Terrestrial Ball
Ptolemy's system was originated not by himself but by earlier astronomers.
Its contemporary acceptance was not universal, but the widespread belief
that has somehow established itself that everyone prior to Christopher
Columbus thought the earth was flat is baseless. When the hymn-writer sings,
"Let every kindred, every tribe,
On this terrestrial ball,
To Him all majesty ascribe,
And crown Him Lord of all;
To Him all majesty ascribe,
And crown Him Lord of all!
(All
Hail the Power of Jesus' Name)
...it is foolish to insist the question of flat-earthism remains open.
And writers in antiquity also called the earth a globe or an orb:
"Military discipline jealously conserved won the leadership of Italy for Roman empire, bestowed rule over many cities, great kings, mighty nations...made it from its origin in Romulus' little cottage into the summit of the entire globe [terrarum orbis]." (Valerius Maximus, 'Memorable Doings and Sayings,' Book II.8).
"For he wisely realized that increase for Roman empire was to be asked for in the days when triumphs were sought on the near side of the seventh milestone, but for a people that possessed the greater part of the whole globe [terrarum orbis] it would be greedy to ask for more and abundantly fortunate if they lost nothing of what was already theirs." (Valerius Maximus, 'Memorable Doings and Sayings,' Book IV.1).
"The magnanimous monarch, who had already embraced the entire globe [terrarum orbem] by his victories or expectations, in so few words shared himself with him companion." (Valerius Maximus, 'Memorable Doings and Sayings,' Book IV.7).
"The signal clemency of the divine leader kept this father safe, but
who would not think his daring more than human in that he did not yield
to one to whom the whole world [terrarum orbis] succumbed?" (Valerius Maximus, 'Memorable Doings and Sayings,' Book V.7).
Since this language is boiler-plate, it comes as no surprise when Eusebius
puts the phrase in the mouth of the Emperor Constantine:
"The stars move in no uncertain orbits round this terrestrial globe." (Eusebius, The Life of Constantine, Book 2, Chapter 58).
This language did not thereafter pass out of fashion:
"For all those things, which at present you witness in the Church of God, and which you see to be taking place under the name
of Christ throughout the whole world [totum orbem terrarum], were predicted long ages ago.
. .It was foretold not only by the prophets, but also by the
Lord Jesus Christ Himself, that His Church would exist
throughout the whole world [universum orbem terrarum], extended
by the martyrdoms and sufferings of the saints. . ."
(Augustine, On Catechizing the Uninstructed, Chapter XXVII,
Section 53.)
It is eccentric to say the very least for speakers who believe the earth is flat to call it an 'orb' or 'globe.'

Talmud
Did the Jews agree with the pagans on the rotundity of the earth? One answer
is found in the Talmud, which discusses statuary. Is it an ornamentation
to a city, or idolatry? According to the Rabbis, if a statue, of an emperor,
say, holds a ball in his hand, this suggests he rules the whole world,
the prerogative of God:
"...Rabbah said: There is difference of opinion [with regard to statues]
in cities; but as for those in villages all agree that they are prohibited.
"BUT THE SAGES DECLARE, [AN IMAGE] IS NOT PROHIBITED etc. [It is prohibited when holding] a staff, because [the implication is] that it rules the whole world as with a staff. [...] [It is prohibited when holding] an orb, because [the implication is] that it grasps the whole world as though it were a ball."
(Babylonian Talmud, Abodah Zara 41a).
But why would holding a ball convey this message, if it were thought the
earth is flat?

Money in the Bank
A round object turns up on Roman coins, such as this one depicting the Emperor Caracalla holding
the world in his hand:

Poets
Some people are willing to concede that the astronomers of
antiquity realized the earth was round, as indeed cannot be denied.
They allege, however, that most people did not know this. While
there are dissenters throughout the period, in fact most people had
good reason to know this. A rotund earth turns up in popular poetry, like
Virgil's Georgics:
"As our globe rises steep
to Scythia and the Riphaean crags, so it slopes downward to Libya's
southland. One pole is ever high above us, while the other,
beneath our feet, is seen of black Styx and the shades
infernal. . .There, men say,
is either the silence of lifeless night, and gloom ever
thickening beneath night's pall; or else Dawn returns from us
and brings them back the day, and when on us the rising Sun
first breathes with panting steeds, there glowing Vesper is
kindling his evening rays." (Virgil,
Georgics, Georgic 1).

Dark Ages
This knowledge was never lost; Thomas Aquinas, writing in the middle ages, boasts of the
improved number his contemporaries had worked up for the circumference of the earth:
"But according to the more careful measurement of present-day astronomers, the earth's
circumference is much less, i.e., 20,000 times 1,000 paces and 400, as Al Fargani says; or 180,000
stades, as Simplicius says — which is about the same, since 20,000 is 1/8 of 160,000. . .And so,
from all of this, we can argue that the earth's quantity is not only spherical, but not large
in comparison to the sizes of the other stars." (Thomas Aquinas,
Commentary on Aristotle's De Caelo, 'On
the Heaven,' Book II, Lecture 28, 543).
People who want to criticize the church's loyalty to Ptolemaic
astronomy will have no difficult finding fault with Ptolemy's model. The system is geocentric,
but not with respect to a fixed point; the whole contraption does a little shimmy, like a grocery
cart with a bumpy wheel. Why they feel to need to make up a non-existent feature: a flat
earth,— is a mystery.

What is the music of the spheres?:
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