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The __ challenged conceptions and beliefs about the nature of the external world and reality that became __. The medieval worldview was formidable. The breakdown of __ during the __and the frequent __ encouraged people to challenge the __ and __. The __ gave a new view of the world, such as __ or __. __ideas were opposed; he was accused of __. The Revolution was gradual.
 scientific revolution
 orthodox
 Christian unity
 Reformation
 religious wars
 ecclesiastical and political realms
 Scientific Revolution
 geocentric or heliocentric
 Galileo’s
 heresy and disobedience

Background to the Scientific Revolution: late medieval scholastic philosophers advanced __ and __ thinking in many ways, but the theological framework and reliance on few ancient authorities, like __, limited their thinking. Many “__” preferred refined __ to __ of the natural world.
 mathematical and physical
 Aristotle
 natural philosophers
 logical analysis
 systematic observations

I. Ancient Authors and Renaissance Artists
 a. Medieval scholars used Aristotle, Galen, and Ptolemy in Latin to develop their ideas in physics, medicine, etc.
 b. Renaissance humanists mastered Greeks and made available new works of Galen, Ptolemy, and Archimedes, Plato, preSocratics
 i. Unquestioned authorities of middle ages (Aristotle, Galen, etc) were being challenged
 c. Desire to discover correct schoolà new scientific work that rejected the classics

I. Ancient Authors and Renaissance Artists
Renaissance artists
 a. Renaissance artists made impact in science too
 i. Desire to imitate natureà closely observe nature
 1. Accurate depiction of natureà study of nature
 ii. “scientific” study of perspective and correct anatomical proportions à artists becoming practicing mathematicians
 1. Da Vinci= war machines
 2. Albrecht Durer= fortifications of cities

I. Technological Innovations and Mathematics
Technological problems
 a. Technical problems like accurately calculating the tonnage of shipsà scientific activity through careful observation and precise measurements
 i. 1516^{th} c: books proliferated about machines and technologyà belief of necessity of new techniques

I. Technological Innovations and Mathematics
Technological experts didn't believe...
 1. Many technological experts didn’t believe in abstract/ academic learning
 In Middle Ages and Renaissance, technical innovations accomplished outside universities by people who emphasized practical rather than theoretical knowledge

I. Technological Innovations and Mathematics
Invention
i. Invention of new machines and instruments, like telescope and microscopeà new scientific discoveries, as well as printing press, which allowed the spread of ideas quickly and easily

I. Technological Innovations and Mathematics
Mathematics
 a. Mathematics promoted in Renaissance by rediscovery of ancient math works and Plato, who emphasized importance in math to explain the universe
 i. Math= key to navigation, military science, and geography, and understanding of nature of things (Renaissance idea)
 1. Da Vinci: God geometrizesà nature mathematical

I. Technological Innovations and Mathematics
Mathematic reasoning and mathematicians
 i. Mathematic reasoning= certainty
 ii. Mathematicians: Kepler, Galileo, Newton, Copernicus
 1. They all believed nature written in language of mathematics

