Apollonius of Perga
Apollonius was a great mathematician, known by his contempories as " The
Great Geometer, " whose treatise Conics is one of the greatest scientific works from the ancient world. Most of his other treatise were lost, although their titles and a general indication of their contents were passed on by later writers, especially Pappus of Alexandria.
As a youth Apollonius studied in Alexandria ( under the pupils of Euclid, according to Pappus ) and subsequently taught at the university there. He visited Pergamum, capital of a Hellenistic kingdom in western Anatolia, where a university and library similar to those in Alexandria had recently been built.
While at Pergamum he met Eudemus and Attaluus, and he wrote the first edition of
Conics. He addressed the prefaces of the first three books of the final edition to Eudemus and the remaining volumes to Attalus, whom some scholars identify as
King Attalus I of Pergamum.
It is clear from Apollonius' allusion to Euclid, Conon of Samos, and
Nicoteles of Cyrene that he made the fullest use of his predecessors' works.
Book 1-4 contain a systematic account of the essential principles of conics, which for the most part had been previously set forth by Euclid, Aristaeus and
Menaechmus. A number of theorems in Book 3 and the greater part of Book 4 are new, however, and he introduced the terms parabola, eelipse, and hyperbola.
Books 5-7 are clearly original. His genius takes its highest flight in Book 5, in which he considers normals as minimum and maximum straight lines drawn from given points to the curve ( independently of tangent properties ), discusses how many normals can be drawn from particular points, finds their feet by construction, and gives propositions determining the center of curvature at any points and leading at once to the Cartesian equation of the evolute of any conic.
The first four books of the Conics survive in the original Grrek and the next three in Arabic translation. Book 8 is lost. The only other extant work of Apollonius is Cutting Off of a Ratio ( or On Proportional Section ), in an
Arabic translation. Pappus mentions five additional works, Cutting off an Area
( or On Spatial Section ) , On Determinate Section, Tangencies, and Plane Loci.
Tangencies embraced the following general problem : given three things, each of which may be a point, straight line, or circle, construct a circle tangent to the three. Sometimes known as the problem of Apollonius, the most difficult case arises when the three given things are circles.
Of the other works of Apollonius referred to by ancient writers, one, On
Plato, and G. M. A. Grube. "Phaedo." Five Dialogues. Indianapolis, IN: Hackett Pub., 2002. 93-
It is believed that Oedipus the King was written around 441 B.C.E. Oedipus the King begins when Oedipus is an infant and his real parents the king and queen of Thebe, Laius and Jocasta want to get rid of him because “…a prophecy warned them that their son would kill his father and marry his mother”(Meyer 1124). Therefore, the king and queen instruct a servant to leave him on a mountain to die. Oedipus’s feet were pierced and pinned together, but the servant did not leave him to die. Instead of leaving Oedipus on the mountain the servant felt pity, and gave him to a shepherd who gave Oedipus to the king and queen of Corinth. They raised Oedipus as their own so and named him Oedipus for “swollen foot” (Meyer 1124). As time passed by Oedipus “… learned from an oracle that he would kill his father and marry his mother” (Meyer 1124). To avoid his fate Oedipus left Corinth forever. On his way to leave Corinth he encountered with a chariot that was blocking his way at a crossroads. He was angry that he killed the servants and their passenger. That passenger was his real father but he was not aware of it. In Thebes, Oedipus answered the riddle of the Sphinx (the face of a woman with the body if a lion and wings). The reward
In the graphic novel, Persepolis, the main character, Marjane, faces many coming of age moments. Each one of these change her in a way that impacts her view on the world around her as her and her family strive for a better life amongst a war that hinders their ability to follow their beliefs. Marjane learns to forgive, experiences pain and suffering, and changes her opinions on God and her own views on religion forever. Marjane’s life has been filled with hard times, but also glorious moments as well.
Rodney, Sydney. "Pericles." Ancient Greece. University Inc., 11 May 2003. Web. 7 Dec. 2013. .
Dodds, E.R. "On Misunderstanding the Oedipus Rex." Greece & Rome, Second Series 13.1 (1996): 37-49. Jstor. Muntz Lib., Tyler, TX. 21 Mar. 2009.
