Ptolemy was the author of several scientific treatises, three of which were of continuing importance to later Byzantine, Islamic and European science. The first is the astronomical treatise now known as the Almagest, although it was originally entitled the "Mathematical Treatise" (Μαθηματικὴ Σύνταξις, Mathēmatikē Syntaxis) and then known as the "Great Treatise" (Ἡ Μεγάλη Σύνταξις, Ē Megálē Syntaxis). The second is the Geography, which is a thorough discussion of the geographic knowledge of the Greco-Roman world. This manuscript was used by Christopher Columbus as the map for his westward-bound path to Asia, in which he discovered the hitherto unknown lands of the Americas. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristoteliannatural philosophy of his day. This is sometimes known as the Apotelesmatika (Ἀποτελεσματικά) but more commonly known as the Tetrabiblos from the Greek (Τετράβιβλος) meaning "Four Books" or by the Latin Quadripartitum.
Claudius (/ˈklɔːdiəs/; Latin:Tiberius Claudius Caesar Augustus Germanicus; 1 August 10 BC – 13 October 54 AD) was Roman emperor from 41 to 54. A member of the Julio-Claudian dynasty, he was the son of Drusus and Antonia Minor. He was born at Lugdunum in Gaul, the first Roman Emperor to be born outside Italy. Because he was afflicted with a limp and slight deafness due to sickness at a young age, his family ostracized him and excluded him from public office until his consulship, shared with his nephew Caligula in 37.
Claudius' infirmity probably saved him from the fate of many other nobles during the purges of Tiberius and Caligula's reigns; potential enemies did not see him as a serious threat. His survival led to his being declared Emperor by the Praetorian Guard after Caligula's assassination, at which point he was the last man of his family.
Despite his lack of experience, Claudius proved to be an able and efficient administrator. He was also an ambitious builder, constructing many new roads, aqueducts, and canals across the Empire. During his reign the Empire began the conquest of Britain (if the earlier invasions of Britain by Caesar and Caligula's aborted attempts are not counted). Having a personal interest in law, he presided at public trials, and issued up to twenty edicts a day.
The gens Claudia (Classical Latin:[ˈklawdɪa]), sometimes written Clodia, was one of the most prominent patrician houses at Rome. The gens traced its origin to the earliest days of the Roman Republic. The first of the Claudii to obtain the consulship was Appius Claudius Sabinus Regillensis, in 495 BC, and from that time its members frequently held the highest offices of the state, both under the Republic and in imperial times.
Plebeian Claudii are found fairly early in Rome's history. Some may have been descended from members of the family who had passed over to the plebeians, while others were probably the descendants of freedmen of the gens.
In his life of the emperor Tiberius, who was a scion of the Claudii, the historian Suetonius gives a summary of the gens, and says, "as time went on it was honoured with twenty-eight consulships, five dictatorships, seven censorships, six triumphs, and two ovations." Writing several decades after the fall of the so-called "Julio-Claudian dynasty", Suetonius took care to mention both the good and wicked deeds attributed to members of the family.
The Ptolemaic Dynasty of Ancient Egypt: From Ptolemy I to Cleopatra VII
The Ptolemaic dynasty in Ancient Egypt began under the rule of Ptolemy I Soter, whose goal was to make Egypt great again and he did that by putting the country back on solid economic and administrative footing, and it ended with Cleopatra VII. When Alexander the Great of Macedon died unexpectedly in 323 BCE he had amassed an enormous empire spanning from Egypt through Anatolia, Mesopotamia and parts of India. In order to stay away from the influence of the priests and officials at Memphis, Ptolemy I moved the capital from its traditional place at Memphis to Alexandria. Alexandria, a city established by Alexander the Great, grew and flourished under the Ptolemies. The city became more of a Greek city than an Egyptian one, with the port giving easy access to the sea and Greece, and with Gree...
published: 22 Feb 2022
Ptolemy's Geocentric Model
Without modern instruments, it was very hard to understand what the planets were, especially since they seemed to wander independently from the stars. Ptolemy provided the definitive answer for the time being. Earth was the centre of the universe and all the heavenly bodies rotated around it.
For inquiry, consider the following:
1. Investigate the work of Aristarchus. What was his model of the universe and why? How did it differ from Ptolemy's?
2. Why is there no gale force wind blowing constantly as the Earth moves about the Sun? What is the cause of wind? How do hurricanes evolve?
3. What was it about the Ptolemaic model that allowed it to last for 1500 years, and what was it that eventually brought about it's demise?
4. Explain why you don't change position in a moving train when you j...
published: 03 Jul 2022
The Purpose of a System Is What It Does
The act of gaming is a gnostic ritual in which God experiences himself in small scale cosmic satire via the player's own engaged consciousness
published: 19 Sep 2024
Ptolemy I: The Founders of Egypt's Final Dynasty
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Fact Fi...
published: 31 May 2024
Overly Sarcastic Podcast: The Ptolemies
Good lord. This is a giant mess of a family tree. Just... Just watch it and see for yourself.
Downloadable audio file can be found here: http://www.mediafire.com/file/7d2fkopglxaasjb/OSPodcast+12.m4a
And all other episodes can be found here: http://www.mediafire.com/?1t64h3ehtg3pe
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published: 23 Feb 2017
A Miraculous Proof (Ptolemy's Theorem) - Numberphile
Featuring Zvezdelina Stankova... Want more?
Part 2 (bringing in Pentagons and the Golden Ratio) is at: https://youtu.be/o3QBgkQi_HA
More links & stuff in full description below ↓↓↓
Zvezda's Numberphile playlist: http://bit.ly/zvezda_videos
Zvezda's webpage: https://math.berkeley.edu/~stankova/
Epic Circles: https://youtu.be/sG_6nlMZ8f4
Triangle Magic Highway: https://youtu.be/wVH4MS6v23U
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/
And support from Math For America - https://www.mathforamerica.org/
NUMBERPHILE
Website: http://...
published: 09 Feb 2020
Ptolemy’s Theorem and the Almagest: we just found the best visual proof in 2000 years
We are making history again by presenting a new visual proof of the 2000+ years old Ptolemy's theorem and Ptolemy's inequality.
00:00 Introduction
04:27 Geometry 101
08:19 Applications
14:46 Ptolemy's inequality
18:34 LIES
25:35 Animated proofs
28:57 Thank you!
30:53 Degenerate Easter Egg
There are some other proofs of Ptolemy's theorem/inequality based on scaling and aligning suitable triangles. However, none of them is as slick, beautiful and powerful as Rainer's new proof. In particular, check out the animated scaling proof on the wiki page for Ptolemy's theorem (and this https://youtu.be/ZK08Z5A9xH4) and check out the scaling proof by Claudi Asina and Roger Nelson: Proof Without Words: Ptolemy’s Inequality in Mathematics Magazine 87, (2014), p. 291. https://www.jstor.org/stable/10.4...
published: 07 Sep 2024
033: Ptolemaic Egypt - Ptolemy I: Son of Lagus, Son of Ra
Ptolemy I Soter, a former commander of Alexander the Great turned King and Pharaoh of Egypt, was perhaps the craftiest out of all of Alexander’s Successors. A talented commander and even more brilliant politician, Ptolemy would wield diplomacy and intrigue with a deft hand, founding what would become the longest lasting Hellenistic Kingdom in his nearly 40-year reign.
Website/Episode Notes:
(https://hellenisticagepodcast.wordpress.com/2019/10/27/033-ptolemaic-egypt-ptolemy-i-son-of-lagus-son-of-ra/)
Title Theme: Seikilos Epitapth with the Lyre of Apollo, played by Lina Palera (https://soundcloud.com/user-994392473)
Support the Show:
Ko-Fi: (https://ko-fi.com/hellenisticagepodcast)
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published: 06 Jul 2020
Ludonarrative Dissidence
Chinese nationalist monkey game Black Myth: Wukong embarrasses entire Western videogame industry
The Ptolemaic dynasty in Ancient Egypt began under the rule of Ptolemy I Soter, whose goal was to make Egypt great again and he did that by putting the country ...
The Ptolemaic dynasty in Ancient Egypt began under the rule of Ptolemy I Soter, whose goal was to make Egypt great again and he did that by putting the country back on solid economic and administrative footing, and it ended with Cleopatra VII. When Alexander the Great of Macedon died unexpectedly in 323 BCE he had amassed an enormous empire spanning from Egypt through Anatolia, Mesopotamia and parts of India. In order to stay away from the influence of the priests and officials at Memphis, Ptolemy I moved the capital from its traditional place at Memphis to Alexandria. Alexandria, a city established by Alexander the Great, grew and flourished under the Ptolemies. The city became more of a Greek city than an Egyptian one, with the port giving easy access to the sea and Greece, and with Greece becoming the language of both commerce and government.
A thing to note about the Ptolemies, although they were Pharaohs of Egypt, they didn’t learn the Egyptian language and pretty much just stayed in Alexandria (which they had made the new capital, moving it from the traditional capital of Memphis). They used Greek for all of their administrative documents, and married within their own family to keep the bloodline pure and also keep their wealth in the family.
