Using the texts stored in the Latin Library as a guide, we can see that the prevalence of eumdem waxes and wanes through history. Its earliest significant use in writing appears to be approximately the 4th century, and it reaches its height in the late Medieval period, but even then it does not displace eundem.
Several works from the post-classical era employ eumdem rather than eundem; here are some examples:
- Lactantius, Divine Institutes, 7 instances in Book I
- The abridgement of Livy's Ab Urbe Condita Libri, the Periochae, is thought to date to the 4th century (30, 59, 85)
- Augustine uses eumdem in several of his sermons, for example, 2, 15, as well as other works, like De Fide et Symbolo
- Festus's Summary has one instance
- Hydatius's Chronicle, of the 5th century, has 5 instances
Of course, this analysis assumes that the transcriptions available on Latin Library have not been altered from the originals. They seem to indicate, however, that eumdem was at least occasionally employed in this time period. Still, many other authors of this time preferred eundem: Augustine himself used that form in several other works, and examples of this usage abound in Ammianus, Justinian, and Bede.
Late Medieval usage
Several prominent authors in the 12th century make extensive use of eumdem, perhaps marking a high point of its usage. They include:
Even in this time period, however, other authors continued to use eundem. The Latin Library includes Aquinas, Gregory VII, Gregory IX, and the Magna Carta in this category, though a more thorough investigation of Aquinas's works reveals a fairly even split between the two forms.
Following the Medieval period, most authors seem to adopt the use of eundem. Among them are Spinoza and Descartes, though Erasmus is a notable exception; his Institutes, for example, include eumdem several times.
I don't see any clear patterns of the use of eumdem, whether by time or by geography. Examples of it exist back to at least Late Latin, and it was more widely employed in the late Medieval period. But it does not appear to have ever achieved dominance over eundem.