#51




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A3 portrait is 297mm X 420mm The sides (long/short) are in the proportion of a:1 where a = the square root of two, which is approx. 1.414213562. The long side of A4 = the short side of A3 and this relation continues through all of the DIN Ax sizes. So, the new scale would be 1:(350 divided by the square root of two) which would be approx. 1:247.487373415. 
#52




If you want it in the same scale, no difference. If you want to scale it proportionally to the new paper size: A size papers are related dimensionally by precisely a factor of two, but the way scale works is logarithmic so the largest you could print on A3 would not be 1:175 but about 1:250, or 140% of original size.
EDIT: I see Lawrence replied at exactly the same moment with a more precise calculation, but I'm pleased that my quick estimation was pretty close!
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#53




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In case anyone doesn't know this already, A_(n+1) is obtained by folding a sheet of A_(n) along the midpoints of its long side, so, for example, one can think of folding one sheet of A3 landscape into two sheets of A4 portrait, and so on through the different sizes. It's a very clever system, but unfortunately the proportions are not particularly attractive, which is why artists' papers are usually not in DIN sizes. Actually, DIN Ax, Cx, etc., are also ISO norms, but the name DIN (Deutsche Industrienorm = German Industrial Norm) seems to have stuck. 
#54




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