— SUPPORT US VIA OUR PATREON—
https://www.patreon.com/join/whencyclopedia
— BUY OUR MERCH —
https://www.worldhistory.store/
— CHAPTERS —
0:00 Introduction
0:51 Lead Up To The Ptolemaic Dynasty
3:50 Egypt During the Ptolemaic Dynasty
7:48 The Ptolemy Family Tree
16:49 Outro
— WANT TO KNOW MORE? —
Ptolemaic Dynasty https://www.worldhistory.org/Ptolemaic_Dynasty/
Ptolemy I https://www.worldhistory.org/Ptolemy_I/
Ptolemy XIII Theos Philopator https://www.worldhistory.org/Ptolemy_XIII_Theos_Philopator/
Arsinoe II Philadelphus https://www.worldhistory.org/Arsinoe_II_Philadelphus/
Cleopatra VII https://www.worldhistory.org/Cleopatra_VII/
The Economy of Ptolemaic Egypt https://www.worldhistory.org/article/1256/the-economy-of-ptolemaic-egypt/
Berenika II Euergetis https://www.worldhistory.org/Berenice_II_Euergetis/
— WATCH NEXT —
Cleopatra VII Philopator: the Last Queen of Ancient Egypt https://www.youtube.com/watch?v=J6bM6ElVO5k
7 Surprising Stories from Herodotus' Histories https://www.youtube.com/watch?v=QRf1jUgXRqQ
Alexander the Great: Life and Reign of the King of the Macedonian Empire https://www.youtube.com/watch?v=_E7JX-rVdFk
The Seven Wonders of the Ancient World: an Overview https://www.youtube.com/watch?v=1YWPMZ6pHm8
Comparing Two Ancient Civilisations: Ancient Egypt vs. Mesopotamia https://www.youtube.com/watch?v=EwY-ziBL1Jw
— ATTRIBUTIONS —
You can find all attribution and credits for images, animations, graphics and music here - https://worldhistory.typehut.com/the-ptolemaic-dynasty-of-ancient-egypt-from-ptolemy-i-to-cleopatra-vii-images-and-attributions-8317
The music used in this recording is the intellectual copyright of Michael Levy, a prolific composer for the recreated lyres of antiquity, and used with the creator's permission. Michael Levy's music is available to stream at all the major digital music platforms. Find out more on:
https://www.ancientlyre.com
https://open.spotify.com/artist/7Dx2vFEg8DmOJ5YCRm4A5v?si=emacIH9CRieFNGXRUyJ9
https://www.youtube.com/channel/UCJ1X6F7lGMEadnNETSzTv8A
— THUMBNAIL IMAGE —
https://www.worldhistory.org/image/15205/family-tree-of-the-ptolemaic-dynasty-of-egypt-305/
Simeon Netchev
CC BY NC SA 4.0 - https://creativecommons.org/licenses/by-nc-sa/4.0/deed.en
https://en.wikipedia.org/wiki/File:Ptolemy_I_as_Pharaoh_of_Egypt.jpg
Stella
CC BY SA 4.0 - https://creativecommons.org/licenses/by-sa/4.0/
World History Encyclopedia
www.worldhistory.org
#ptolemy #ptolemaicdynasty #cleopatravii
The Ptolemaic dynasty in Ancient Egypt began under the rule of Ptolemy I Soter, whose goal was to make Egypt great again and he did that by putting the country back on solid economic and administrative footing, and it ended with Cleopatra VII. When Alexander the Great of Macedon died unexpectedly in 323 BCE he had amassed an enormous empire spanning from Egypt through Anatolia, Mesopotamia and parts of India. In order to stay away from the influence of the priests and officials at Memphis, Ptolemy I moved the capital from its traditional place at Memphis to Alexandria. Alexandria, a city established by Alexander the Great, grew and flourished under the Ptolemies. The city became more of a Greek city than an Egyptian one, with the port giving easy access to the sea and Greece, and with Greece becoming the language of both commerce and government.
A thing to note about the Ptolemies, although they were Pharaohs of Egypt, they didn’t learn the Egyptian language and pretty much just stayed in Alexandria (which they had made the new capital, moving it from the traditional capital of Memphis). They used Greek for all of their administrative documents, and married within their own family to keep the bloodline pure and also keep their wealth in the family.
— SUPPORT US VIA OUR PATREON—
https://www.patreon.com/join/whencyclopedia
— BUY OUR MERCH —
https://www.worldhistory.store/
— CHAPTERS —
0:00 Introduction
0:51 Lead Up To The Ptolemaic Dynasty
3:50 Egypt During the Ptolemaic Dynasty
7:48 The Ptolemy Family Tree
16:49 Outro
— WANT TO KNOW MORE? —
Ptolemaic Dynasty https://www.worldhistory.org/Ptolemaic_Dynasty/
Ptolemy I https://www.worldhistory.org/Ptolemy_I/
Ptolemy XIII Theos Philopator https://www.worldhistory.org/Ptolemy_XIII_Theos_Philopator/
Arsinoe II Philadelphus https://www.worldhistory.org/Arsinoe_II_Philadelphus/
Cleopatra VII https://www.worldhistory.org/Cleopatra_VII/
The Economy of Ptolemaic Egypt https://www.worldhistory.org/article/1256/the-economy-of-ptolemaic-egypt/
Berenika II Euergetis https://www.worldhistory.org/Berenice_II_Euergetis/
— WATCH NEXT —
Cleopatra VII Philopator: the Last Queen of Ancient Egypt https://www.youtube.com/watch?v=J6bM6ElVO5k
7 Surprising Stories from Herodotus' Histories https://www.youtube.com/watch?v=QRf1jUgXRqQ
Alexander the Great: Life and Reign of the King of the Macedonian Empire https://www.youtube.com/watch?v=_E7JX-rVdFk
The Seven Wonders of the Ancient World: an Overview https://www.youtube.com/watch?v=1YWPMZ6pHm8
Comparing Two Ancient Civilisations: Ancient Egypt vs. Mesopotamia https://www.youtube.com/watch?v=EwY-ziBL1Jw
— ATTRIBUTIONS —
You can find all attribution and credits for images, animations, graphics and music here - https://worldhistory.typehut.com/the-ptolemaic-dynasty-of-ancient-egypt-from-ptolemy-i-to-cleopatra-vii-images-and-attributions-8317
The music used in this recording is the intellectual copyright of Michael Levy, a prolific composer for the recreated lyres of antiquity, and used with the creator's permission. Michael Levy's music is available to stream at all the major digital music platforms. Find out more on:
https://www.ancientlyre.com
https://open.spotify.com/artist/7Dx2vFEg8DmOJ5YCRm4A5v?si=emacIH9CRieFNGXRUyJ9
https://www.youtube.com/channel/UCJ1X6F7lGMEadnNETSzTv8A
— THUMBNAIL IMAGE —
https://www.worldhistory.org/image/15205/family-tree-of-the-ptolemaic-dynasty-of-egypt-305/
Simeon Netchev
CC BY NC SA 4.0 - https://creativecommons.org/licenses/by-nc-sa/4.0/deed.en
https://en.wikipedia.org/wiki/File:Ptolemy_I_as_Pharaoh_of_Egypt.jpg
Stella
CC BY SA 4.0 - https://creativecommons.org/licenses/by-sa/4.0/
World History Encyclopedia
www.worldhistory.org
#ptolemy #ptolemaicdynasty #cleopatravii
Without modern instruments, it was very hard to understand what the planets were, especially since they seemed to wander independently from the stars. Ptolemy p...
Without modern instruments, it was very hard to understand what the planets were, especially since they seemed to wander independently from the stars. Ptolemy provided the definitive answer for the time being. Earth was the centre of the universe and all the heavenly bodies rotated around it.
For inquiry, consider the following:
1. Investigate the work of Aristarchus. What was his model of the universe and why? How did it differ from Ptolemy's?
2. Why is there no gale force wind blowing constantly as the Earth moves about the Sun? What is the cause of wind? How do hurricanes evolve?
3. What was it about the Ptolemaic model that allowed it to last for 1500 years, and what was it that eventually brought about it's demise?
4. Explain why you don't change position in a moving train when you jump up in the air. Why does the train not move out from under you?
5. Use this website as a starting point to do some research and reporting into the great minds that have influenced our understanding of the heavens: https://starchild.gsfc.nasa.gov/docs/StarChild/universe_level2/cosmology.html
6. In Western society, we often hear only about the Greeks and perhaps the Egyptians, with regard to astronomy. Find one major astronomical contribution made by the Chinese, the Indian and at least one First Nation.
Without modern instruments, it was very hard to understand what the planets were, especially since they seemed to wander independently from the stars. Ptolemy provided the definitive answer for the time being. Earth was the centre of the universe and all the heavenly bodies rotated around it.
For inquiry, consider the following:
1. Investigate the work of Aristarchus. What was his model of the universe and why? How did it differ from Ptolemy's?
2. Why is there no gale force wind blowing constantly as the Earth moves about the Sun? What is the cause of wind? How do hurricanes evolve?
3. What was it about the Ptolemaic model that allowed it to last for 1500 years, and what was it that eventually brought about it's demise?
4. Explain why you don't change position in a moving train when you jump up in the air. Why does the train not move out from under you?
