searchers such as Ross, Lothar, Filipas or Hurst for the most known on the web.
I am in resaerch to determine if :
Was it already influencial in 1451 (when Geroge Trebizond made the translation for Pope Nicolas V : was the intial page of the Almagest of Ptolemyidentical to the later edition : Venice edition of 1515)?
In this case, the VS could have been an attempt towards a 78 structure
Was it influential only at the time of Boïardo (inference from the brotherhood between the two Viti's: Raphael's Protagoras)?
Even if the data actually known is unsufficient, I've gathered the actual different informations relatives to my "thesis" of a *possible*Byzantium influence upon the 78 structure.
Summary :
1)Each element (triangular, square, pyramidal numbers) of the
arithmological structure is known since at least the XIth-XIIth
centuries iin the West and is present in the ancient hellenical
tradition of Byzantium.
Now, the complete structure is known since Nicomaque of Gerase (II century)(Alexandrian civilisation ) and his followers such as Theon of Smyrme.
2)The neo-pythagorean disposition of the 78 as shown in the Almagest
of Ptolemy :
<<
http://www.dudleyobservatory.org/Logo/Ptolomey.jpg>>
The title page of Ptolemy's 'Almagest', from the first edition,
Venice 1515.
Image credit: Royal Astronomical Society
I haven't seen older editions such as the two following for example :
In Latin, Translated by Gerard of Cremona
The most important medieval Latin translation of the "Almagest,"
which is found in many manuscripts, was made from the Arabic in Spain
in 1175 by Gerard of Cremona, the most prolific of all medieval
translators from Arabic into Latin.
In Latin, Translated by George Trebizond, 1481
George Trebizond, one of the notable Greek scholars who came to Italy
in the early fifteenth century, made a new translation of
the "Almagest" from the Greek for Pope Nicholas V between March and
December of 1451. Due to a dispute about the quality of Trebizond's
commentary on the text, the translation was never dedicated to
Nicholas. This very elaborate manuscript of the translation, with the
figures drawn in several colors, was dedicated to Pope Sixtus IV by
George's son Andreas.
In Latin, ca. 1482
During the same nine months that George Trebizond made his
translation of the "Almagest," he also wrote a commentary as long as
the original text. The commentary was severely criticized, however,
which resulted in a falling out with Pope Nicholas V. This opulent
manuscript was dedicated to Pope Sixtus IV by George's son Andreas
along with Vat. lat. 2055 of the translation.
3)Comments :
There should be more ancient examples but this alphabetical one
directly linked to Ptolemy's Almagest translated is most interesting.
The initial suggestion given is :
the first line : 1 dot,
the second line : 2 dots
Anybodody aware of neo-pythagorean arithmology reads that the
following lines will be :
third line :3 dots
...
12th line : 12 dots
So:
1+2+3+4+5+6+7+8+9+10+11+12=78
BTW, there are only 12 lines in the Triangle under the intial name :
Almagest...
IF the translaytion of the Almagest by George Trebizond (1451)had the
initial page with the neo-pythagorean triangular disposition specific
of the number 78, THEN it is interesting to study ideological context.
Alain
A good starting point :
The Civilization of the Renaissance in Italy
by Jacob Burckhardt
translated by S.G.C. Middlemore, 1878
----------------------------------------------------------------------
----------
Part Three
The Revival of Antiquity
The Classics
"But the literary bequests of antiquity, Greek as well as Latin, were
of far more importance than the architectural, and indeed than all
the artistic remains which it had left. They were held in the most
absolute sense to be the springs of all knowledge. The literary
conditions of that age of great discoveries have often been set
forth; no more can here be attempted than to point out a few less-
known features of the picture.
Great as was the influence of the old writers on the Italian mind in
the fourteenth century and before, yet that influence was due rather
to the wide diffusion of what bad long been known than to the
discovery of much that was new. The most popular latin poets,
historians, orators and letter-writers, to- gether with a number of
Latin translations of single works of Aristotle, Plutarch, and a few
other Greek authors, constituted the treasure from which a few
favored individuals in the time of Petrarch and Boccaccio drew their
inspiration. The former, as is well known, owned and kept with
religious care a Greek Homer, which he was unable to read. A complete
Latin translation of the Iliad and Odyssey, though a very bad one,
vas made at Petrarch's suggestion, and with Boccaccio's help, by a
Calabrian Greek, Leonzio Pilato. But with the fifteenth century began
the long list of new discoveries, the systematic creation of
libraries by means of copies, and the rapid multiplication of
translations from the Greek.
