I am learning to play on the violin. On my score sheet there is a chord with the notes C,E,G in C major (the scale is not relevant). I do not understand how one can play two notes on the same string simultaneously. Can somebody tell me how one would play such a chord in terms of how to place the fingers given that E and G are on the same string ? Thanks.
Those pitches are not meant to be played; they're providing a little music theory along with the scales. The German text at the top of the page translates to "In the following 24 scales, at the end of each the root, third, fifth, and octave of the key are provided, so the student can be acquainted with the triad of the key." (At least I hope that's a reasonable translation; I'm not fluent!) In other words, the scale "represents" a musical key, and this chord also represents it in a harmonic way.
You might benefit from a more modern beginner's method book, in your primary language, and published within the past century. I use "Essential Elements" when starting new students.
To answer the core question as it was intended, in case others find this question while looking for something similar: No, you can't play those three pitches simultaneously on the violin. If you just took the top two pitches, the E and G that would be played on D string in first position, those could be played simultaneously by shifting into another position so that the E could be played on G string. But then you could no longer play the middle C; that's lower in pitch than D string and all the higher strings, and no string can play a lower pitch than its open pitch. If you used a non-standard tuning, like lowering the A string by a whole step, it could be done.
But to @user996159, I'd ignore all that for now. Don't worry about shifting to other positions until you're very comfortable in first position, probably a year or more. And I wouldn't recommend messing around with alternate tunings at first, especially while getting familiar with fingerings.