5. Use this website as a starting point to do some research and reporting into the great minds that have influenced our understanding of the heavens: https://starchild.gsfc.nasa.gov/docs/StarChild/universe_level2/cosmology.html
6. In Western society, we often hear only about the Greeks and perhaps the Egyptians, with regard to astronomy. Find one major astronomical contribution made by the Chinese, the Indian and at least one First Nation.
Head to Squarespace.com for a free trial, and when you're ready to launch, go to http://squarespace.com/biographics to save 10% off on your first purchase of a ...
Head to Squarespace.com for a free trial, and when you're ready to launch, go to http://squarespace.com/biographics to save 10% off on your first purchase of a website/domain using the code BIOGRAPHICS
→ Subscribe for new videos at least twice a week!
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Eric's Stuff:
Storyrant: https://www.youtube.com/@UC6Sk2h2WsYMxnGERAH_FbGg
OEI analog horror experiment: https://www.youtube.com/@UCsz5l0hY67TGoJR0CZiWVnA
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Untitled Side Channel: https://www.youtube.com/@untitledsidechannel
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Further Reading:
Samuel Sharpe - The History of Egypt under the Ptolemies
C. A. Kincaid - Successors of Alexander the Great
Ian Shaw - The Oxford History of Ancient Egypt
Diodorus Siculus - Library of History
Livius
WorldHistory
Head to Squarespace.com for a free trial, and when you're ready to launch, go to http://squarespace.com/biographics to save 10% off on your first purchase of a website/domain using the code BIOGRAPHICS
→ Subscribe for new videos at least twice a week!
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Geographics: https://www.youtube.com/channel/UCHKRfxkMTqiiv4pF99qGKIw
TopTenz: https://www.youtube.com/user/toptenznet
Eric's Stuff:
Storyrant: https://www.youtube.com/@UC6Sk2h2WsYMxnGERAH_FbGg
OEI analog horror experiment: https://www.youtube.com/@UCsz5l0hY67TGoJR0CZiWVnA
Free Scifi-Horror Ebook: https://dl.bookfunnel.com/1cw07o2uyb
Link Tree to Other Books and Socials: https://linktr.ee/EricMalikyte
Karl's Socials:
Fact Fiend: https://www.youtube.com/@FactFiend
Wiki Weekends: https://www.youtube.com/@wikiweekends
Untitled Side Channel: https://www.youtube.com/@untitledsidechannel
Twitter: https://twitter.com/KarlSmallwood
Further Reading:
Samuel Sharpe - The History of Egypt under the Ptolemies
C. A. Kincaid - Successors of Alexander the Great
Ian Shaw - The Oxford History of Ancient Egypt
Diodorus Siculus - Library of History
Livius
WorldHistory
Good lord. This is a giant mess of a family tree. Just... Just watch it and see for yourself.
Downloadable audio file can be found here: http://www.mediafire.c...
Good lord. This is a giant mess of a family tree. Just... Just watch it and see for yourself.
Downloadable audio file can be found here: http://www.mediafire.com/file/7d2fkopglxaasjb/OSPodcast+12.m4a
And all other episodes can be found here: http://www.mediafire.com/?1t64h3ehtg3pe
PATREON: www.patreon.com/user?u=4664797
MERCH LINKS:
Shirts - https://overlysarcasticproducts.threadless.com/designs
All the other stuff - http://www.cafepress.com/OverlySarcasticProducts
Find us on Twitter @OSPYouTube!
Good lord. This is a giant mess of a family tree. Just... Just watch it and see for yourself.
Downloadable audio file can be found here: http://www.mediafire.com/file/7d2fkopglxaasjb/OSPodcast+12.m4a
And all other episodes can be found here: http://www.mediafire.com/?1t64h3ehtg3pe
PATREON: www.patreon.com/user?u=4664797
MERCH LINKS:
Shirts - https://overlysarcasticproducts.threadless.com/designs
All the other stuff - http://www.cafepress.com/OverlySarcasticProducts
Find us on Twitter @OSPYouTube!
Featuring Zvezdelina Stankova... Want more?
Part 2 (bringing in Pentagons and the Golden Ratio) is at: https://youtu.be/o3QBgkQi_HA
More links & stuff in full ...
Featuring Zvezdelina Stankova... Want more?
Part 2 (bringing in Pentagons and the Golden Ratio) is at: https://youtu.be/o3QBgkQi_HA
More links & stuff in full description below ↓↓↓
Zvezda's Numberphile playlist: http://bit.ly/zvezda_videos
Zvezda's webpage: https://math.berkeley.edu/~stankova/
Epic Circles: https://youtu.be/sG_6nlMZ8f4
Triangle Magic Highway: https://youtu.be/wVH4MS6v23U
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/
And support from Math For America - https://www.mathforamerica.org/
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Videos by Brady Haran
Additional editing and animation by Pete McPartlan
Patreon: http://www.patreon.com/numberphile
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Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
Featuring Zvezdelina Stankova... Want more?
Part 2 (bringing in Pentagons and the Golden Ratio) is at: https://youtu.be/o3QBgkQi_HA
More links & stuff in full description below ↓↓↓
Zvezda's Numberphile playlist: http://bit.ly/zvezda_videos
Zvezda's webpage: https://math.berkeley.edu/~stankova/
Epic Circles: https://youtu.be/sG_6nlMZ8f4
Triangle Magic Highway: https://youtu.be/wVH4MS6v23U
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/
And support from Math For America - https://www.mathforamerica.org/
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Videos by Brady Haran
Additional editing and animation by Pete McPartlan
Patreon: http://www.patreon.com/numberphile
Numberphile T-Shirts and Merch: https://teespring.com/stores/numberphile
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
We are making history again by presenting a new visual proof of the 2000+ years old Ptolemy's theorem and Ptolemy's inequality.
00:00 Introduction
04:27 Geomet...
We are making history again by presenting a new visual proof of the 2000+ years old Ptolemy's theorem and Ptolemy's inequality.
00:00 Introduction
04:27 Geometry 101
08:19 Applications
14:46 Ptolemy's inequality
18:34 LIES
25:35 Animated proofs
28:57 Thank you!
30:53 Degenerate Easter Egg
There are some other proofs of Ptolemy's theorem/inequality based on scaling and aligning suitable triangles. However, none of them is as slick, beautiful and powerful as Rainer's new proof. In particular, check out the animated scaling proof on the wiki page for Ptolemy's theorem (and this https://youtu.be/ZK08Z5A9xH4) and check out the scaling proof by Claudi Asina and Roger Nelson: Proof Without Words: Ptolemy’s Inequality in Mathematics Magazine 87, (2014), p. 291. https://www.jstor.org/stable/10.4169/math.mag.87.4.291
Rainer was inspired by a classic scaling based proof of Pythagoras theorem that I presented here https://youtu.be/p-0SOWbzUYI?si=GeGzZ0R_Dj1AsXqR&t=371
You can find a couple of full text versions of the Almagest here
https://www.wilbourhall.org/index.html#ptolemy
https://classicalliberalarts.com/resources/PTOLEMY_ALMAGEST_ENGLISH.pdf
For more background info check out the very comprehensive wiki pages on:
Ptolemy’s theorem
https://en.wikipedia.org/wiki/Ptolemy%27s_theorem
Ptolemy’s inequality
https://en.wikipedia.org/wiki/Ptolemy%27s_inequality
Claudius Ptolemy
https://en.wikipedia.org/wiki/Ptolemy
The Almagest
https://sco.wikipedia.org/wiki/Almagest
Trigonometric identities
https://en.wikipedia.org/wiki/List_of_trigonometric_identities
Cyclic quadrilateral
https://en.wikipedia.org/wiki/Cyclic_quadrilateral
The optic equation
https://en.wikipedia.org/wiki/Optic_equation
There are very interesting higher-dimensional versions of Ptolemy's theorem just like there are higher-dimensional versions of Pythagoras theorem. I did not get around to talking them today. Google ...
Highly recommended:
T. Brendan, How Ptolemy constructed trigonometry tables, The Mathematics Teacher 58 (1965), pp. 141-149 https://www.jstor.org/stable/27967990
Tom M. Apostol, Ptolemy's Inequality and the Chordal Metric, Mathematics Magazine 40 (1967), pp. 233-235 https://www.jstor.org/stable/2688275
https://demonstrations.wolfram.com/PtolemysTableOfChords/ an interactive exploration of Ptolemy's table of chords
Ptolemy's theorem made a guest appearance in the the previous Mathologer video on the golden ratio: https://youtu.be/cCXRUHUgvLI
Here is a nice trick to make Ptolemy counterparts of Pythagorean triples. Take any two sets of Pythagorean triples:
5² = 3² + 4², 13² = 12² + 5², and combine them like this:
65² = 13² × 5²= 13²(4² + 3²) = 52² + 39²= 5²(12² + 5²) = 60² + 25².
Now combining the two right angled triangles 52-39-65 and 25-60-65 along the common diagonal in any of four different ways gives a convex quadrilateral with all sides integers. Note that you automatically get 5 integer lengths and then Ptolemy's theorem guarantees that the remaining side is a fraction. Scaling up everything by the denominator of that fraction gives one of the special integer-everywhere quadrilaterals. See also Brahmagupta quadrilaterals.
