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Short Summary of chapter 1 to 4 of History of Science (X_400652)
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Very short summary of the first four chapters of history of science X_400652
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Chapter 1 before 1200Everything was about understanding God with geometria as a part of philosophy.
With more understanding of geometria (and practical “mathematics” with Archimedes) there
came pragmatic interest from kings.
Where Romans were more practically minded about Geometria. With the pax romana the
Greek and Roman culture spread, early Christians distanced themselves from these “pagan”
Greek philosophers.
Until Saint Augustine became an ideal icon to Christianity since he wasn’t versed in the
Greek philosophers. Saint Augustine was impressed about geometria and arithmetica, this
impression was seen as sanctifying this form of knowledge. Saint Augustine compared
arithmetic knowledge to devine revelation. Somebody that was versed in Greek philosophy
was Boethius, he translated Aristotle and Plato. He offered the rules of computus, which
gave a practical use for arithmetica.
It was said that God revealed arithmetica to Abraham.
In these times, the taught came that every free man had to be versed in the Artes Liberales:
the trivium and Quadrivium. Where trivium contained Grammar, rhetorics and dialects.
Quadrivium is arithmetica, geometria, musica and astronomia.
An important person for the rise of mathematical thinking in Europa was Gerbert of Aurillac,
who had new ideals of studying: understanding something new by studying different
sources. He was a stark contrast with the people in those times who didn’t trust the heretic
sources.
Monasteries were the place of knowledge. Cities also benefitted from the knowledge of
places like these and universitas started to pop up everywhere, in which a subculture within
society was created.
Chapter 2 1200-1568
Two sides of mathematics started to form. The mathematical sciences (mathematica) and
the mathematical arts. Where mathematica is the quadrivium and mathematics for trades is
the mathematical arts.
The mathematics in trade rose due to the rise of trade and banking.
Education changed from a master-mate relationships to schools and universitas. Abacus
schools providing education for merchants and artisans where you learn the rules of the
trade you would become, the modern languages and rules for behaviour.
William de Moerbeke was an important man for the spread of knowledge since he translated
the work of Archimedes into latin, the original works were lost to time. Thomas Aquinas
connected Christianity and mathematics even more, he wrote proofs of the existence of God.
This shows that the Quadrivum gained importance and that theologians found mathematics
useful. This also boosted the subjects of mathematics in the Artes Liberales. Another person
who bridged the gap between mathematics and christianity was Nicole Oresme who mixed
, ideas of mathematics into theological problems, studying infinite sums. He explained how
God could combine infinite and finite. Which showed that there was real use for the
quadrivium in Theology.
Mathematics around 1500s showed that it had moved on from the Carolingian days: Logic,
physics and metaphysics were now the most important subjects and geometry had changed
from the names of figures into calculating unknown distances.
There was, however, still distrust in mathematics. This can be shown with Mariken van
Nimwegen.
The importance of mathematics can be seen with Gerolamo Cardano, who could hold a
position at the university of Bologna due to his knowledge in mathematica. He was known for
calculating the horoscope of Jesus. Cardano shows two things: mathematica was a way to
gain respect from the upper class and the anonymity of the monastery was gone.
The anonymity of monasteries disappearing can also be seen with Nicolo Tartaglia who had
a solution to the general third degree equation which he kept secret, this secret was
published by Cardano.
Tartaglia also shows that more people wanted to get mathematical knowledge since he
translated six books of elements in italian. This can also be seen with Leonardo of Pisa who
published his book, Liber Abaci, in both latin and Tuscan. Also choosing for Latin so it would
become acceptable knowledge. In this book he used arab numerals and bookkeeping was
introduced to Europe. Another person that taught in the Vernacular was Adam Riese. Who
introduced his readers to knowledge in mathematical arts in vernacular. He published the
rule of Coss. The spreading of knowledge was also helped by the printing press.
Abacus schools now came under local governments to prevent competition between
schools. And two new school types came to be: Latin schools and Grammar schools. The
latin schools taught in Latin and prepared for studying for universitas with the trivium.
Grammar schools taught in the modern languages.
The court mathematician also became a more prevelant with Leonardo da Vinci and Luca
Pacioli as examples. Known for building war machines and double entry bookkeeping
respectively.
Chapter 3 1568-1648
Mathematica at the universitas expanded, adding subjects like pyrotechnica and navigation
and mathematics was split into two subjects: mathesis pura and mixta. Mathesis pura being
the pure mathematics associated with the ancient subject and mixta about the connection to
the physical world. Mathematics’ popularity expanded even more, as seen with the
translation of Euclid into the vernacular.
Universitas became less about the Church and more a place of old knowledge. Seen as the
birth of the modern university.
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