Scaliger inspired some mathematicians with great respect for his
geometrical knowledge. Vieta, the first man of his time, who answered him,
had such regard for his opponent {111} as made him conceal Scaliger's name.
Not that he is very respectful in his manner of proceeding: the following
dry quiz on his opponent's logic must have been very cutting, being true.
"In grammaticis, dare navibus Austros, et dare naves Austris, sunt aeque
significantia. Sed in Geometricis, aliud est adsumpsisse circulum BCD non
esse majorem triginta sex segmentis BCDF, aliud circulo BCD non esse majora
triginta sex segmenta BCDF. Illa adsumptiuncula vera est, haec falsa."[205]
Isaac Casaubon,[206] in one of his letters to De Thou,[207] relates that,
he and another paying a visit to Vieta, the conversation fell upon
Scaliger, of whom the host said that he believed Scaliger was the only man
who perfectly understood mathematical writers, especially the Greek ones:
and that he thought more of Scaliger when wrong than of many others when
right; "pluris se Scaligerum vel errantem facere quam multos [Greek:
katorthountas]."[208] This must have been before Scaliger's quadrature
(1594). There is an old story of some one saying, "Mallem cum Scaligero
errare, quam cum Clavio recte sapere."[209] This I cannot help suspecting
to have been a version of Vieta's speech with Clavius satirically inserted,
on account of the great hostility which Vieta showed towards Clavius in the
latter years of his life.
Montucla could not have read with care either Scaliger's quadrature or
Clavius's refutation. He gives the first a wrong date: he assures the world
that there is no question about Scaliger's quadrature being wrong, in the
eyes of geometers at least: and he states that Clavius mortified him {112}
extremely by showing that it made the circle less than its inscribed
dodecagon, which is, of course, equivalent to asserting that a straight
line is not always the shortest distance between two points. Did _Clavius_
show this? No, it was Scaliger himself who showed it, boasted of it, and
declared it to be a "noble paradox" that a theorem false in geometry is
true in arithmetic; a thing, he says with great triumph, not noticed by
Archimedes himself! He says in so many words that the periphery of the
dodecagon is greater than that of the circle; and that the more sides there
are to the inscribed figure, the more does it exceed the circle in which it
is. And here _are_ the words, on the independent testimonies of Clavius and
Kastner:
"Ambitus dodecagoni circulo inscribendi plus potest quam circuli ambitus.
Et quanto deinceps plurium laterum fuerit polygonum circulo inscribendum,
tanto plus poterit ambitus polygoni quam ambitus circuli."[210]
There is much resemblance between Joseph Scaliger and William
Hamilton,[211] in a certain impetuousity of character, and inaptitude to
think of quantity. Scaliger maintained that the arc of a circle is less
than its chord in arithmetic, though greater in geometry; Hamilton arrived
at two quantities which are identical, but the greater the one the less the
other. But, on the whole, I liken Hamilton rather to Julius than to Joseph.
On this last hero of literature I repeat Thomas Edwards,[212] who says that
a man is unlearned who, be his other knowledge what it may, does not {113}
understand the subject he writes about. And now one of many instances in
which literature gives to literature character in science. Anthony
Teissier,[213] the learned annotator of De Thou's biographies, says of
Finaeus, "Il se vanta sans raison avoir trouve la quadrature du cercle; la
gloire de cette admirable decouverte etait reservee a Joseph Scalinger,
comme l'a ecrit Scevole de St. Marthe."[214]