Here is a nice application of Ptolemy's theorem to a International Maths Olympiad problem https://www.youtube.com/watch?v=NHjtHOE1lks
In a cyclic quadrilateral the ratio of the diagonals equals the ratio of the sums of products of the sides that share the diagonals' end points: https://www.geogebra.org/m/XQr5jJQg This extension of Ptolemy's theorem is part of the thumbnail for this video.
T-shirt: cowsine :)
Music: Floating branch by Muted and I promise by Ian Post.
Enjoy,
burkard
We are making history again by presenting a new visual proof of the 2000+ years old Ptolemy's theorem and Ptolemy's inequality.
00:00 Introduction
04:27 Geometry 101
08:19 Applications
14:46 Ptolemy's inequality
18:34 LIES
25:35 Animated proofs
28:57 Thank you!
30:53 Degenerate Easter Egg
There are some other proofs of Ptolemy's theorem/inequality based on scaling and aligning suitable triangles. However, none of them is as slick, beautiful and powerful as Rainer's new proof. In particular, check out the animated scaling proof on the wiki page for Ptolemy's theorem (and this https://youtu.be/ZK08Z5A9xH4) and check out the scaling proof by Claudi Asina and Roger Nelson: Proof Without Words: Ptolemy’s Inequality in Mathematics Magazine 87, (2014), p. 291. https://www.jstor.org/stable/10.4169/math.mag.87.4.291
Rainer was inspired by a classic scaling based proof of Pythagoras theorem that I presented here https://youtu.be/p-0SOWbzUYI?si=GeGzZ0R_Dj1AsXqR&t=371
You can find a couple of full text versions of the Almagest here
https://www.wilbourhall.org/index.html#ptolemy
https://classicalliberalarts.com/resources/PTOLEMY_ALMAGEST_ENGLISH.pdf
For more background info check out the very comprehensive wiki pages on:
Ptolemy’s theorem
https://en.wikipedia.org/wiki/Ptolemy%27s_theorem
Ptolemy’s inequality
https://en.wikipedia.org/wiki/Ptolemy%27s_inequality
Claudius Ptolemy
https://en.wikipedia.org/wiki/Ptolemy
The Almagest
https://sco.wikipedia.org/wiki/Almagest
Trigonometric identities
https://en.wikipedia.org/wiki/List_of_trigonometric_identities
Cyclic quadrilateral
https://en.wikipedia.org/wiki/Cyclic_quadrilateral
The optic equation
https://en.wikipedia.org/wiki/Optic_equation
There are very interesting higher-dimensional versions of Ptolemy's theorem just like there are higher-dimensional versions of Pythagoras theorem. I did not get around to talking them today. Google ...
Highly recommended:
T. Brendan, How Ptolemy constructed trigonometry tables, The Mathematics Teacher 58 (1965), pp. 141-149 https://www.jstor.org/stable/27967990
Tom M. Apostol, Ptolemy's Inequality and the Chordal Metric, Mathematics Magazine 40 (1967), pp. 233-235 https://www.jstor.org/stable/2688275
https://demonstrations.wolfram.com/PtolemysTableOfChords/ an interactive exploration of Ptolemy's table of chords
Ptolemy's theorem made a guest appearance in the the previous Mathologer video on the golden ratio: https://youtu.be/cCXRUHUgvLI
Here is a nice trick to make Ptolemy counterparts of Pythagorean triples. Take any two sets of Pythagorean triples:
5² = 3² + 4², 13² = 12² + 5², and combine them like this:
65² = 13² × 5²= 13²(4² + 3²) = 52² + 39²= 5²(12² + 5²) = 60² + 25².
Now combining the two right angled triangles 52-39-65 and 25-60-65 along the common diagonal in any of four different ways gives a convex quadrilateral with all sides integers. Note that you automatically get 5 integer lengths and then Ptolemy's theorem guarantees that the remaining side is a fraction. Scaling up everything by the denominator of that fraction gives one of the special integer-everywhere quadrilaterals. See also Brahmagupta quadrilaterals.
Here is a nice application of Ptolemy's theorem to a International Maths Olympiad problem https://www.youtube.com/watch?v=NHjtHOE1lks
In a cyclic quadrilateral the ratio of the diagonals equals the ratio of the sums of products of the sides that share the diagonals' end points: https://www.geogebra.org/m/XQr5jJQg This extension of Ptolemy's theorem is part of the thumbnail for this video.
T-shirt: cowsine :)
Music: Floating branch by Muted and I promise by Ian Post.
Enjoy,
burkard
Ptolemy I Soter, a former commander of Alexander the Great turned King and Pharaoh of Egypt, was perhaps the craftiest out of all of Alexander’s Successors. A t...
Ptolemy I Soter, a former commander of Alexander the Great turned King and Pharaoh of Egypt, was perhaps the craftiest out of all of Alexander’s Successors. A talented commander and even more brilliant politician, Ptolemy would wield diplomacy and intrigue with a deft hand, founding what would become the longest lasting Hellenistic Kingdom in his nearly 40-year reign.
Website/Episode Notes:
(https://hellenisticagepodcast.wordpress.com/2019/10/27/033-ptolemaic-egypt-ptolemy-i-son-of-lagus-son-of-ra/)
Title Theme: Seikilos Epitapth with the Lyre of Apollo, played by Lina Palera (https://soundcloud.com/user-994392473)
Support the Show:
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Social Media:
Twitter (https://twitter.com/HellenisticPod)
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Ptolemy I Soter, a former commander of Alexander the Great turned King and Pharaoh of Egypt, was perhaps the craftiest out of all of Alexander’s Successors. A talented commander and even more brilliant politician, Ptolemy would wield diplomacy and intrigue with a deft hand, founding what would become the longest lasting Hellenistic Kingdom in his nearly 40-year reign.
Website/Episode Notes:
(https://hellenisticagepodcast.wordpress.com/2019/10/27/033-ptolemaic-egypt-ptolemy-i-son-of-lagus-son-of-ra/)
Title Theme: Seikilos Epitapth with the Lyre of Apollo, played by Lina Palera (https://soundcloud.com/user-994392473)
Support the Show:
Ko-Fi: (https://ko-fi.com/hellenisticagepodcast)
Etsy: (https://www.etsy.com/shop/Hellenistic...)
Amazon Wishlist: (https://www.amazon.com/hz/wishlist/ls...)
Social Media:
Twitter (https://twitter.com/HellenisticPod)
Facebook (www.facebook.com/hellenisticagepodcast/)
Discord (https://discord.gg/VJcyUcN)
Join us in War Thunder for free using this link and get a premium
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Our companion website for more: http://biographics.org
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Credits:
Host - Simon Whistler
Author - Morris M.
Producer - Jennifer Da Silva
Executive Producer - Shell Harris
Business inquiries to [email protected]
Other Biographics Videos:
Tiberius: The Reluctant Empero...
published: 20 Nov 2019
Claudius: Reformer, Conqueror of Britain - Roman Emperors DOCUMENTARY
Download WARPATH through my link https://patron.me/KingsandGWarpath and get a special startpack! Use our code: @KandG
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Kings and Generals historical animated documentary series on Roman history continues with a video on the emperor Claudius, an unlikely good emperor, who come to power after Caligula and managed to right the ship of the empire. He was known as a reformer, who curbed the power of the aristocracy, and improved the finances of the empire, as well as the conqueror of Britain.
Our video on Marcus Aurelius: https://youtu.be/cLtDWIsOs1E
Aurelian: https://youtu.be/YQHNaemGOoI
Commodus: https://youtu.be/nVW5R...
published: 19 Mar 2021
Life of Emperor Claudius #4 - The Invalid Emperor, Roman History Documentary Series
Emperor Claudius, he was probably the least likely male in the Julio-Claudian dynasty to become Emperor of Rome. However, due to the high mortality rate of males in the dynasty… he was proclaimed Emperor by the Praetorian Guard...
Born August the 1st in 10 BC, in Lugdunum in Gaul, He was the son of Drusus who was Emperor Tiberius' brother. His mother was Antonia, daughter of Mark Anthony and Octavia, Augustus' sister.
On this channel we focus on Roman History and right now we're doing a video on every Roman Emperor, if you're interested in that subscribe or watch the playlist here:
https://bit.ly/32CUA2g
The SPQR Store: https://tinyurl.com/y7sep8ty
Sources and Suggested reading:
Annals and Histories - (Tacitus)
https://amzn.to/2LfzPFB
The Twelve Caesars - (Suetonius)
https://amzn...
published: 11 Jul 2019
MAX MANIE - Claudius (Original Mix)
MAX MANIE - Claudius (Original Mix).
Add to your collection:
Spotify: https://open.spotify.com/album/0aiw4n4Fw0GPa0LZVHfeBe?si=CILeNaDASVWbvoNSRKjO8g
Apple Music: https://music.apple.com/it/album/the-ocean-ep/1501726087?app=itunes
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Max Manie is a young and talented producer, born in Salzburg and now living and studying in Vienna. Industries and audience’s eyes are stuck on him. All started from his track “Sunday”, a little shining pearl found on Soundcloud with over 4 million combined plays and big names supporting, ranging from Bakermat to Robin Schulz and Tiesto.