There are four more attributes added to the transactional leadership theory and forms the transformational theory. Basically, it is the process where the leader and follower raises their hand for each other towards a greater benefit (Dems, 2015). This type of leadership style is very energetic, enthusiastic and passionate and it’s not confined in a hierarchical relation. Here leader exposed the clear goal to the follower and having a high expectation. But he never forgets about his follower to help them, encourage the. Leader shares his opinion and welcome every input from group members (Transformational Leadership, 2015) . The four qualities are intellectual stimulation to followers to explore new ideas. Considering each individual despite only group or team. Inspirational motivation for creating an inspiring vision to the group which is really achievable. Most important thing the behavior of transformational leader is being a role model to follow (Dawes,
The Iliad and the Fate Of Patroclus Throughout The Iliad Of Homer, the constant theme of death is inherently. apparent. The snares are not. Each main character, either by a spear or merely a scratch from an arrow, was wounded or killed during the progression of the story. For Zeus' son, a king.
When writing any sort of narrative, be it novel or poem, fiction or non-fiction, scholarly or frivolous, an author must take into account the most effective manner in which to effectively convey the message to their audience. Choosing the wrong form, or method of speaking to the reader, could lead to a drastic misunderstanding of the meaning within an author’s content, or what precisely the author wants to say (Baldick 69). Even though there are quite a bit fewer words in a graphic novel than in the average novel, an author can convey just as much content and meaning through their images as they could through 60,000 words. In order to do that though, their usage of form must be thoughtfully considered and controlled. Marjane Satrapi, author of the graphic memoir The Complete Persepolis, took great pains in the creation of her panels in order to reinforce and emphasize her narrative, much like a novelist utilizes punctuation and paragraph breaks. Through her portrayal of darkness and lightness, Satrapi demonstrates that literary content influences, and is primary to, the form.
In Virgil’s poem, The Aeneid, the ideal Roman hero is depicted in the form of Aeneas. Not only does Aeneas represent the Roman hero, but he also represents what every Roman citizen is called to be. Each Roman citizen must posses two major virtues, he must remain pious, and he must remain loyal to the Roman race. In the poem, Aeneas encompasses both of these virtues, and must deal with both the rewards and costs of them.
Many people seem to be under the impression that the Aeneid is a celebration of Roman glory, led by the hero of fate Aeneas. I find these preconceived ideas hard to reconcile with my actual reading of the text. For starters, I have a hard time viewing Aeneas as a hero at all. Almost any other main characters in the epic, from Dido to Camilla to Turnus, have more heroic qualities than Aeneas. This is especially noteworthy because many of these characters are his enemies. In addition, Aeneas is presented as a man with no free will. He is not so much bound to duty as he is shielded by it. It offers a convenient way for hum to dodge crucial moral questions. Although this doesn’t necessarily make him a bad person, it certainly makes him a weak one. Of course some will argue that it takes greater moral conviction to ignore personal temptation and act for the good of the people. These analysts are dodging the issue just like Aeneas does. The fact is that Aeneas doesn’t just sacrifice his own personal happiness for the common good; he also sacrifices the past of the Trojan people, most notably when he dishonors the memory of his fallen city by becoming the men he hated most, the Greek invaders. The picture of Aeneas as seen in the end of the Aeneid bears some sticking resemblances to his own depiction of the savage and treacherous Greeks in the early books.
Burn, A. R.. Pericles and Athens. London: Hodder & Stoughton for the English Universities Press, 1948.
1) Marra, James L., Zelnick, Stephen C., and Mattson, Mark T. IH 51 Source Book: Plato, The Republic, pp. 77-106
1. "The Internet Classics Archive | Phaedo by Plato." The Internet Classics Archive | Phaedo by
Initially, transactional and transformational leadership are different in terms of implementation and its outcomes. However, transformational leadership was developed from transactional leadership (Downton, 1973). Bass (1985) defined transactional leadership as an exchange activity that leaders execute to motivate subordinates in order to achieve their tasks by giving out reward or punishment correspond with their performance. Additionally, active and passive management by exception are taken into account when it comes to misconception and faults. Bass (1985) stated that transformational leadership emphasizes the value of subordinates, encourages them to perform extra effort, and assures their comprehension on organization’s goals and objectives. Besides, idealised influence, inspirational motivation, intellectual stimulatio...
Transformational leaders are needed to transform low performing organizations to acceptable to high performance. At other times, the leader is expected to move an organization from a crisis. In order to accomplish these tasks, the leader must overhaul the organization culture or subculture. This task is accomplished by nine ways of transforming others: 1. Raise others awareness. The leader makes others aware of the rewards and how to achieve them, i.e. pride in the job or financial incentives. 2. Help others look beyond self-interest. The transformational leader helps others to look at the “big picture” by describing an entire scenario, i.e. if we hire more employees to do x, we will have to make cuts in other areas. 3. Help people find self-fulfillment. The leader helps others not to focus on minor satisfactions, i.e. getting a job done before the deadline ...