Question: Which Roman emperor was personally known by or written about by both Thrasyllus of Mendes and Tacitus?

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Vibia Aurelia Sabina: Vibia Aurelia Sabina (170 AD – before 217 AD) was a Roman Princess.  She was the youngest daughter and child born to Roman Emperor Marcus Aurelius and Roman Empress Faustina the Younger.  She was a sister to Roman Empress Lucilla and Roman Emperor Commodus.  Her maternal grandparents were Roman Emperor Antoninus Pius and Roman Empress Faustina the Elder and her paternal grandparents were Domitia Lucilla and praetor Marcus Annius Verus.

John Giffard (1602–1665): Colonel John Giffard (1602–1665), (pron.  "Jiffard") of Brightley in the parish of Chittlehampton, Devon, England was a Royalist leader during the Civil War.  Giffard commanded the Devon Pikemen at the Battle of Lansdowne in 1634 in which his 3rd cousin the Royalist commander of the Cornish forces Sir Bevil Grenville (1596-1643) was killed in heroic circumstances.  Giffard's loyalty to the Royalist cause led to him being proposed in 1660 as a knight of the intended Order of the Royal Oak.  He was personally known to the biographer John Prince (1643–1723) who included him as one of his "Worthies of Devon".  He was buried in Chittlehampton Church, where his small kneeling effigy survives on the base of the monument he erected in 1625 to his grandfather.

Apostolic Fathers: The Apostolic Fathers were Christian theologians who lived in the 1st and 2nd centuries AD, who are believed to have personally known some of the Twelve Apostles, or to have been significantly influenced by them.  Their writings, though popular in Early Christianity, were ultimately not included in the canon of the New Testament once it reached its final form.  Many of the writings derive from the same time period and geographical location as other works of early Christian literature that did come to be part of the New Testament, and some of the writings found among the Apostolic Fathers' seem to have been just as highly regarded as some of the writings that became the New Testament.

Tacitus: Publius (or Gaius) Cornelius Tacitus ( ; ] ;  56 AD –  120 AD ) was a senator and a historian of the Roman Empire.  The surviving portions of his two major works—the "Annals" and the "Histories"—examine the reigns of the Roman emperors Tiberius, Claudius, Nero, and those who reigned in the Year of the Four Emperors (69 AD).  These two works span the history of the Roman Empire from the death of Augustus, in 14 AD, to the years of the First Jewish–Roman War, in 70 AD.  There are substantial lacunae in the surviving texts, including a gap in the "Annals" that is four books long.

Tacitus (emperor): Tacitus ( ; Latin: "Marcus Claudius Tacitus Augustus" ; c. 200 – June 276), was Roman Emperor from 275 to 276.  During his short reign he campaigned against the Goths and the Heruli, for which he received the title "Gothicus Maximus".

Country lawyer: In the United States, the term country lawyer or county-seat lawyer may be applied to identify an attorney living and practicing primarily in a rural area or town, or an attorney pursuing a legal practice that displays certain (potentially idealized) hallmarks of rural or small-town legal practice.  In such areas, the county seat is likely to be an important center of government and home to the county courthouse, the forum for local criminal trials and civil litigation.  The legal community may be small and close-knit (at the extreme, with only a few attorneys, all of whom know each other, and all of whom may be personally known to the community), and each individual attorney may handle a wide variety of legal matters as local needs dictate.  Historically, such an attorney may have been more likely to have joined the bar by reading law rather than attending school, and in modern times may have (or may be assumed to have) graduated from a lower tier legal program.

Junia Calvina: Junia Calvina was a Roman noblewoman who lived in the 1st century AD.  The daughter of Aemilia Lepida and Marcus Junius Silanus Torquatus, Calvina belonged to two patrician houses: the "gens Aemilia" and "gens Junia" respectively.  She was also the great-great-granddaughter of the Roman emperor Caesar Augustus on her mother's side of the Imperial family.  As such, she was also related by blood to the "gens Julia, the aristocratic family of the Roman dictator Julius Caesar.  Tacitus calls Calvina "festivissima puella" and the Emperor Vespasian, in one of his jokes, mentions her as living in AD 79.

Thrasyllus of Mendes: Thrasyllus of Mendes ( ; Greek: Θράσυλλος Μενδήσιος ), also known as Thrasyllus of Alexandria and by his Roman citizenship name Tiberius Claudius Thrasyllus ( Τιβέριος Κλαύδιος Θράσυλλος ; fl.  second half of the 1st century BC and first half of the 1st century – died 36,), was an Egyptian Greek grammarian and literary commentator.  Thrasyllus was an astrologer and a personal friend of the Roman emperor Tiberius, as mentioned in the "Annals" by Tacitus and "The Twelve Caesars" by Suetonius.

Fadilla: Annia Aurelia Fadilla, most commonly known as Fadilla (159-died after 211) was an influential Roman Princess and was one of the daughters born to Roman Emperor Marcus Aurelius and Roman Empress Faustina the Younger.  She was a sister to Roman Empress Lucilla and Roman Emperor Commodus.  Fadilla was named in honor of her late maternal aunt Aurelia Fadilla.  The cognomen Fadilla, was the cognomen of the mother and a half-sister of the previous Roman Emperor Antoninus Pius.  Her maternal grandparents were Roman Emperor Antoninus Pius and Roman Empress Faustina the Elder and her paternal grandparents were Domitia Lucilla and praetor Marcus Annius Verus.

Claudia Capitolina: Claudia Capitolina (Greek: η Κλαuδία Καπιτωλίνα ) was an Egyptian Greek woman who lived in the Roman Empire, in the 1st century and possibly in the 2nd century.  Capitolina came from a distinguished family of Equestrian rank.  She was born and raised in Alexandria, Egypt.  Capitolina was the daughter and only child of Tiberius Claudius Balbilus by his unnamed wife.  The cognomen "Capitolina", is probably from her maternal side.  Her father was one of the highest magistrates of Equestrian rank that served in Rome.  Balbilus was an astrologer and a learned scholar, who was later Prefect of Egypt.  Capitolina’s paternal grandfather, was an Egyptian Greek Grammarian and Astrologer called Thrasyllus of Mendes or Tiberius Claudius Thrasyllus, who was a friend of the Roman Emperor Tiberius, while her paternal grandmother was Greek Princess Aka II of Commagene, who was a great, granddaughter of King Antiochus I Theos of Commagene.  Her paternal cousin was Ennia Thrasylla who married the Praetorian prefect of the Praetorian Guard, Naevius Sutorius Macro.

Supporting paragraphs: Thrasyllus of Mendes Tacitus
Answer: Tiberius