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Alan J. CainFrançois Viète (= Franciscus Vieta; 1540–1603) Viète described as ‘elegant and very beautiful [elegans & perpulchræ]’ the result shown in the original Latin and using his original notation in the 1st attached image.
Translated into English and into modern algebraic notation, Viète's result says: If, for an unknown $a$ and known $b$, $d$, $g$, $h$, and $k$, the equality shown in the 2nd attached image holds, then $a$ is either $b$, $d$, $g$, $h$, or $k$.
A mathematician today, working with this modern notation, would presumably notice that if one sets $a = b$ and multiplies out the brackets on the left hand side, all terms except $bdghk$ cancel; by symmetry, the same reasoning applies for $d$, $g$, $h$, $k$.
Thus, to modern eyes, the result collapses into near-triviality and seems to deserve little if any aesthetic praise. Perhaps the notation Viète had to work with made the result seem more mysterious and thus more aesthetically pleasing.
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