User:Cole Quade/Science in the Renaissance

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Astronomy:

The astronomy of the late Middle Ages was based on the geocentric model described by Claudius Ptolemy in antiquity. Probably very few practicing astronomers or astrologers actually read Ptolemy's Almagest, which had been translated into Latin by Gerard of Cremona in the 12th century. Instead they relied on introductions to the Ptolemaic system such as the De sphaera mundi of Johannes de Sacrobosco and the genre of textbooks known as Theorica planetarum. For the task of predicting planetary motions they turned to the Alfonsine tables, a set of astronomical tables based on the Almagest models but incorporating some later modifications, mainly the trepidation model attributed to Thabit ibn Qurra. Contrary to popular belief, astronomers of the Middle Ages and Renaissance did not resort to "epicycles on epicycles" in order to correct the original Ptolemaic models—until one comes to Copernicus himself. With addition of more advanced tables and mathematics it would allow for the lasting advancement of the creation of the Gregorian Calendar, in the year 1583 to replace the Julian calendar that had several errors. The driving force behind this new change was for the purpose of calculating the exact date of Easter as the older Julian calendar was off by several minutes.

Sometime around 1450, mathematician Georg Purbach (1423–1461) began a series of lectures on astronomy at the University of Vienna. Regiomontanus (1436–1476), who was then one of his students, collected his notes on the lecture and later published them as Theoricae novae planetarum in the 1470s. This "New Theorica" replaced the older theorica as the textbook of advanced astronomy. Purbach also began to prepare a summary and commentary on the Almagest. He died after completing only six books, however, and Regiomontanus continued the task, consulting a Greek manuscript brought from Constantinople by Cardinal Bessarion. When it was published in 1496, the Epitome of the Almagest made the highest levels of Ptolemaic astronomy widely accessible to many European astronomers for the first time.

The last major event in Renaissance astronomy is the work of Nicolaus Copernicus (1473–1543). He was among the first generation of astronomers to be trained with the Theoricae novae and the Epitome. Shortly before 1514 he began to revive Aristarchus's idea that the Earth revolves around the Sun. He spent the rest of his life attempting a mathematical proof of heliocentrism. When De revolutionibus orbium coelestium was finally published in 1543, Copernicus was on his deathbed. A comparison of his work with the Almagest shows that Copernicus was in many ways a Renaissance scientist rather than a revolutionary, because he followed Ptolemy's methods and even his order of presentation. Not until the works of Johannes Kepler (1571–1630) and Galileo Galilei (1564–1642) was Ptolemy's manner of doing astronomy superseded.

Mathematics:

The accomplishments of Greek mathematicians survived throughout Late Antiquity and the Middle Ages through a long and indirect history. Much of the work of Euclid, Archimedes, and Apollonius, along with later authors such as Hero and Pappus, were copied and studied in both Byzantine culture and in Islamic centers of learning. Translations of these works began already in the 12th century, with the work of translators in Spain and Sicily, working mostly from Arabic and Greek sources into Latin. Two of the most prolific were Gerard of Cremona and William of Moerbeke. The purposes of astronomy was a major driving force behind the need for this form of math and refinement was required as the measure technology became more advanced for the times.

The greatest of all translation efforts, however, took place in the 15th and 16th centuries in Italy, as attested by the numerous manuscripts dating from this period currently found in European libraries. Virtually all leading mathematicians of the era were obsessed with the need for restoring the mathematical works of the ancients. Not only did humanists assist mathematicians with the retrieval of Greek manuscripts, they also took an active role in translating these work into Latin, often commissioned by religious leaders such as Nicholas V and Cardinal Bessarion.

Some of the leading figures in this effort include Regiomontanus, who made a copy of the Latin Archimedes and had a program for printing mathematical works. Published post-mortem De triangulis omnimodis libri quinque the treatise by Regiomontaus has become the base for what we know today as modern trigonometry ; Commandino (1509–1575), who likewise produced an edition of Archimedes, as well as editions of works by Euclid, Hero, and Pappus; and Maurolyco (1494–1575), who not only translated the work of ancient mathematicians but added much of his own work to these. Their translations ensured that the next generation of mathematicians would be in possession of techniques far in advance of what it was generally available during the Middle Ages. New inventions like the compass were needed to calculate longitudinal positioning for the new regions of the world that explorers were finding. The range with which these new mathematical principles could be applied were quite broad, with new opportunities in both civilian and defense applications. The application through architecture was critical at this time, with optimization of cities and structures being important during this time.

It must be borne in mind that the mathematical output of the 15th and 16th centuries was not exclusively limited to the works of the ancient Greeks. Some mathematicians, such as Tartaglia and Luca Paccioli, welcomed and expanded on the medieval traditions of both Islamic scholars and people like Jordanus and Fibonnacci. Giordano Bruno was one to critique the works of the ancients, like Aristotle, who he believed to have a flawed logic and developed a mathematical doctrine for the computation of partial physics, with Bruno attempting to transform theories of nature.

