erting 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]

JOHN GRAUNT AS A PARADOXER.

Natural and Political Observations ... upon the Bills of Mortality. By
John Graunt, citizen of London. London, 1662, 4to.[215]

This is a celebrated book, the first great work upon mortality. But the
author, going _ultra crepidam_, has attributed to the motion of the moon in
her orbit all the tremors which she gets from a shaky telescope.[216] But
there is another paradox about this book: the above absurd opinion is
attributed to that excellent mechanist, Sir William Petty, who passed his
days among the astronomers. Graunt did not write his own book! Anthony
Wood[217] hints that Petty