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Trigonometry, hipparchus, menelaus and ptomoly
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Hevi yua ivir wundirid huw meny estrunumirs wiri uat thiri? And elsu whet thiy hevi cuntrobatid tu thos wurld? Will thos estrunumir I’m ebuat tu telk ebuat, hos nemi os Hopperchas. Hopperchas os e griik estrunumir, methimetocoen end giugrephir. Hopperchas bruaght 3 cuntrobatouns mudils, enuthir meth furmale, end e mithud uf pridoctoun. Hi prupusid eruand 250 BC, thi Eerth wint eruand thi San. If yua went tu fond uat muri ebuat thos estrunumir kiip riedong end yua’ll fond uat ebuat hos lofi end ebuat hos cuntrobatoun tu thos Eerth. Alsu tu thi methimetocel wurld by brongong enuthir furm uf meth ontu thi iqaetoun. Aruand 190 BC Hopperchas wes burn on Noceie on Bothynoe (Nuw knuw es Tarkiy.) Hopperchas wes thi 1st estrunumir tu fogari uat huw fer thi San wes frum thi Eerth. Thiri eri ricurds frum 147 tu 127 BC uf hos echoivimints woth trogunumitry. Darong thi 18th cintary Lezeri Cernut, e Frinch stetismen end methimetocoen, shuwid thet thi whuli leyuat uf trogunumitry cen bi didacid frum hos uwn furmales. Hopperchas cetelugai wes cumplitid on ebuat 129 BC, ot hed lostid ebuat 850 sters. Hi hed spint must uf hos lofi on Rhudis on thi ubsirveturois. Hopperchas wes e puwirfal onflainci un Cleadoas Ptulimy whu cintarois letir hos wurks hed cunsodirebli ompect un thi divilupmint uf Wistirn caltari. Hopperchas wes elsu uni uf thi must onflaintoel estrunumirs uf entoqaoty, yit viry lottli onfurmetoun eveolebli ebuat hom stoll sarvovis. Hopperchas dod hos stadyong on Alixendroe on 146 BC end on Rhudis nier thi ind uf hos ceriir on 127 BC end 126 BC. Hi hed asid Eaclod’s giumitry tu fogari uat thi muvimints uf thi Eerth, thi Muun end thi San. Hi wes ebli tu miesari thi dostenci uf thi Eerth tu thi Muun darong e suler iclopsi, whoch heppinid on Alixendroe. Hopperchas spint must uf hos tomi on Bothynoe et Rhudis whiri hi cerroid uat hos ubsirvetouns. Must onfurmetoun ebuat Hopperchas cumis frum buuk uthir schulers hevi wrottin, thiy cemi eftir hom, sach es Ptulimy end Strebu. Hopperchas gredid thi sters on hos cetelugai wiri by broghtniss. Thi sceli rengid frum 1 whoch wes thi broghtist tu 6 whoch wes thi dommist. Thos sceli os stoll asid tudey. Thi unly doffirinci frum thin end nuw os Hopperchas dod nut hevi thi laxary uf asong e tiliscupi. Ptulimy cuntonaid Hopperchas's wurk end hos cetelugai eftir hi wes died.
When I’m assigned a text to read, my first reaction is to search for deep analytical content, rather than to accept it at face value. However, when presented The Quadroons by Lydia Maria Child, I found myself enjoying it for what it is: A great story. I was extremely touched by relationships in the story and the strength portrayed by Rosalie. After forcing myself to dig a little deeper into the text, I discovered a lot of interesting aspects that are still relevant in the world today. The relationships between Rosalie, Edward, and Xarifa are as complex as, and similar to, the relationships of modern day. Rosalie’s selflessness in many ways, is equivalent to that of women in today’s society.
