I am confused and hope that you can help. When I do an Internet search for "the die is cast" it comes up spelled two different ways: Iacta alea est and Jacta alea est (and for that matter Alea jacta est). How do I know which one is the correct derivation?
In Roman times, there was no J in Latin; the letter I served both as a vowel and as a consonant similar to Y. In the late 15th to early 16th Century, a variant form of I -- which we now know as J -- began to be used to differentiate between the vowel and consonant forms of the letter. Thus Iulius became Julius, and so on. Even at that point, the two were seen as variant forms of one letter; the two became entirely separated only in the 19th century.
As the function of J has changed, editors have made different decisions about how to present texts that were written before the distinction was made. Editors working while I and J were considered two ways of representing the same letter tended to print it as J whenever it was being used as a consonant: thus, Alexander's comment was presented as "jacta alea est." Editors working now that I and J are seen as distinct letters usually keep the words the way they were written at the time: thus, "iacta alea est." The phrase is exactly the same in both cases; the only difference is in how it's presented on the page.