Now Max keeps the great work coming and thrills us with another ...
published: 01 Sep 2014
Roman History 13 - Claudius And The Rise Of Nero 41 - 54 AD
This is from the podcast series The History Of Rome by Mike Duncan.
He currently does The Revolutions podcast
http://www.revolutionspodcast.com/
published: 24 Sep 2016
The Reign and Death of Emperor Claudius | Dr. Andrew Traver
In the final episode on our trilogy on Emperor Claudius Dr. Andrew Traver takes us into the very heart of his reign in the roman empire and into the very deaths of his mortality.
After the shocking rise of Claudius to power the Roman Empire went under expansion not seen since Emperor Augustus as Claudius launched campaigns and especially into Britain finalizing the dream of Julius Caesar.
But from bloody conquests to senate intrigue Claudius launches major reform throughout the Justice system and within the Roman courts as he strives to become more active while even hearing cases himself.
From investigating senators to carrying out strategic attacks against conspirators Claudius continues to establish himself and to secure his reign.
From social | political reform to showing mercy on f...
published: 06 Jul 2021
"Claudius Caesar" with Mary Beard | The Past Is Present
How can we tell what’s fake and what’s real? What’s the difference between a forgery and a replica? Which was Giovanni da Cavino trying to make when he created his medals? Mary Beard explores the motives behind Cavino’s creations.
Learn more about this work of art and come see it in person: https://www.nga.gov/collection/art-object-page.45042.html
Hear more from Mary Beard on the “Twelve Caesars” here: https://youtube.com/playlist?list=PLErBGbWC2wSO8DCCSR3s-QZ3FoArssQYU
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published: 29 Jun 2022
Claudius : Rome's unexpected Emperor | Roman Empire
#Claudius #RomanEmpire #RomeHistory
published: 08 Oct 2021
❌EXTREME GAME OF SCOOT❌ Ryan Williams VS Claudius Vertesi
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family friendly pg clean
Today we played an Extreme Game of Scoot!
The Legend Ryan Williams VS Claudius Vertesi at Allin Indoor Skatepark in Canada! We both did insane Scooter Tricks & pushed ourselves a lot! It was a very special Game of Scoot, because we both have a very unique...
Join us in War Thunder for free using this link and get a premium
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Join us in War Thunder for free using this link and get a premium
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→ Subscribe for new videos four times per week.
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This video is #sponsored by War Thunder.
TopTenz Properties
Our companion website for more: http://biographics.org
Our sister channel TopTenz: https://www.youtube.com/channel/UCQ-hpFPF4nOKoKPEAZM_THw/
Our Newest Channel about Interesting Places: https://studio.youtube.com/channel/UCHKRfxkMTqiiv4pF99qGKIw
Credits:
Host - Simon Whistler
Author - Morris M.
Producer - Jennifer Da Silva
Executive Producer - Shell Harris
Business inquiries to [email protected]
Other Biographics Videos:
Tiberius: The Reluctant Emperor
https://youtu.be/jTOLCWtnKbA
Caligula – Rome’s Mad Emperor
https://youtu.be/3zgJ1Cb99uA
Source/Further reading:
Excellent podcast series, a few episodes on Claudius here: https://thehistoryofrome.typepad.com/the_history_of_rome/2009/07/61-what-me-claudius.html
Podcast on Claudius’s life (the following two episodes are also worth hearing): https://podcasts.google.com/?feed=aHR0cHM6Ly93d3cubGF0cm9iZS5lZHUuYXUvbWFya2V0aW5nL2Fzc2V0cy9wb2RjYXN0cy9yc3NmZWVkcy9jYWVzYXIueG1s&episode=NzZFNkMyRjYtRTVBOS00MjA5LUI4REUtNTU2OTg2RTEzQUUw&hl=en-CZ
Podcast on Claudius’s early life: https://partialhistorians.com/2013/09/08/episode-12-claudius-an-imperial-life-with-unusual-twists/
Britannica’s biography: https://www.britannica.com/biography/Claudius-Roman-emperor
Suetonius’s biography in full: http://penelope.uchicago.edu/Thayer/e/roman/texts/suetonius/12caesars/claudius*.html
(Father): https://www.britannica.com/biography/Nero-Claudius-Drusus-Germanicus
(Cerebral palsy): https://www.historytoday.com/archive/months-past/death-emperor-claudius
Biographics on Caligula: https://www.youtube.com/watch?v=3zgJ1Cb99uA
Biographics on Nero: https://www.youtube.com/watch?v=WIW10E1xAOI
Join us in War Thunder for free using this link and get a premium
tank or aircraft and three days of premium time as a bonus: http://v2.xyz/BiographicsWarThunder
→ Subscribe for new videos four times per week.
https://www.youtube.com/c/biographics?sub_confirmation=1
This video is #sponsored by War Thunder.
TopTenz Properties
Our companion website for more: http://biographics.org
Our sister channel TopTenz: https://www.youtube.com/channel/UCQ-hpFPF4nOKoKPEAZM_THw/
Our Newest Channel about Interesting Places: https://studio.youtube.com/channel/UCHKRfxkMTqiiv4pF99qGKIw
Credits:
Host - Simon Whistler
Author - Morris M.
Producer - Jennifer Da Silva
Executive Producer - Shell Harris
Business inquiries to [email protected]
Other Biographics Videos:
Tiberius: The Reluctant Emperor
https://youtu.be/jTOLCWtnKbA
Caligula – Rome’s Mad Emperor
https://youtu.be/3zgJ1Cb99uA
Source/Further reading:
Excellent podcast series, a few episodes on Claudius here: https://thehistoryofrome.typepad.com/the_history_of_rome/2009/07/61-what-me-claudius.html
Podcast on Claudius’s life (the following two episodes are also worth hearing): https://podcasts.google.com/?feed=aHR0cHM6Ly93d3cubGF0cm9iZS5lZHUuYXUvbWFya2V0aW5nL2Fzc2V0cy9wb2RjYXN0cy9yc3NmZWVkcy9jYWVzYXIueG1s&episode=NzZFNkMyRjYtRTVBOS00MjA5LUI4REUtNTU2OTg2RTEzQUUw&hl=en-CZ
Podcast on Claudius’s early life: https://partialhistorians.com/2013/09/08/episode-12-claudius-an-imperial-life-with-unusual-twists/
Britannica’s biography: https://www.britannica.com/biography/Claudius-Roman-emperor
Suetonius’s biography in full: http://penelope.uchicago.edu/Thayer/e/roman/texts/suetonius/12caesars/claudius*.html
(Father): https://www.britannica.com/biography/Nero-Claudius-Drusus-Germanicus
(Cerebral palsy): https://www.historytoday.com/archive/months-past/death-emperor-claudius
Biographics on Caligula: https://www.youtube.com/watch?v=3zgJ1Cb99uA
Biographics on Nero: https://www.youtube.com/watch?v=WIW10E1xAOI
Download WARPATH through my link https://patron.me/KingsandGWarpath and get a special startpack! Use our code: @KandG
Join the event and you will have a chance ...
Download WARPATH through my link https://patron.me/KingsandGWarpath and get a special startpack! Use our code: @KandG
Join the event and you will have a chance to win PS5, Switch or tons of Amazon cards. Check the link for more details: https://warpath-us-kol.lilith.com/?name=kingsandgenerals
Kings and Generals historical animated documentary series on Roman history continues with a video on the emperor Claudius, an unlikely good emperor, who come to power after Caligula and managed to right the ship of the empire. He was known as a reformer, who curbed the power of the aristocracy, and improved the finances of the empire, as well as the conqueror of Britain.
Our video on Marcus Aurelius: https://youtu.be/cLtDWIsOs1E
Aurelian: https://youtu.be/YQHNaemGOoI
Commodus: https://youtu.be/nVW5RJj6CTo
Sejanus: https://youtu.be/f2iFXVdkw4w
History of Rome: https://www.youtube.com/watch?v=lIuNd9KulZM&list=PLaBYW76inbX6WrNCeL_AdR36ZIODiGNzq
Support us on Patreon: http://www.patreon.com/KingsandGenerals or Paypal: http://paypal.me/kingsandgenerals or by joining the youtube membership: https://www.youtube.com/channel/UCMmaBzfCCwZ2KqaBJjkj0fw/join We are grateful to our patrons and sponsors, who made this video possible: https://docs.google.com/document/d/1ooKPbpq0z8ciEjz5Zmrga4-gWRmripm0u4BHMkkXHVc/edit?usp=sharing
The video was made by Lito Areta, while the script was researched and written by Ivan Moran
This video was narrated by Officially Devin (https://www.youtube.com/channel/UCU0-VII-V376zFxiRGMeZGg & https://www.youtube.com/channel/UC79s7EdN9uXX77-Ly2HmEjQ)
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#Documentary #Claudius #RomanEmpire
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Join the event and you will have a chance to win PS5, Switch or tons of Amazon cards. Check the link for more details: https://warpath-us-kol.lilith.com/?name=kingsandgenerals
Kings and Generals historical animated documentary series on Roman history continues with a video on the emperor Claudius, an unlikely good emperor, who come to power after Caligula and managed to right the ship of the empire. He was known as a reformer, who curbed the power of the aristocracy, and improved the finances of the empire, as well as the conqueror of Britain.
