If you stop to think about it, what he said makes good logical sense. It's like something that half the population had already thought about at one time or another, like hmm, as you go up in the tree, the branches get smaller and smaller, and vice-versa. It's just that he was able to use the language of science and math to help explain what we already sort of knew to be true. That's all. Da Vinci was a pretty cool guy, though, it's true. I think he saw the face of God and then spent his life trying to explain to the world what it looked like in every facet of every topic. Very cool.

If I understood that right, if you are able to promote a thicker trunk, you'll promote thicker top growth. That brings to mind advice on strengthening a long whip to face coming winds. Give the whip a slight shake when yo can, daily or more if possible and apparently the trunk will benefit.
The one whip I tried this out on was under an inch diameter and about 7 foot tall with probably the correct area of top growth, not good. :) I doubt my occasional shakes did much else than remind it that in any wind it would thrash about against the floor and surrounding objects. I just couldn't seem to stabilise it without it breaking free or losing branches. Several years later and it's my favorite tree with a very strong, 8 foot, 3 - 4" diameter trunk and a glorious crown (as you might imagine) which delivers abundant fruit. The only problem I have with it is Crataegus pinnatifida major 'Big Golden Star' is rather inedible without processing so this year I'll be doing just that.
Don't give up on those skinny whips.

If da Vinci really said that as you state it, I'm sure it wasn't the first time he was wrong. Unless it is in regards to a specific type of tree. It is easy to come up with counter examples to the claim.

I agree with murky. Da Vinci was obviously brilliant and way ahead of his time in many regards but what's posted above can't logically be true.

Lol!! So shakin your whip made it bigger huh? lol

And I worded it to avoid the obvious double-entendre too, can't win em all. :p

I doubt da Vinci is right in the OP's quote as it stands but it opened my eyes to the thought behind it, that there could even be a fairly accurate ratio to areas and volumes on trees. I think that's a definite possibility, with different trees using various fractal ratios in growth the blanket quote is bound to be off. It's still a eureka moment if he was the first to define this, if it's true of course. Like Pi, you'd always get a recurring number with fractals or you'd have some incredibly useless seeds :) so sounds like it's just a case of fractal area differences, like A1, A2, A3, A4 paper areas.

It's thought da Vinci was gay, using se ual sublimation to channel his mind in to creative thought rather than entertain the abominable, they weren't too tolerant in the 15th century.