Physics also played a major during this time with many advancements being made in mechanics, optics, and navigation. Mechanical theories started as many ideas of this time with the Greeks specifically Aristotle and Archimedes. Mechanics and philosophy were combined into a similar streams of thought during the time of the Greeks and it wasn't until the Renaissance era that the two ideas begin to split from one another. Alot of the work into developing these new ideas of theories came down to work from the Italians chiefly Rafael Bombelli. Fleming Stevin also contributed alot to the ideas deriving work from the ancients such as Archimedes. Through these new ideas related field soon opened up as technology and warfare advanced that being the development of firearms and the need for new ballistic calculations.

Additions:
While most works of the time were based on ancient works, Giordano Bruno was one to critique the works of people like Aristotle, whom he believed to have a flawed logic and developed a mathematical doctrine for the computation of partial physics, with Bruno attempting to transform theories of nature. (Needs to be changed in the article itself.)

Astronomy: With the addition of more advanced tables and mathematics, it would allow for the lasting advancement of the creation of the Gregorian calendar in the year 1583 to replace the Julian calendar, which had several errors. The driving force behind this new change was for the purpose of calculating the exact date of Easter.

Mathematics:

The use of math was advanced in tandem with some of new inventions of the time like the compass, which was used to calculate longitudinal positioning to allow more effective navigation.

The range to which these new mathematical principles could be applied was quite broad, with new opportunities in both civilian and defense applications. Application through architecture was critical at this time, with optimization of cities and structures being important during this time.(Add Source for both sentences) (Science: 14, and 22)

Trigonometry: Many advancements were made on the Greek's work during this time; the published post-mortem, the De triangulis omnimodis libri quinque, the treatise by Regiomontaus, has become the basis for what we know today as modern trigonometry. Astronomy was a major driving force behind the need for this form of math, and refinement was required as the measurement technology became more advanced for the time. (Cut out alot of math sections and focus on physics section.)

Physics:
In addition to the progress being made in math, this was being complemented by advancements in physics, with people like Galileo attempting to bridge the gap between the two topics and go against original Aristotelian ideas. This new field of study opens up many opportunities in subfields like mechanics, optics, navigation, and cartography, to name a few.

Mechanical theories started ideas of this time with the Greeks, specifically Aristotle and Archimedes. During this time, mechanics and philosophy were combined into similar streams of thought, and it wasn't until the Renaissance era that the two ideas began to separate from one another. A lot of the work into developing these new ideas and theories came down to the Italians, chiefly Rafael Bombelli. Fleming Stevin also contributed a lot to the ideas deriving from the work of the ancients, such as Archimedes. Galileo also played a hand in the advancement of this field with a treatise on mechanics written in 1634. He helped develop ideas on relativity, freely falling bodies, and accelerated linear motion, to name a few. (Came from the article) Unfortunately, Galileo didn't have the proper means to communicate his findings due to his university courses at the time. Due to this, in June of 1609, Galileo switched to the application of the telescope after having been close to founding the science of mechanics off of two theories that he had discovered.

This led to the opening up of the field as technology and warfare advanced that being the development of firearms and the need for new ballistic calculations.

The navigation field was an important topic of the time, with many moving parts and advances that needed to be made that would later lead to geographical discoveries, but to do this, the technology had to be there with better ships and the application of the compass. With the first being in 1487–1488, Bartholomeu Dias embarked on the first navigational expedition on the high seas. Creating a method of calculation for traveling proved to be difficult, with weather being impossible to predict accurately with the current technology of the time, along with finding latitude and longitude. To measure latitude, a user only needed a few charts for the positions of the sun and planets and an instrument to find the position of the sun to do the calculations required. Longitude proved to be more of a challenge. To find longitude, local times need to be known and calculated based on an astonomical event. The theory that was tested was to wait for an eclipse and compare it based on Regiomontanus' Ephemerides with Nuremberg time or Zacuto's Almanach perpetuum with Salamanca time. This method leads to a high margin of error of around 25.5 degrees when tested. The solution that then had to be relied on was dead reckoning. There are many variables to this, and without proper tools, it is a hard task to complete accurately.

Peer Review Response
Katefogarty7: The information in the additions section is not cited after every sentence mainly just to keep things things not quite as cluttered. In the actual article I have been using citations after every sentence besides one sentence where I made a mistake that has since been corrected. I do have other sources that I haven't used yet that I plan on implimenting. The first sentence is a slightly pulled out from the rest of the article I will admit if only read from the additions and not the article itself. The astronomy section with the Gregorian calander needs to be reworded. Overall adjust the pharsing of the additions to be more clear. It shouldn't be that hard ot notice coming back after a small break. I would agree that the first two sentences under the mechanics section is a repedative and needs to be changed. The last sentence of the mechanics section does need to have a slight adjustment done to it to make it flow better.

Kwyle1604: The additions section is a formatted strangly for the information that is presented but the first sentence is meant to be read in the context of the original article not just in the additions section. I would agree that there are some issues with grammer and phrasing. The rephrasing provided I would agree that it does sound better and I will be changing that for the first sentence. I do plan to change the format of some of the sentences in the astronomy sections. I would also agree that the final sentence of the physics section does need a small reformat.