Our video on Marcus Aurelius: https://youtu.be/cLtDWIsOs1E
Aurelian: https://youtu.be/YQHNaemGOoI
Commodus: https://youtu.be/nVW5RJj6CTo
Sejanus: https://youtu.be/f2iFXVdkw4w
History of Rome: https://www.youtube.com/watch?v=lIuNd9KulZM&list=PLaBYW76inbX6WrNCeL_AdR36ZIODiGNzq
Support us on Patreon: http://www.patreon.com/KingsandGenerals or Paypal: http://paypal.me/kingsandgenerals or by joining the youtube membership: https://www.youtube.com/channel/UCMmaBzfCCwZ2KqaBJjkj0fw/join We are grateful to our patrons and sponsors, who made this video possible: https://docs.google.com/document/d/1ooKPbpq0z8ciEjz5Zmrga4-gWRmripm0u4BHMkkXHVc/edit?usp=sharing
The video was made by Lito Areta, while the script was researched and written by Ivan Moran
This video was narrated by Officially Devin (https://www.youtube.com/channel/UCU0-VII-V376zFxiRGMeZGg & https://www.youtube.com/channel/UC79s7EdN9uXX77-Ly2HmEjQ)
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#Documentary #Claudius #RomanEmpire
Emperor Claudius, he was probably the least likely male in the Julio-Claudian dynasty to become Emperor of Rome. However, due to the high mortality rate of male...
Emperor Claudius, he was probably the least likely male in the Julio-Claudian dynasty to become Emperor of Rome. However, due to the high mortality rate of males in the dynasty… he was proclaimed Emperor by the Praetorian Guard...
Born August the 1st in 10 BC, in Lugdunum in Gaul, He was the son of Drusus who was Emperor Tiberius' brother. His mother was Antonia, daughter of Mark Anthony and Octavia, Augustus' sister.
On this channel we focus on Roman History and right now we're doing a video on every Roman Emperor, if you're interested in that subscribe or watch the playlist here:
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Annals and Histories - (Tacitus)
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The Twelve Caesars - (Suetonius)
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Dio's Roman history - (Cassius Dio)
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From the Gracchi to Nero: A History of Rome from 133 BC to AD 68 (H. H. Scullard) https://amzn.to/2DYhNCQ
The Penguin Historical Atlas of Ancient Rome (Chris Scarre):
https://amzn.to/2YTPAW8
#Emperorsofrome #Romanemperors #SPQR #Romanhistory
Emperor Claudius, he was probably the least likely male in the Julio-Claudian dynasty to become Emperor of Rome. However, due to the high mortality rate of males in the dynasty… he was proclaimed Emperor by the Praetorian Guard...
Born August the 1st in 10 BC, in Lugdunum in Gaul, He was the son of Drusus who was Emperor Tiberius' brother. His mother was Antonia, daughter of Mark Anthony and Octavia, Augustus' sister.
On this channel we focus on Roman History and right now we're doing a video on every Roman Emperor, if you're interested in that subscribe or watch the playlist here:
https://bit.ly/32CUA2g
The SPQR Store: https://tinyurl.com/y7sep8ty
Sources and Suggested reading:
Annals and Histories - (Tacitus)
https://amzn.to/2LfzPFB
The Twelve Caesars - (Suetonius)
https://amzn.to/2HRSNBq
Dio's Roman history - (Cassius Dio)
https://amzn.to/2Li9arQ
From the Gracchi to Nero: A History of Rome from 133 BC to AD 68 (H. H. Scullard) https://amzn.to/2DYhNCQ
The Penguin Historical Atlas of Ancient Rome (Chris Scarre):
https://amzn.to/2YTPAW8
#Emperorsofrome #Romanemperors #SPQR #Romanhistory
MAX MANIE - Claudius (Original Mix).
Add to your collection:
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MAX MANIE - Claudius (Original Mix).
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Max Manie is a young and talented producer, born in Salzburg and now living and studying in Vienna. Industries and audience’s eyes are stuck on him. All started from his track “Sunday”, a little shining pearl found on Soundcloud with over 4 million combined plays and big names supporting, ranging from Bakermat to Robin Schulz and Tiesto.
Now Max keeps the great work coming and thrills us with another amazing work, “The Ocean EP”. It includes two incredibly beautiful tracks, “Ocean” and “Claudius”. They are filled with deepness, melody and the power of creation.
“Claudius” contains elements from “Stubborn Kind of Fellow” written and composed by Marvin Gaye. It’s an intense track, able to bring us on a never ending emotional journey...
Max Manie is a rising star ready to be in the spotlight and shine in the sky.
MAX MANIE - Claudius (Original Mix).
Add to your collection:
Spotify: https://open.spotify.com/album/0aiw4n4Fw0GPa0LZVHfeBe?si=CILeNaDASVWbvoNSRKjO8g
Apple Music: https://music.apple.com/it/album/the-ocean-ep/1501726087?app=itunes
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Subscribe to EgoTV NOW: http://bit.ly/1hzlXkS
Max Manie is a young and talented producer, born in Salzburg and now living and studying in Vienna. Industries and audience’s eyes are stuck on him. All started from his track “Sunday”, a little shining pearl found on Soundcloud with over 4 million combined plays and big names supporting, ranging from Bakermat to Robin Schulz and Tiesto.
Now Max keeps the great work coming and thrills us with another amazing work, “The Ocean EP”. It includes two incredibly beautiful tracks, “Ocean” and “Claudius”. They are filled with deepness, melody and the power of creation.
“Claudius” contains elements from “Stubborn Kind of Fellow” written and composed by Marvin Gaye. It’s an intense track, able to bring us on a never ending emotional journey...
Max Manie is a rising star ready to be in the spotlight and shine in the sky.
In the final episode on our trilogy on Emperor Claudius Dr. Andrew Traver takes us into the very heart of his reign in the roman empire and into the very deaths...
In the final episode on our trilogy on Emperor Claudius Dr. Andrew Traver takes us into the very heart of his reign in the roman empire and into the very deaths of his mortality.
After the shocking rise of Claudius to power the Roman Empire went under expansion not seen since Emperor Augustus as Claudius launched campaigns and especially into Britain finalizing the dream of Julius Caesar.
But from bloody conquests to senate intrigue Claudius launches major reform throughout the Justice system and within the Roman courts as he strives to become more active while even hearing cases himself.
From investigating senators to carrying out strategic attacks against conspirators Claudius continues to establish himself and to secure his reign.
From social | political reform to showing mercy on foreign enemies he oversees the most stable Roman government since Augustus.
From marital issues to assassinations this finale dives into the very heart of Claudius and his complicated world.
Finally after a period of unsuccessful and or doomed marriages we approach the end of the story as he marries Agrippina the Younger and a new chapter of intrigue, murder and conspiracy begins as Agrippina attempts to establish her own powerbase and place for her son Nero in the very heart of Roman power.
Alas we come to the death or as many say the assassination of Claudius and we review his legacy and all that he achieved as an unlikely individual who became on of the greatest Emperors in Roman history.
Support Dr. Traver and his works at these links below!
Academia Page: https://selu.academia.edu/ATraver
Faculty Page: http://www.southeastern.edu/acad_research/depts/hist_ps/faculty/bio/traver.html
Attribution: I, Claudius : https://www.youtube.com/watch?v=0dvbX8imXnI&t=18s
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In the final episode on our trilogy on Emperor Claudius Dr. Andrew Traver takes us into the very heart of his reign in the roman empire and into the very deaths of his mortality.
After the shocking rise of Claudius to power the Roman Empire went under expansion not seen since Emperor Augustus as Claudius launched campaigns and especially into Britain finalizing the dream of Julius Caesar.
But from bloody conquests to senate intrigue Claudius launches major reform throughout the Justice system and within the Roman courts as he strives to become more active while even hearing cases himself.
From investigating senators to carrying out strategic attacks against conspirators Claudius continues to establish himself and to secure his reign.
From social | political reform to showing mercy on foreign enemies he oversees the most stable Roman government since Augustus.
From marital issues to assassinations this finale dives into the very heart of Claudius and his complicated world.
Finally after a period of unsuccessful and or doomed marriages we approach the end of the story as he marries Agrippina the Younger and a new chapter of intrigue, murder and conspiracy begins as Agrippina attempts to establish her own powerbase and place for her son Nero in the very heart of Roman power.
Alas we come to the death or as many say the assassination of Claudius and we review his legacy and all that he achieved as an unlikely individual who became on of the greatest Emperors in Roman history.
Support Dr. Traver and his works at these links below!
Academia Page: https://selu.academia.edu/ATraver
Faculty Page: http://www.southeastern.edu/acad_research/depts/hist_ps/faculty/bio/traver.html
Attribution: I, Claudius : https://www.youtube.com/watch?v=0dvbX8imXnI&t=18s
To my dear subscribers, thank you all. You have my love and appreciation. Support Ancient Origins above! Look below to support this channel!
Check out our store! History Merch: https://www.youtube.com/c/TheStudyofAntiquityandtheMiddleAges/store
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How can we tell what’s fake and what’s real? What’s the difference between a forgery and a replica? Which was Giovanni da Cavino trying to make when he created ...
