In my timeline i know the position of the first & last date:
1914-02-10 = (79.5, 0)
2018-08-12 = (823.5, 0)
How can i calculate the position(x-coordinate) of a third date, for example:
1974-2-10 (is already on the timeline)
1993-15-11 (isn't on the timeline)
Enter the known dates in an excel spreadsheet and find the difference. (Excel does a wonderful job of showing date differences as a number of days and a decimal fraction of days.) Enter the known coordinates in the spreadsheet and find the difference. Find the ratio between date-difference and coordinate-difference. Then enter the unknown date on the spreadsheet, take the difference between it and either known date, and multiply the result by the ratio you found for the known dates. Add or subtract this result from whichever known coordinate corresponds to the last date-difference you took. This should be the coordinate of whatever unknown date you are working on at the moment.
There are $38169.00$ days between $1914-02-10$ and $2018-08-12$. There is also a difference of $744$ units between $79.5$ and $823.5$. The date (corrected?) $1993-11-15$ is $0.763263381$ of the way between the two end dates. So, that fraction of the way between the two number line points is $567.8679557$.