Had it not been for the enthusiasm of a few collectors of that age,
who shrank from no effort or privation in their researches, we should
certainly possess only a small part of the literature, especially
that of the Greeks, which is now in our hands. Pope Nicholas V, when
only a simple monk, ran deeply into debt through buying manuscripts
or having them copied. Even then he made no secret of his passion for
the two great interests of the Renaissance, books and buildings. As
Pope he kept his word. Copyists wrote and spies searched for him
through half the world. Perotto received 500 ducats for the Latin
translation of Polybius; Guarino, 1,000 gold florins for that of
Strabo, and he would have been paid 500 more but for the death of the
Pope. Filelfo was to have received 10,000 gold florins for a metrical
translation of Homer, and was only prevented by the Pope's death from
coming from Milan to Rome. Nicholas left a collection of 5,000 or,
according to another way of calculating, of 6,000 volumes, for the
use of the members of the Curia, which became the foundation of the
library of the Vatican. It was to be preserved in the palace itself,
as its noblest ornament, the library of Ptolemy Philadelphus at
Alexandria. When the plague (1450) drove him and his court to
Fabriano, whence then, as now, the best paper was procured, he took
his translators and compilers with him, that he might run no risk of
losing them.
The Florentine Niccolo Niccoli, a member of that accomplished circle
of friends which surrounded the elder Cosimo de' Medici, spent his
whole fortune in buying books. At last, when his money was all gone,
the Medici put their purse at his disposal for any sum which his
purpose might require. We owe to him the later books of Ammianus
Marcellinus, the 'De Oratore' of Cicero, and other works; he
persuaded Cosimo to buy the best manuscript of Pliny from a monastery
at Lubeck. With noble confidence he lent his books to those who asked
for them, allowed all comers to study them in his own house, and was
ready to converse with the students on what they had read. His
collection of 800 volumes, valued at 6,000 gold florins, passed after
his death, through Cosimo's intervention, to the monastery of San
Marco, on the condition that it should be accessible to the public.
Of the two great book-finders, Guarino and Poggio, the latter, on the
occasion of the Council of Constance and acting partly as the agent
of Niccoli, searched industriously among the abbeys of South Germany.
He there discovered six orations of Cicero, and the first complete
Quintilian, that of St. Gallen, now at Zurich; in thirty-two days he
is said to have copied the whole of it in a beautiful handwriting. He
was able to make important additions to Silius Italicus, Manilius,
Lucretius, Valerius Flaccus, Asconius Pedianus, Columella, Celsus,
Aulus Gellius, Statius, and others; and with the help of Leonardo
Aretino he unearthed the last twelve comedies of Plautus, as well as
the Verrine orations.
The famous Greek, Cardinal Bessarion, in whom patriotism was mingled
with a zeal for letters, collected, at a great sacrifice, 600
manuscripts of pagan and Christian authors. He then looked round for
some receptacle where they could safely lie until his unhappy
country, if she ever regained her freedom, could reclaim her lost
literature. The Venetian government declared itself ready to erect a
suitable building, and to this day the Biblioteca Marciana retains a
part of these treasures.
The formation of the celebrated Medicean library has a history of its
own, into which we cannot here enter. The chief collector for Lorenzo
il Magnifico was Johannes Lascaris. It is well known that the
collection, after the plundering in the year 1494, had to be
recovered piecemeal by the Cardinal Giovanni Medici, afterwards Leo X.
