ement of facts."

[224] It is difficult to estimate William Lilly (1602-1681) fairly. His
_Merlini Anglici ephemeris_, issued annually from 1642 to 1681, brought him
a great deal of money. Sir George Wharton (1617-1681) also published an
almanac annually from 1641 to 1666. He tried to expose John Booker
(1603-1677) by a work entitled _Mercurio-Coelicio-Mastix; or, an
Anti-caveat to all such, as have (heretofore) had the misfortune to be
Cheated and Deluded by that Grand and Traiterous Impostor of this
Rebellious Age, John Booker_, 1644. Booker was "licenser of mathematical
[astrological] publications," and as such he had quarrels with Lilly,
Wharton, and others.

[225] See note 171 on page 100.

[226] This is the _Ars Signorum, vulgo character universalis et lingua
philosophica_, that appeared at London in 1661, 8vo. George Dalgarno
anticipated modern methods in the teaching of the deaf and dumb.

[227] See note 200 on page 110.

[228] If the hyperbola is referred to the asymptotes as axes, the area
between two ordinates (x = a, x = b) is the difference of the logarithms of
a and b to the base e. E.g., in the case of the hyperbola xy = 1, the area
between x = a and x = 1 is log a.

[229] "On ne peut lui refuser la justice de remarquer que personne avant
lui ne s'est porte dans cette recherche avec autant de genie, & meme, si
nous en exceptons son objet principal, avec autant de succes." _Quadrature
du Cercle_, p. 66.

[230] The title proceeds: _Seu duae mediae proportionales inter extremas
datas per circulum et per infinitas hyperbolas, vel ellipses et per
quamlibet exhibitae_.... Rene Francois, Baron de Sluse (1622-1685) was
canon and chancellor of Liege, and a member of the Royal Society. He also
published a work on tangents (1672). The word _mesolabium_ is from the
Greek [Greek: mesolabion] or [Greek: mesolabon], an instrument invented by
Eratosthenes for finding two mean proportionals.

[231] The full title has some interest: _Vera circuli et hyperbolae
quadratura cui accedit geometriae pars universalis inserviens quantitatum
curvarum transmutationi et mensurae. Authore Jacobo Gregorio Abredonensi
Scoto ... Patavii_, 1667. That is, James Gregory (1638-1675) of Aberdeen
(he was really born near but not in the city), a good Scot, was publishing
his work down in Padua. The reason was that he had been studying in Italy,
and that this was a product of his youth. He had already (1663) published
his _Optica promot