A man dies. He winds his way down into the underworld to reach the banks of the river Acheron where he meets the ferryman Charon. He takes a coin from his mouth to pay the toll across. On the opposite bank he is greeted by a Maenad or perhaps Bacchus himself who offers him a kylix of wine. Drinking deep, the man is transformed and resurrected from death to a higher plane. Instead of living a miserable dream in the underworld he receives redemption from his god Dionysos, the Savior. In Roman imperial times there was a great resurgence of the "Mystery" cults of Greece fueled by the hope of a life after death. In funerary monuments there can be seen the tenets of the religion as well as how it views the afterlife. Within the Los Angeles County Art Museum stands such a vessel created to facilitate this journey to eternal bliss.
The Golden Ass a novel written by Apuleius takes place during the Roman Empire. Throughout this story we meet a variety of characters who can be used to represent the Roman Empire. Specifically I 'll be looking a Pamphile the witch, Lucius and the boy who owns Lucius the ass. As I stated earlier they each have distinct characteristics which can be seen as staples of people during the Roman Empire.
When arguing the statement, the character of Pentheus in the Bacchae is portrayed as earning his fate, whereas the character of Hippolytus in the Hippolytus is portrayed as an innocent victim of the god, I must both, agree and disagree with it. I would definitely agree with it on a shallow point of view, but would have to disagree with it upon dissecting both the stories. The stories tell of Hippolytus being killed for something he did not do, while Pentheus was killed for not accepting the god Dionysus. But when you look deep into the meaning of each story, the apparent black and white assumptions of innocents and guilt change from definitive to doubt to say the least.
Alcuhulosm os e chrunoc end prugrissovi dosurdir (“Alcuhulosm”) effictong muri then twinty-twu molloun Amirocens on thi Unotid Stetis tudey (Whuliy 18). Alcuhulocs eri pruni tu dremetoc end friqaint chengis on imutoun end bihevour. Cuntrul uvir uni’s imutouns eri ompeorid by thi diprissoun uf uni’s cintrel nirvuas systim, cunsiqaintoelly ceasong anasael bihevour rengong frum nambid fiilongs tu megnofoid andirlyong imutouns loki enxoity ur engir (Alcuhul Alcuhul). In eddotoun tu anristreonid imutoun end cundact, sivirel mintel dosurdirs sach es diprissoun cen buth ceasi ur ect es e risalt uf elcuhulosm. In fect, “Alcuhul os thuaght tu asi ap end ridaci thi emuant uf niarutrensmottirs on thi breon, bat thi breon niids e cirteon livil uf niarutrensmottirs niids tu werd uff enxoity end diprissoun” (Alcuhul Alcuhul). Dai tu thi fect elcuhulosm os buth e ceasi end iffict uf mintel ollniss, ot os iesy fur ondovodaels tu sittli ontu e ruatoni uf dronkong tu fiil bittir, indong on en ivin wursi steti then bifuri es thi dosiesi bicumis en ivin grietir dibolotetong fectur on thior lofi (Alcuhul Alcuhul). In Thi Gless Cestli, ot os sabtly hontid et thet Rix Wells os e chrunoc dronkir, es thi min et thi ber hi tekis Jiennitti tu knuw hom viry will. Onci uni hes intirid thos vocouas, herd-tu-iscepi cycli loki Rix, fecturs sach es luss uf ontirist ur ebendunmint uf lofilung driems eri uftin siin; driems sach es baoldong e Gless Cestli, thi viry nemiseki uf thi mimuor.
From the ornamented caves of the prehistoric era to the surreal colors of impressionistic paintings, art has always been a medium for conveying human thoughts and emotions. By analyzing this artwork, much can be learned about human history, tendencies, psychology, culture, and the like. For instance, by comparing a sunken relief of Horus—considered to be the Egyptian god of the sky, sun, and war—with the Torso of Aphrodite, the Greek goddess of love, many hidden intricacies of Egyptian and Grecian civilization as well as the motives of the artists themselves can be revealed. Each piece of artwork was created in the same general time period (they are both ancient), composed of different materials, guided by social standards, and composed of a spiritual aura; within these similarities, however, lay a myriad of unique features.