The library of Urbino, now in the Vatican, was wholly the work of the
great Federigo of Montefeltro. As a boy he had begun to collect; in
after years he kept thirty or forty 'scrittori' employed in various
places, and spent in the course of time no less than 30,000 ducats on
the collection. It was systematically extended and completed, chiefly
by the help of Vespasiano, and his account of it forms an ideal
picture of a library of the Renaissance. At Urbino there were
catalogues of the libraries of the Vatican, of St. Mark at Florence,
of the Visconti at Pavia, and even of the library at Oxford. It was
noted with pride that in richness and completeness none could rival
Urbino. Theology and the Middle Ages were perhaps most fully
represented. There was a complete Thomas Aquinas, a complete Albertus
Magnus, a complete Bonaventura. The collection, however, was a many-
sided one, and included every work on medicine which was then to be
had. Among the 'moderns' the great writers of the fourteenth century--
Dante and Boccaccio, with their complete works--occupied the first
place. Then followed twenty-five select humanists, invariably with
both their Latin and Italian writings and with all their
translations. Among the Greek manuscripts the Fathers of the Church
far outnumbered the rest; yet in the list of the classics we find all
the works of Sophocles, all of Pindar, and all of Menander. The last
codex must have quickly disappeared from Urbino, else the
philologists would have soon edited it.
We have, further, a good deal of information as to the way in which
manuscripts and libraries were multiplied. The purchase of an ancient
manuscript, which contained a rare, or the only complete, or the only
existing text of an old writer, was naturally a lucky accident of
which we need take no further account. Among the professional
copyists those who understood Greek took the highest place, and it
was they especially who bore the honorable name of 'scrittori.' Their
number was always limited, and the pay they received very large. The
rest, simply called 'copisti,' were partly mere clerks who made their
living by such work, partly schoolmasters and needy men of learning,
who desired an addition to their income. The copyists at Rome in the
time of Nicholas V were mostly Germans or Frenchmen--'barbarians' as
the Italian humanists called them, probably men who were in search of
favours at the papal court, and who kept themselves alive meanwhile
by this means. When Cosimo de' Medici was in a hurry to form a
library for his favorite foundation, the Badia below Fiesole, he sent
for Vespasiano, and received from him the advice to give up all
thoughts of purchasing books, since those which were worth getting
could not be had easily, but rather to make use of the copyists;
whereupon Cosimo bargained to pay him so much a day, and Vespasiano,
with forty-five writers under him, delivered 200 volumes in twenty-
two months. The catalogue of the works to be copied was sent to
Cosimo by Nicholas V, who wrote it with his own hand. Ecclesiastical
literature and the books needed for the choral services naturally
held the chief place in the list.
The handwriting was that beautiful modern Italian which was already
in use in the preceding century, and which makes the sight of one of
the books of that time a pleasure. Pope Nicholas V, Poggio, Gianozzo
Manetti, Niccolo Niccoli, and other distinguished scholars,
themselves wrote a beautiful hand, and desired and tolerated none
other. The decorative adjuncts, even when miniatures formed no part
of them, were full of taste, as may be seen especially in the
Laurentian manuscripts, with the light and graceful scrolls which
begin and end the lines. The material used to write on, when the work
was ordered by great or wealthy people, was always parchment; the
binding, both in the Vatican and at Urbino, was a uniform crimson
velvet with silver clasps. Where there was so much care to show
honour to the contents of a book by the beauty of its outward form,
it is intelligible that the sudden appearance of printed books was
greeted at first with anything but favour. Federigo of Urbino 'would
have been ashamed to own a printed book.'
But the weary copyists--not those who lived by the trade, but the
many who were forced to copy a book in order to have it--rejoiced at
the German invention. It was soon applied in Italy to the
multiplication first of the Latin and then of the Greek authors, and
for a long period nowhere but in Italy, yet it spread with by no
means the rapidity which might have been expected from the general
enthusiasm for these works. After a while the modern relation between
author and publisher began to develop itself, and under Alexander VI,
when it was no longer easy to destroy a book, as Cosimo could make
Filelfo promise to do, the prohibitive censorship made its appearance.
The growth of textual criticism which accompanied the advancing study
of languages and antiquity belongs as little to the subject of this
book as the history of scholarship in general. We are here occupied,
not with the learning of the Italians in itself, but with the
reproduction of antiquity in literature and life. One word more on
the studies themselves may still be permissible.