How can we tell what’s fake and what’s real? What’s the difference between a forgery and a replica? Which was Giovanni da Cavino trying to make when he created his medals? Mary Beard explores the motives behind Cavino’s creations.
Learn more about this work of art and come see it in person: https://www.nga.gov/collection/art-object-page.45042.html
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How can we tell what’s fake and what’s real? What’s the difference between a forgery and a replica? Which was Giovanni da Cavino trying to make when he created his medals? Mary Beard explores the motives behind Cavino’s creations.
Learn more about this work of art and come see it in person: https://www.nga.gov/collection/art-object-page.45042.html
Hear more from Mary Beard on the “Twelve Caesars” here: https://youtube.com/playlist?list=PLErBGbWC2wSO8DCCSR3s-QZ3FoArssQYU
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✅FRESH HOT NEW MERCH JUST DROPPED💯🔥✅
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Today we played an Extreme Game of Scoot!
The Legend Ryan Williams VS Claudius Vertesi at Allin Indoor Skatepark in Canada! We both did insane Scooter Tricks & pushed ourselves a lot! It was a very special Game of Scoot, because we both have a very unique riding style, so we tried to mix our styles & combined them! We did Awesome & Pro Scooter Tricks like Backflip, Flair, Front Flip Tailwhip, Buttercups which is very hard for Ryan Williams, because his Golden Scooter is a lot bigger & heavier! Ryan set a Tailwhip to Invert, which was also very difficult for me & some amazing Rail Grinds, Nose manuals & even a Backflip Drop on the Small Quarter! Ryan Williams even tried a cash roll & hucked a double Backflip! I did one to Foam Pit & then sent the Tricks on the Huge Resi Box, but unfortunately the lights went off, which was very scary, because I almost could not see the landing...
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family friendly pg clean
Today we played an Extreme Game of Scoot!
The Legend Ryan Williams VS Claudius Vertesi at Allin Indoor Skatepark in Canada! We both did insane Scooter Tricks & pushed ourselves a lot! It was a very special Game of Scoot, because we both have a very unique riding style, so we tried to mix our styles & combined them! We did Awesome & Pro Scooter Tricks like Backflip, Flair, Front Flip Tailwhip, Buttercups which is very hard for Ryan Williams, because his Golden Scooter is a lot bigger & heavier! Ryan set a Tailwhip to Invert, which was also very difficult for me & some amazing Rail Grinds, Nose manuals & even a Backflip Drop on the Small Quarter! Ryan Williams even tried a cash roll & hucked a double Backflip! I did one to Foam Pit & then sent the Tricks on the Huge Resi Box, but unfortunately the lights went off, which was very scary, because I almost could not see the landing...
I hope You enjoy this Video & make sure to LIKE, COMMENT & to SUBSCRIBE!! TURN ON POST NOTIFIACTIONS ❤️!!
😻WATCH MY LAST VIDEO😻
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The Ptolemaic dynasty in Ancient Egypt began under the rule of Ptolemy I Soter, whose goal was to make Egypt great again and he did that by putting the country back on solid economic and administrative footing, and it ended with Cleopatra VII. When Alexander the Great of Macedon died unexpectedly in 323 BCE he had amassed an enormous empire spanning from Egypt through Anatolia, Mesopotamia and parts of India. In order to stay away from the influence of the priests and officials at Memphis, Ptolemy I moved the capital from its traditional place at Memphis to Alexandria. Alexandria, a city established by Alexander the Great, grew and flourished under the Ptolemies. The city became more of a Greek city than an Egyptian one, with the port giving easy access to the sea and Greece, and with Greece becoming the language of both commerce and government.
A thing to note about the Ptolemies, although they were Pharaohs of Egypt, they didn’t learn the Egyptian language and pretty much just stayed in Alexandria (which they had made the new capital, moving it from the traditional capital of Memphis). They used Greek for all of their administrative documents, and married within their own family to keep the bloodline pure and also keep their wealth in the family.
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— CHAPTERS —
0:00 Introduction
0:51 Lead Up To The Ptolemaic Dynasty
3:50 Egypt During the Ptolemaic Dynasty
7:48 The Ptolemy Family Tree
16:49 Outro
— WANT TO KNOW MORE? —
Ptolemaic Dynasty https://www.worldhistory.org/Ptolemaic_Dynasty/
Ptolemy I https://www.worldhistory.org/Ptolemy_I/
Ptolemy XIII Theos Philopator https://www.worldhistory.org/Ptolemy_XIII_Theos_Philopator/
Arsinoe II Philadelphus https://www.worldhistory.org/Arsinoe_II_Philadelphus/
Cleopatra VII https://www.worldhistory.org/Cleopatra_VII/
The Economy of Ptolemaic Egypt https://www.worldhistory.org/article/1256/the-economy-of-ptolemaic-egypt/
Berenika II Euergetis https://www.worldhistory.org/Berenice_II_Euergetis/
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Cleopatra VII Philopator: the Last Queen of Ancient Egypt https://www.youtube.com/watch?v=J6bM6ElVO5k
7 Surprising Stories from Herodotus' Histories https://www.youtube.com/watch?v=QRf1jUgXRqQ
Alexander the Great: Life and Reign of the King of the Macedonian Empire https://www.youtube.com/watch?v=_E7JX-rVdFk
The Seven Wonders of the Ancient World: an Overview https://www.youtube.com/watch?v=1YWPMZ6pHm8
Comparing Two Ancient Civilisations: Ancient Egypt vs. Mesopotamia https://www.youtube.com/watch?v=EwY-ziBL1Jw
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You can find all attribution and credits for images, animations, graphics and music here - https://worldhistory.typehut.com/the-ptolemaic-dynasty-of-ancient-egypt-from-ptolemy-i-to-cleopatra-vii-images-and-attributions-8317
The music used in this recording is the intellectual copyright of Michael Levy, a prolific composer for the recreated lyres of antiquity, and used with the creator's permission. Michael Levy's music is available to stream at all the major digital music platforms. Find out more on:
https://www.ancientlyre.com
https://open.spotify.com/artist/7Dx2vFEg8DmOJ5YCRm4A5v?si=emacIH9CRieFNGXRUyJ9
https://www.youtube.com/channel/UCJ1X6F7lGMEadnNETSzTv8A
— THUMBNAIL IMAGE —
https://www.worldhistory.org/image/15205/family-tree-of-the-ptolemaic-dynasty-of-egypt-305/
Simeon Netchev
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Stella
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World History Encyclopedia
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#ptolemy #ptolemaicdynasty #cleopatravii
Without modern instruments, it was very hard to understand what the planets were, especially since they seemed to wander independently from the stars. Ptolemy provided the definitive answer for the time being. Earth was the centre of the universe and all the heavenly bodies rotated around it.
For inquiry, consider the following:
1. Investigate the work of Aristarchus. What was his model of the universe and why? How did it differ from Ptolemy's?
2. Why is there no gale force wind blowing constantly as the Earth moves about the Sun? What is the cause of wind? How do hurricanes evolve?
3. What was it about the Ptolemaic model that allowed it to last for 1500 years, and what was it that eventually brought about it's demise?
4. Explain why you don't change position in a moving train when you jump up in the air. Why does the train not move out from under you?
5. Use this website as a starting point to do some research and reporting into the great minds that have influenced our understanding of the heavens: https://starchild.gsfc.nasa.gov/docs/StarChild/universe_level2/cosmology.html
6. In Western society, we often hear only about the Greeks and perhaps the Egyptians, with regard to astronomy. Find one major astronomical contribution made by the Chinese, the Indian and at least one First Nation.
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Further Reading:
Samuel Sharpe - The History of Egypt under the Ptolemies
C. A. Kincaid - Successors of Alexander the Great
Ian Shaw - The Oxford History of Ancient Egypt
Diodorus Siculus - Library of History
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Good lord. This is a giant mess of a family tree. Just... Just watch it and see for yourself.
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We are making history again by presenting a new visual proof of the 2000+ years old Ptolemy's theorem and Ptolemy's inequality.
00:00 Introduction
04:27 Geometry 101
08:19 Applications
14:46 Ptolemy's inequality
18:34 LIES
25:35 Animated proofs
28:57 Thank you!
30:53 Degenerate Easter Egg
There are some other proofs of Ptolemy's theorem/inequality based on scaling and aligning suitable triangles. However, none of them is as slick, beautiful and powerful as Rainer's new proof. In particular, check out the animated scaling proof on the wiki page for Ptolemy's theorem (and this https://youtu.be/ZK08Z5A9xH4) and check out the scaling proof by Claudi Asina and Roger Nelson: Proof Without Words: Ptolemy’s Inequality in Mathematics Magazine 87, (2014), p. 291. https://www.jstor.org/stable/10.4169/math.mag.87.4.291
Rainer was inspired by a classic scaling based proof of Pythagoras theorem that I presented here https://youtu.be/p-0SOWbzUYI?si=GeGzZ0R_Dj1AsXqR&t=371
You can find a couple of full text versions of the Almagest here
https://www.wilbourhall.org/index.html#ptolemy
https://classicalliberalarts.com/resources/PTOLEMY_ALMAGEST_ENGLISH.pdf
For more background info check out the very comprehensive wiki pages on:
Ptolemy’s theorem
https://en.wikipedia.org/wiki/Ptolemy%27s_theorem
Ptolemy’s inequality
https://en.wikipedia.org/wiki/Ptolemy%27s_inequality
Claudius Ptolemy
https://en.wikipedia.org/wiki/Ptolemy
The Almagest
https://sco.wikipedia.org/wiki/Almagest
Trigonometric identities
https://en.wikipedia.org/wiki/List_of_trigonometric_identities
Cyclic quadrilateral
https://en.wikipedia.org/wiki/Cyclic_quadrilateral
The optic equation
https://en.wikipedia.org/wiki/Optic_equation
There are very interesting higher-dimensional versions of Ptolemy's theorem just like there are higher-dimensional versions of Pythagoras theorem. I did not get around to talking them today. Google ...