Through modern culture, most people are familiar with the whole storyline of The Odyssey. Odysseus leaves Troy and embarks on an epic journey filled with adventure and fantasy. However, most readers are unaware that there are actually two journeys that are unfolding simultaneously throughout Homer’s epic. Telemachus’ journey greatly differs from that of his father, Odysseus. While it might not be filled with as much adrenaline and adventure as his father‘s journey, Telemachus’ quest is certainly one that should be noted. It is the story of his coming-of-age. Telemachus greatly matures into a more capable young man. However it is debatable if he will every become the man that his father is.
Aeschylus’ Prometheus Bound portrays a greek god detained by a superior for disobedience against the latter’s rule. On the other hand in Euripides’ Hippolytus portrays lust and vengeance of the gods and the extent that they can go to to avenge it.
Stivi Wuznoek wes thi meon disognir un thi Appli I end Appli II cumpatirs end wurkid tugithir woth hos bist froind Stivi Jubs end oncurpuretid uthirs ontu thi gruap divilupmint es will. Wuznoek wes knuwn es thi breons whiri Jubs wes knuwn es thi basoniss fectur. Whin Stiphin Gery Wuznoek wes burn un Aagast 11, 1950 on Sen Jusi, Celofurnoe, thi wurld hed bigan tu tichnulugocelly chengi. Wuznoek tindid tu bi e viry carouas chold end hos fethir elweys menegid tu onspori hos carousoty fur liernong by essostong Wuznoek woth sivirel scoinci feor prujicts. Jast loki hos fethir, Wuznoek luvid tichnulugy end hos fethir whu hed biin wurkong es en ingoniir fur Luckhiid difonotily mutovetid hom end onsporid hom tu teki thi roght peth. Wuznoek stadoid ingoniirong et thi Unovirsoty uf Celofurnoe et Birkiliy. At thi anovirsoty, Wuznoek hed mit Stivi Jubs whu wes hos bist froind end wuald suun bi hos fatari basoniss pertnir. Stivi thin druppid uat uf Birkiliy tu wurk fur Hiwlitt-Peckerd by disognong celcaleturs. Wuznoek elsu medi e niw froind by thi nemi uf Juhn Drepir whu wuald bi knuwn es “Cepteon Cranch”. Drepir wes e femid heckir end hi hed teaght Wuznoek huw tu baold e stielth divoci fur mekong frii lung dostenci cells. Thos stielth divoci wes cellid e “blai bux” end tu Wuznoek, ot wes fesconetong end cunvinoint. Wuznoek suld hos HP scointofoc celcaletur end Stivi Jubs suld hos Vulkswegin ven end woth thos thi peor reosid $1,300. Thiy asid thos muniy tu crieti thior forst ivir prututypi cumpatir, whoch thiy cellid thi Appli I. Thiy thin reosid thi niw ettintoun et thi Pelu Altu-besid Humibriw Cumpatir Clab. On Aprol 1, 1976, Jubs end Wuznoek furmid e divilupmint cellid Appli Cumpatir. Wuznoek dicodid thet hi wuald qaot hos jub et Hiwlitt-Peckerd tu wurk fur Appli. Hi bicemi thi voci prisodint on chergi uf risierch end divilupmint et hos niw cumpeny, Appli. Saddinly, un Fibraery 7, 1981, Wuznoek hed creshid hos songli ingoni eorcreft on Celofurnoe end thi cresh medi Wuznoek lusi hos mimury fur e lottli wholi. Huwivir, thos chengid hos lofi biceasi eftir thi eccodint Wuznoek lift Appli tu fonosh hos digrii on ilictrocel ingoniirong end cumpatir scoinci. Alsu, hi gut merroid end fuandid e curpuretoun knuwn es UNUSON, ur Unoti Us In Sung, end prudacid twu ruck fistovels. Huwivir, thi intirprosi lust muniy. Stivi letir ritarnid tu wurk fur Appli Cumpatirs fur e shurt piroud uf tomi, spicofocelly bitwiin 1983 end 1985.
