
Okay, someone take pity on a math moron who's eyes glaze over at the first hint of an equation and tell me what extension from the negative plane would be required with an 180mm enlarging lens to get the 7" dimension to fit on an 8x10 piece of paper (7" enlarged to 9.5").

Hey, I'm an artist. I'm mathematically impaired also. (and I have a Philosophy degree to prove it!)
If you want, tonight when I get home, I'll measure the distance from the negative carrier to the end of the bellows/lenscone with my 5x7 enlarger with a 210 componons on it, with an image size of 9.5 inches on the long side.
I assume your bellows extention with the 180 would be slightly shorter.
OK?
Tom

Thanks Tom, that'll get me partly there. Right now I've got a 210 Rodagon on it but only with a cone that gets me to 12" as the smallest enlargement. It's a royal pain to break out the 11x14 paper and trays every time I want to proof anything. Come to think of it, I may just improvise a longer cone for the 210 with the number you provide. I made a cone for my 4x5 enlarger out of 4" PVC pipe and a toilet flange (not used)  it ain't pretty but gets the job done.

Negative to paper: 73,7cm (28 7/8 in).
Negative to lens nodal point: 31,3cm (12 1/4 in)
Lens to paper: 42,4cm (16 5/8 in)
Assuming nothing (including the lens) has any optical thickness, which isn't true  and there are rounding off errors as well. But it's in the right range.

how does Ole know how to do these things?!! (probably did it his head, besides.)
doing it the old fashioned try it and measure with a ruler way, I have a good correlation with Ole's number. A total extension of 15 inches from the negative to the "lens nodal point" (I would have said middle of the lens, but Ole has taught me to say "lens nodal point") with my 210 CompononS gives me a 6x9 inch print.

Thanks, Tom and Ole.
It looks like I'm 3 1/2 inches shy of the proper extension from the negative stage with my 210.
Ole, are your numbers for a 180mm?

The theory is easy, the calculation is hard. Besides, I was bored and thought this might keep me occupied for a while. And yes, my numbers are for a 180mm lens!
The basic equations are:
1/F=1/U+1/V
where F is the Focal length of the lens, U is the distance from negative to lens, and V the distance from lens to paper.
and
d/D=U/V
where d is the size of the negative, D the size of the paper, U and V as above.
I just now realized that the 7" dimension of a 5x7" film isn't 7". That changes everything a little, but not too much. You need a little more extension, is all. If I'd had a negative with me I could have measured the image area, but I don't, so I can't.
Assuming 6 1/2" image area, it's
30.3cm neg to lens,
44.3cm lens to paper
74.6cm total.

Just to follow up, I picked up a 180 Componons and it works like a charm. I'm now able to print on 8x10 easily.
As an aside, I bought the lens used from Robert White for an appropriately discounted price. When I got the lens I was shocked to see it was still shrinkwrapped in the original packaging. The cardboard box had been opened, but that's it. I have no doubt that any of the US dealers would have sold the lens as "new"  which is pretty much exactly what it is. I can't recommend Robert White highly enough.

thanks for the update, always good to hear how the story ended, especially if well!