Continental border east of Tian Shan

The Greeks established by time of Herodotus that the border between Asia and Europe started at the mouth of Tanais. They were, however, unfamiliar with the countries further northeast.
Now, when Alexander in central Asia reached Syrdarya, he crossed it only slightly... and then turned back south. To invade India rather than China.
And called the river "Tanais".
If you look at large scale maps, it actually makes some sense. Mouth of Don in Sea of Azov is latitude 47. Mouth of Syrdarya in Sea of Aral is around latitude 46 - Alexander did not visit it, but he could observe Syrdarya flowing away northwest. A logical conclusion might be that Syrdarya is the upper course of Don, flowing east-west. If and when the Greeks learned more about the actual geography in between, the closed basins of Caspian and Aral, they might extend the continental border between Don and Caspian - like along Kuma-Manych depression, as we have done - and then somewhere from Caspian to Aral. So winding up at the known section of Syrdarya.
Note the conclusions. Alexander turned back around Syrdarya because north of Syrdarya was return to Europe - and he was chasing to conquer all Asia. If Alexander had agreed that the border of Europe and Asia went north of Caspian along Urals, he would have been obliged to conquer the Scythians of Kazakhstan - which the Persians had not done - and then march north all the way down the Ob to Arctic Ocean, all the way north to Cape Chelyushkin, all the way east to Cape Dezhnev... Logistical nuisance for little reward.
Alexander did not attempt to conquer Siberia because Siberia is in Europe. Vice versa, Siberia is in Europe because Alexander did not try to conquer it.
But taking the same reasoning - if Alexander did not attempt to conquer Siberia because it is in Europe, he also did not try to conquer China because China is also in Europe.
Taking the premises:
  • Alexander turned back from Syrdarya voluntarily, because it was the border of Europe. Continuing north (Kazakhstan to Siberia) or east (Xinjiang to China) was, first section, a feasible option but Alexander freely chose not to do either because both ways went back to Europe
  • Alexander turned back from Sutlej forced by mutiny, and recognized that India east of Sutlej was part of Asia he was unable to conquer due to ill omens.
So where would the border between Europe and Asia go east of the headwaters of Syrdarya?
 
So where would the border between Europe and Asia go east of the headwaters of Syrdarya?
The closest thing, especially if you jog over from the Syr Darya to the Chüy, to a river valley extending further east would be a route across the Gobi to the Amur River. For China to end up north of the line you pretty much have to cut across Tibet somehow.
 
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