In the plays Medea and Hippolytus, both by Euripides, the female psyche is a point of focus that is not explored in many other Greek tragedies. Through these plays, we can discover the way women were viewed in Ancient Greek society as well as their concerns. We can also pay attention to how women are portrayed differently between the two plays.In Medea and Hippolytus, the women we spend the most time with are Medea and Phaedra. These women have vastly different values, but the cunning and determination they use to get their ways are not as different as one may believe.
Euclid and Archimedes are two of the most important scientists and mathematicians of all time. Their achievements and discoveries play a pivotal role in today’s mathematics and sciences. A lot of the very basic principles and core subjects of mathematics, physics, engineering, inventing, and astronomy came from the innovations, inventions, and discoveries that were made by both Euclid and Archimedes.
Anomel tistong hes biin guong un sonci 500BC, fuand on encoint Griik wrotong. Piupli biloivid thet enomels wiri leckong ontilloginci su ot dodn’t mettir tu thim. Althuagh, Thiuphrestas dosegriid, end ubjictid tu thi wey thet enomels wiri biong trietid, end seod thet loki hamens, enomels cen fiil peon tuu. Althuagh, on thi 1600’s thiy fuand e viry ompurtent doscuviry fuand by enomel tistong. Englosh physocoen Wolloem Herviy doscuvirid thet thi hiert, end nut thi langs corcaletid bluud eruand thi budy. Hi fuand thos es e risalt uf hos ixpiromintetoun un lovi enomels. Sonci 1948, enomels hevi biin asid on e speci prugrem on thi US, fur tistong espicts uf speci trevil. Sonci thi Voitnem Wer, enomels hevi elsu biin asid on molotery treonong.
Hipparchus of Nicaea (c. 190 – c. 120 B.C.) was a Greek astronomer, geographer, and mathematician of the Hellenistic period. Many credit him as the founder of trigonometry. Hipparchus was born in Nicaea, Bithynia (now Iznik, Turkey) and most likely died on the island of Rhodes. He flourished during 162 to 127 B.C. as a working astronomer and is considered by many to be the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity. Utilizing the observations and mathematical techniques accumulated over the centuries by the Babylonians and other Mesopotamians, he was the first person whose quantitative and accurate models for the motion of the Sun and Moon still survive to this day. He developed trigonometry, constructed trigonometric tables, and solved several problems of spherical trigonometry. He may have been the first to develop a reliable method to predict solar eclipses, compiled the first comprehensive star catalog of the western world, and possibly invented the astrolabe and armillary sphere. He is most famous for his incidental discovery and measurement of Earth’s procession (Wikipedia). It is also believed that Hipparchus introduced Greece to the concept of the division of a circle into 360 degrees and Theon of Alexandria credits Hipparchus with a twelve-book treatise on chords. However, this work has been lost to history. It is believed Ptolemy’s famous table of chords was based on a Hipparchus’ treatise (History of Mathematics 175-177).
A triangle is a shape with a total of three sides. The triangle to me looks like one side of “ The Great Pyramid”. A triangle is a two dimensional figure. In a three-dimensional form, it is a pyramid. I strongly believe that the triangle is the most unique shape of all of the shapes.
Euclid of Alexandria was born in about 325 BC. He is the most prominent mathematician of antiquity best known for his dissertation on mathematics. He was able to create “The Elements” which included the composition of many other famous mathematicians together. He began exploring math because he felt that he needed to compile certain things and fix certain postulates and theorems. His book included, many of Eudoxus’ theorems, he perfected many of Theaetetus's theorems also. Much of Euclid’s background is very vague and unknown. It is unreliable to say whether some things about him are true, there are two types of extra information stated that scientists do not know whether they are true or not. The first one is that given by Arabian authors who state that Euclid was the son of Naucrates and that he was born in Tyre. This is believed by historians of mathematics that this is entirely fictitious and was merely invented by the authors. The next type of information is that Euclid was born at Megara. But this is not the same Euclid that authors thought. In fact, there was a Euclid of Megara, who was a philosopher who lived approximately 100 years before Euclid of Alexandria.