Greek scholarship was chiefly confined to Florence and to the
fifteenth and the beginning of the sixteenth centuries. The impulse
which had proceeded from Petrarch and Boccaccio, superficial as was
their own acquaintance with Greek, was powerful, but did not tell
immediately on their contemporaries, except a few; on the other hand,
the study of Greek literature died out about the year 1520 with the
last of the colony of learned Greek exiles, and it was a singular
piece of fortune that northerners like Erasmus, the Stephani, and
Budaeus had meanwhile made themselves masters of the language. That
colony had begun with Manuel Chrysoloras and his relation John, and
with George of Trebizond. Then followed, about and after the time of
the conquest of Constantinople, John Argyropulos, Theodore Gaza,
Demetrios Chalcondylas, who brought up his sons Theophilos and
Basilios to be excellent Hellenists, Andronikos Kallistos, Marcos
Musuros and the family of Lascaris, not to mention others. But after
the subjection of Greece by the Turks was completed, the succession
of scholars was maintained only by the sons of the fugitives and
perhaps here and there by some Candian or Cyprian refugee. That the
decay of Hellenistic studies began about the time of the death of Leo
X was due partly to a general change of intellectual attitude, and to
a certain satiety of classical influences which now made itself felt;
but its coincidence with the death of the Greek fugitives was not
wholly a matter of accident. The study of Greek among the Italians
appears, if we take the year 1500 as our standard, to have been
pursued with extraordinary zeal. Many of those who then learned the
language could still speak it half a century later, in their old age,
like the Popes Paul III and Paul IV. But this sort of mastery of the
study presupposes intercourse with native Greeks.
Besides Florence, Rome and Padua nearly always maintained paid
teachers of Greek, and Verona, Ferrara, Venice, Perugia, Pavia and
other cities occasional teachers. Hellenistic studies owed a
priceless debt to the press of Aldo Manuzio at Venice, where the most
important and voluminous writers were for the first time printed in
the original. Aldo ventured his all in the enterprise; he was an
editor and publisher whose like the world has rarely seen.
Along with this classical revival, Oriental studies now assumed
considerable proportions. The controversial writings of the great
Florentine statesman and scholar, Giannozzo Manetti (d. 1459) against
the Jews afford an early instance of a complete mastery of their
language and science. His son Agnolo was from his childhood
instructed in Latin, Greek and Hebrew. The father, at the bidding of
Nicholas V, translated the whole Bible afresh, as the philologists of
the time insisted on giving up the 'Vulgata.'
Many other humanists devoted themselves before Reuchlin to the study
of Hebrew, among them Pico della Mirandola, who was not satisfied
with a knowledge of the Hebrew grammar and ScriptureS, but penetrated
into the Jewish Cabbalah and even made himself as familiar with the
literature of the Talmud as any Rabbi.
Among the Oriental languages, Arabic was studied as well as Hebrew.
The science of medicine, no longer satisfied with the older Latin
translations of the great Arab physicians, had constant recourse to
the originals, to which an easy access was offered by the Venetian
consulates in the East, where Italian doctors were regularly kept.
Hieronimo Ramusio, a Venetian physician, translated a great part of
Avicenna from the Arabic and died at Damascus in 1486. Andrea Mongaio
of Belluno lived long at Damascus for the purpose of studying
Avicenna, learnt Arabic, and emended the author's text. The Venetian
government afterwards appointed him professor of this subject at
Padua.
We must here linger for a moment over Pico della Mirandola, before
passing on to the general effects of humanism. He was the only man
who loudly and vigorously defended the truth and science of all ages
against the one-sided worship of classical antiquity. He knew how to
value not only Averroes and the Jewish investigators, but also the
scholastic writers of the Middle Ages, according to the matter of
their writings. In one of his writings he makes them say, 'We shall
live for ever, not in the schools of word-catchers, but in the circle
of the wise, where they talk not of the mother of Andromache or of
the sons of Niobe, but of the deeper causes of things human and
divine; he who looks closely will see that even the barbarians had
intelligence (mercurium), not on the tongue but in the breast.'
Himself writing a vigorous and not inelegant Latin, and a master of
clear exposition, he despised the purism of pedants and the current
over-estimate of borrowed forms, especially when joined, as they
often are, with one-sidedness, and involving indifference to the
wider truth of the things themselves. Looking at Pico, we can guess
at the lofty flight which Italian philosophy would have taken had not
the counter-reformation annihilated the higher spiritual life of the
people."