Highly recommended:
T. Brendan, How Ptolemy constructed trigonometry tables, The Mathematics Teacher 58 (1965), pp. 141-149 https://www.jstor.org/stable/27967990
Tom M. Apostol, Ptolemy's Inequality and the Chordal Metric, Mathematics Magazine 40 (1967), pp. 233-235 https://www.jstor.org/stable/2688275
https://demonstrations.wolfram.com/PtolemysTableOfChords/ an interactive exploration of Ptolemy's table of chords
Ptolemy's theorem made a guest appearance in the the previous Mathologer video on the golden ratio: https://youtu.be/cCXRUHUgvLI
Here is a nice trick to make Ptolemy counterparts of Pythagorean triples. Take any two sets of Pythagorean triples:
5² = 3² + 4², 13² = 12² + 5², and combine them like this:
65² = 13² × 5²= 13²(4² + 3²) = 52² + 39²= 5²(12² + 5²) = 60² + 25².
Now combining the two right angled triangles 52-39-65 and 25-60-65 along the common diagonal in any of four different ways gives a convex quadrilateral with all sides integers. Note that you automatically get 5 integer lengths and then Ptolemy's theorem guarantees that the remaining side is a fraction. Scaling up everything by the denominator of that fraction gives one of the special integer-everywhere quadrilaterals. See also Brahmagupta quadrilaterals.
Here is a nice application of Ptolemy's theorem to a International Maths Olympiad problem https://www.youtube.com/watch?v=NHjtHOE1lks
In a cyclic quadrilateral the ratio of the diagonals equals the ratio of the sums of products of the sides that share the diagonals' end points: https://www.geogebra.org/m/XQr5jJQg This extension of Ptolemy's theorem is part of the thumbnail for this video.
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Ptolemy I Soter, a former commander of Alexander the Great turned King and Pharaoh of Egypt, was perhaps the craftiest out of all of Alexander’s Successors. A talented commander and even more brilliant politician, Ptolemy would wield diplomacy and intrigue with a deft hand, founding what would become the longest lasting Hellenistic Kingdom in his nearly 40-year reign.
Website/Episode Notes:
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Ptolemy was the author of several scientific treatises, three of which were of continuing importance to later Byzantine, Islamic and European science. The first is the astronomical treatise now known as the Almagest, although it was originally entitled the "Mathematical Treatise" (Μαθηματικὴ Σύνταξις, Mathēmatikē Syntaxis) and then known as the "Great Treatise" (Ἡ Μεγάλη Σύνταξις, Ē Megálē Syntaxis). The second is the Geography, which is a thorough discussion of the geographic knowledge of the Greco-Roman world. This manuscript was used by Christopher Columbus as the map for his westward-bound path to Asia, in which he discovered the hitherto unknown lands of the Americas. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristoteliannatural philosophy of his day. This is sometimes known as the Apotelesmatika (Ἀποτελεσματικά) but more commonly known as the Tetrabiblos from the Greek (Τετράβιβλος) meaning "Four Books" or by the Latin Quadripartitum.
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Source/Further reading:
Excellent podcast series, a few episodes on Claudius here: https://thehistoryofrome.typepad.com/the_history_of_rome/2009/07/61-what-me-claudius.html
Podcast on Claudius’s life (the following two episodes are also worth hearing): https://podcasts.google.com/?feed=aHR0cHM6Ly93d3cubGF0cm9iZS5lZHUuYXUvbWFya2V0aW5nL2Fzc2V0cy9wb2RjYXN0cy9yc3NmZWVkcy9jYWVzYXIueG1s&episode=NzZFNkMyRjYtRTVBOS00MjA5LUI4REUtNTU2OTg2RTEzQUUw&hl=en-CZ
Podcast on Claudius’s early life: https://partialhistorians.com/2013/09/08/episode-12-claudius-an-imperial-life-with-unusual-twists/
Britannica’s biography: https://www.britannica.com/biography/Claudius-Roman-emperor
Suetonius’s biography in full: http://penelope.uchicago.edu/Thayer/e/roman/texts/suetonius/12caesars/claudius*.html
(Father): https://www.britannica.com/biography/Nero-Claudius-Drusus-Germanicus
(Cerebral palsy): https://www.historytoday.com/archive/months-past/death-emperor-claudius
Biographics on Caligula: https://www.youtube.com/watch?v=3zgJ1Cb99uA
Biographics on Nero: https://www.youtube.com/watch?v=WIW10E1xAOI
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Kings and Generals historical animated documentary series on Roman history continues with a video on the emperor Claudius, an unlikely good emperor, who come to power after Caligula and managed to right the ship of the empire. He was known as a reformer, who curbed the power of the aristocracy, and improved the finances of the empire, as well as the conqueror of Britain.
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Aurelian: https://youtu.be/YQHNaemGOoI
Commodus: https://youtu.be/nVW5RJj6CTo
Sejanus: https://youtu.be/f2iFXVdkw4w
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#Documentary #Claudius #RomanEmpire
Emperor Claudius, he was probably the least likely male in the Julio-Claudian dynasty to become Emperor of Rome. However, due to the high mortality rate of males in the dynasty… he was proclaimed Emperor by the Praetorian Guard...
Born August the 1st in 10 BC, in Lugdunum in Gaul, He was the son of Drusus who was Emperor Tiberius' brother. His mother was Antonia, daughter of Mark Anthony and Octavia, Augustus' sister.
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Max Manie is a young and talented producer, born in Salzburg and now living and studying in Vienna. Industries and audience’s eyes are stuck on him. All started from his track “Sunday”, a little shining pearl found on Soundcloud with over 4 million combined plays and big names supporting, ranging from Bakermat to Robin Schulz and Tiesto.
Now Max keeps the great work coming and thrills us with another amazing work, “The Ocean EP”. It includes two incredibly beautiful tracks, “Ocean” and “Claudius”. They are filled with deepness, melody and the power of creation.
“Claudius” contains elements from “Stubborn Kind of Fellow” written and composed by Marvin Gaye. It’s an intense track, able to bring us on a never ending emotional journey...
Max Manie is a rising star ready to be in the spotlight and shine in the sky.
In the final episode on our trilogy on Emperor Claudius Dr. Andrew Traver takes us into the very heart of his reign in the roman empire and into the very deaths of his mortality.
After the shocking rise of Claudius to power the Roman Empire went under expansion not seen since Emperor Augustus as Claudius launched campaigns and especially into Britain finalizing the dream of Julius Caesar.
But from bloody conquests to senate intrigue Claudius launches major reform throughout the Justice system and within the Roman courts as he strives to become more active while even hearing cases himself.
From investigating senators to carrying out strategic attacks against conspirators Claudius continues to establish himself and to secure his reign.
From social | political reform to showing mercy on foreign enemies he oversees the most stable Roman government since Augustus.
From marital issues to assassinations this finale dives into the very heart of Claudius and his complicated world.
Finally after a period of unsuccessful and or doomed marriages we approach the end of the story as he marries Agrippina the Younger and a new chapter of intrigue, murder and conspiracy begins as Agrippina attempts to establish her own powerbase and place for her son Nero in the very heart of Roman power.
Alas we come to the death or as many say the assassination of Claudius and we review his legacy and all that he achieved as an unlikely individual who became on of the greatest Emperors in Roman history.
Support Dr. Traver and his works at these links below!
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Attribution: I, Claudius : https://www.youtube.com/watch?v=0dvbX8imXnI&t=18s
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How can we tell what’s fake and what’s real? What’s the difference between a forgery and a replica? Which was Giovanni da Cavino trying to make when he created his medals? Mary Beard explores the motives behind Cavino’s creations.
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Today we played an Extreme Game of Scoot!
The Legend Ryan Williams VS Claudius Vertesi at Allin Indoor Skatepark in Canada! We both did insane Scooter Tricks & pushed ourselves a lot! It was a very special Game of Scoot, because we both have a very unique riding style, so we tried to mix our styles & combined them! We did Awesome & Pro Scooter Tricks like Backflip, Flair, Front Flip Tailwhip, Buttercups which is very hard for Ryan Williams, because his Golden Scooter is a lot bigger & heavier! Ryan set a Tailwhip to Invert, which was also very difficult for me & some amazing Rail Grinds, Nose manuals & even a Backflip Drop on the Small Quarter! Ryan Williams even tried a cash roll & hucked a double Backflip! I did one to Foam Pit & then sent the Tricks on the Huge Resi Box, but unfortunately the lights went off, which was very scary, because I almost could not see the landing...
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