According to Pappus ' theorem, the resulting system of nine points and eight lines always has a ninth line containing the three intersection points X, Y, and Z.

According to the 4th-century report of Pappus of Alexandria, Apollonius ' own book on this problem — entitled (, " Tangencies "; Latin: De tactionibus, De contactibus )— followed a similar progressive approach.

According to Lampridius, the emperor Alexander Severus ( 222 – 235 ), who was not a Christian, had kept a domestic chapel for the veneration of images of deified emperors, of portraits of his ancestors, and of Christ, Apollonius, Orpheus and Abraham.

According to sources, Theseus also was one of the Argonauts, although Apollonius of Rhodes states in the Argonautica that Theseus was still in the underworld at this time.

According to Philostratus ' Life, en route to the Far East, Apollonius reached Hierapolis Bambyce ( Manbij ) in Syria ( not Nineveh, as some scholars believed ), where he met Damis, a native of that city who became his lifelong companion.

According to the Historia Augusta he abstained from destroying the city after having a vision of Apollonius admonishing him to spare the innocent citizens.

Medieval alchemist Jabir ibn Hayyan's Book of Stones According to the Opinion of Balīnās contains an exposition and analysis of views expressed in Arabic occult works attributed to Apollonius.

According to Apollonius of Rhodes, he was a son of Agenor, but the Bibliotheca says that other authors named his father as Poseidon.

According to Pindar's ninth Pythian Ode and Apollonius ' Argonautica ( II. 522ff ), Cyrene despised spinning and other womanly arts and instead spent her days hunting, but, in a prophecy he put in the mouth of the wise centaur Chiron, Apollo would spirit her to Libya and make her the foundress of a great city, Cyrene, in a fertile coastal plain.

According to Apollonius Rhodius and Pausanias he was the first king ever to have made a treasury, of which the ruins were still extant in Pausanias ' times.

According to Apollonius Rhodius, Iris turned back the Argonauts Zetes and Calais who had pursued the Harpies to the Strophades (' Islands of Turning ').

According to Vita A, he was a famous teacher in Rhodes, but it may have confused him with yet another Apollonius ( Apollonius the Effeminate ) who taught rhetoric there.

According to Apollonius of Rhodes and Ovid, amber originated from the tears of the Heliades, encased in poplars as dryads, shed when their brother, Phaeton, died and fell from the sky, struck by Zeus ' thunderbolt, and tumbled into the Eridanos, where " to this very day the marsh exhales a heavy vapour which rises from his smouldering wound ; no bird can stretch out its fragile wings to fly over that water, but in mid-flight it falls dead in the flames ;" " along the green banks of the river Eridanos ," Cygnus mourned him — Ovid told — and was transformed into a swan.

According to Josephus, in Against Apion, Apollonius Molon slandered the Jews.

According to Apollonius of Rhodes, the cave where Macris once lived was later the marriage chamber for Jason and Medea, and the marriage was consummated there on the Golden Fleece.

According to Philostratus, Apollonius met Damis in a city which Philostratus calls " Old Ninos ", which from its location cannot be Nineveh, but is in fact the " holy city " of Hierapolis Bambyce ( Manbij ) in Syria.

According to Apollonius Rhodius, the figurehead of Jason's ship, the Argo, was built of oak from the sacred grove at Dodona and could speak the language of birds.

According to the official interpretation of the Charter, a member cannot be penalized by not having the right to vote in the General Assembly for nonpayment of financial obligations to the `` special '' United Nations' budgets, and of course cannot be expelled from the Organization ( which you suggested in your editorial ), due to the fact that there is no provision in the Charter for expulsion.

According to the myth, Old Order then vanishes at stage left and reappears at extreme stage right, but Director Shuz skillfully sidesteps the rather gooshey problem of stage effects by simply having Miss Arapacis walk across the stage.

According to The Annotated Alice, Carroll had originally had the characters dry off by having the Dodo lead them to a nearby house for towels.

According to the accounts given by Pindar and the tragedians, Agamemnon was slain in a bath by his wife alone, a blanket of cloth or a net having first been thrown over him to prevent resistance.

According to a controversial tradition reported by several medieval sources, Narses, out of spite for having been removed by Justinian's successor Justin II, called the Lombards to Italy.

According to Ovid's Metamorphoses, while in labour, Alcmene was having difficulty giving birth to such a large child.

According to the U. S. Centers for Disease Control and Prevention ( CDC ), risk factors for BV include douching and having new or multiple sex partners, although it is unclear what role sexual activity plays in the development of BV.

According to the 802. 16-2004 standard, broadband means " having instantaneous bandwidths greater than 1 MHz and supporting data rates greater than about 1. 5 Mbit / s.

According to United Nations High Commissioner for Refugees, around 125, 000 ethnic Serbs who fled the 1991 – 1995 conflict are registered as having returned to Croatia, of whom around 55, 000 remain permanently.

" According to this definition, celibacy ( even short-term celibacy that is pursued for non-religious reasons ) is much more than not having sex.

According to the American Bar Association, a lawyer that is a certified specialist has been recognized by an independent professional certifying organization as having an enhanced level of skill and expertise, as well as substantial involvement in an established legal specialty.

According to many of Descartes ' specialists, including Étienne Gilson, the goal of Descartes in establishing this first truth is to demonstrate the capacity of his criterion — the immediate clarity and distinctiveness of self-evident propositions — to establish true and justified propositions despite having adopted a method of generalized doubt.

According to his biography, A Life Decoded, he was said to never be a terribly engaged student, having Cs and Ds on his eighth-grade report cards.

According to a 1999 estimate, there are no merchant marines and there are two airports, both having paved runways of 914 to 1, 523 meters.

According to Coppola, the studio's objection stemmed from the belief that audiences would be reluctant to see a film with such a title, as the audience would supposedly believe that, having already seen The Godfather, there was little reason to see an addition to the original story.

" According to America's Best Franchises, there are many benefits to choosing to become a home-based franchisee, " but having a home based business doesn't offer any guarantees as you will encounter many challenges you'll have to learn to overcome.

According to documents found in the possession of a descendant of the Manfredi family, Nadia Manfredi, in 2007, Puccini was actually having an affair with Giulia Manfredi, Doria's cousin.

According to the Mishnah and Tosefta, in the Maccabean, Herodian, and Mishnaic periods, new months were determined by the sighting of a new crescent, with two eye witnesses required to testify to the Sanhedrin to having seen the new lunar crescent at sunset.

According to Adrian Fortescue, the Scholastic theory that God is pure actuality prevented Palamism from having much influence in the West.

According to Mark Kurlansky, " Smoked foods almost always carry with them legends about their having been created by accident — usually the peasant hung the food too close to the fire, and then, imagine his surprise the next morning when …".

According to the agreements reached at San Remo, France had its control over what was termed Syria recognised, the French having taken Damascus in 1920.

( According to the prose introduction to the poem Tyr is now one-handed from having his arm bitten off by Loki's son Fenrir while Fenrir was bound.

According to Agassiz ’ s theory of polygenism animals, plants and humans were all created in “ special provinces ” each having distinct populations of species created in and for that province.

According to contemporary royalist legal theory, the Long Parliament was regarded as having been automatically dissolved from the moment of Charles I's execution on 30 January 1649.