You missed another shortcoming of Isidore's book: [....]  The point is, Africa is joined to Asia by continuous land mass north of the Red Sea, which only was breached by the building of the Suez Canal in modern times.  But there is no such isthmus connecting Europe to Asia. [....]  Even to our day, the distinction between Europe and Asia remains, rendering it two  continents, even while it is most obviously one continuous land mass. [....]

It wasn't "obvious" to the ancients at all:

On the divisions and boundaries of Europe, Asia and Africa, [Pomponius Mela (c. 43 CE)] repeats Eratosthenes [(276–194 BCE)]; like all classical geographers from Alexander the Great (except Ptolemy [(c. 150)]) he regards the Caspian Sea as an inlet of the Northern Ocean, corresponding to the Persian (Persian Gulf) and Arabian (Red Sea) gulfs on the south. [^Δ]

So as those geographers mapped what they knew of the Earth, the isthmus that connects Europe to Asia was obviously the Caucasus, in which a continental dividing-line could've been most sensibly drawn along either:
•  watershed of those mountains (conveniently only a single ridge-line), which crosses that isthmus from N.W. to S.E.; or
•  water course combining rivers connected by stretches of the artificial irrigation canal in the Kuma-Manych Depression, which is immediately north of the mountain range, and on a parallel path which crosses that isthmus from N.W. to S.E. [^∇]

Let get real!  How could classical or early mediaeval geographers have corrected that error?  It seems that no literate Europeans ever travelled W.-to-E. north of the Caspian Sea, where they could disprove the assumption that the Caspian "Sea" was was merely a northward-opening inlet of a Northern Ocean--or at least none that survived to report it.

Up there, travellers would risk seasonal conditions comparable to those that were docuмented by the nαzι besiegers of Stalingrad (later renamed Volgograd).  But whom--instead of nαzιs--might those classical or mediaeval travellers encounter?  Militarily powerful cold-blooded pagans, exactly who depending on the century: Scythians, Sarmatian mounted warriors, westward migrating Huns, westward migrating Magyars (d.b.a. "Hungarians"), and worst of all, the Mongols (light-cavalry reconnaissance-in-force: 1223, then Batu's invasion of Europe: 1236--1238, 1240--1242).

Far safer to travel thro' the warmer climate south of the Caspian Sea, following relatively well-known routes (e.g., Alexander the Great's astonishing string of victories), and perhaps never straying too far from ports for travel on boats or ships, via the Persian Gulf or Indian Ocean.  Here, the pagans encountered might be only the devils you already know, notably the Great Oriental Enemy of Greeks & Romans: the Persians (of various dynasties), and the Saracens, whose purported "Religion of Peace" later assimilated Mesopotamia (A.D. 641), Persia (A.D. 652) and other nations farther east.

It wasn't until the High Middle Ages that the "one continuous land mass" became a fact established among Western geographers, after Fr. William of Rubruck had returned from his daring mission to the the Mongols (1253--1255), which took him all the way to Great Khan Möngke [‡], reigning in Karakorum (in Mongolia) [†].  There was reasonable hope of surviving such a mission during the Pax Mongolica, which appeared after the Mongols had mellowed from having no outside military forces that dared to challenge them, and learned to enjoy the luxury of receiving tribute instead of destroying cities and slaughtering their inhabitants.  It worked for travellers because few sane people dared to challenge Mongol concepts of justice.

Therefore, the popular concept of Europe being a continent and Asia being another continent, making two continents (instead of one) survives even to this day. This fact goes to show how old ideas die so very slowly.

The remarkably straight N.-to-S. Ural Mountains make a pretty good substitute for an isthmus as a continental separator.  Especially if one uses the Ural River as the S. extension of that separator.

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Note ^Δ: <https://en.wikipedia.org/wiki/Ancient_world_maps#Pomponius_Mela_(c._43_CE)>.  Actually, the reconstruction of the map by Eratosthenes depicted in an earlier section of the article makes the point more effectively, so it's odd that but nothing like the crucial excerpt I quoted above appears under his name.  Wikipedia's map-makers & map-enthusiasts seem to me to comprise one of its most valuable volunteer communities.  Those people do things like "converting"--really creating de novo--modern illustration-file-format maps in full-color from sometimes scholarly maps (now public-domain) published as 1-color engravings.  Seems like tedious work, done without much reward except personal pride and maybe eventual recognition from your peers.  Maybe interest in old/antique maps (as in geneaology) arises far less often in one's youth than in more mature years?

Note ^∇: I hadn't known about it myself, until yesterday.  There is a governmental proposal to glorify the "irrigation canal" into a serious shipping canal, which I assume would be more clearly visible from space than the irrigation canal.  <https://en.wikipedia.org/wiki/Kuma%E2%80%93Manych_Depression>.

Note †: "William of Rubruck's Account of the Mongols".   <http://depts.washington.edu/silkroad/texts/rubruck.html>.  Also "Rubruck's Route (1253-1255)".   Map with informal indication of topography, but displaying few place-names.  <http://depts.washington.edu/silkroad/maps/rubruck.html>.

Note ‡: When reading mediaeval history involving the Mongols, be mentally flexible about the spelling of names.  Their history was assembled from written sources in languages exemplifying dramatically different language-families, including Arabic, Persian, Russian, Chinese, and of course, Mongolian (which is Turkic and not closely related to Chinese).  Consider published spellings of their most-nearly deified Great Khan, variously, e.g., "Genghis", "Jenghiz", and the apparent preference of the field's scholars: "Chingis" (1162--1227).

The remarkably straight N.-to-S. Ural Mountains make a pretty good substitute for an isthmus as a continental separator.  Especially if one uses the Ural River as the S. extension of that separator.

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That's pretty weak. If large mountain ranges were equivalent to continent separators why not the Alps to separate Germany from Italy, or the Andes to make South America into two continents, or the Rockies on the east and the Sierra Nevada on the west to make 3 continents instead of one North America?