ed edition of the _Elements_
(Venice, 1482) was from his translation. In this work he probably depended
not a little upon at least two or three earlier scholars. He also wrote _De
computo ecclesiastico Calendarium_, and _De quadratura circuli_.

[28] Archimedes gave 3-1/7, and 3-10/71 as the limits of the ratio of the
circumference to the diameter of a circle.

[29] Friedrich W. A. Murhard was born at Cassel in 1779 and died there in
1853. His _Bibliotheca Mathematica_, Leipsic, 1797-1805, is ill arranged
and inaccurate, but it is still a helpful bibliography. De Morgan speaks
somewhere of his indebtedness to it.

[30] Abraham Gotthelf Kaestner was born at Leipsic in 1719, and died at
Goettingen in 1800. He was professor of mathematics and physics at
Goettingen. His _Geschichte der Mathematik_ (1796-1800) was a work of
considerable merit. In the text of the _Budget of Paradoxes_ the name
appears throughout as Kastner instead of Kaestner.

[31] Lucas Gauricus, or Luca Gaurico, born at Giffoni, near Naples, in
1476; died at Rome in 1558. He was an astrologer and mathematician, and was
professor of mathematics at Ferrara in 1531. In 1545 he became bishop of
Civita Ducale.

[32] John Couch Adams was born at Lidcot, Cornwall, in 1819, and died in
1892. He and Leverrier predicted the discovery of Neptune from the
perturbations in Uranus.

[33] Urbain-Jean-Joseph Leverrier was born at Saint-Lo, Manche, in 1811,
and died at Paris in 1877. It was his data respecting the perturbations of
Uranus that were used by Adams and himself in locating Neptune.

[34] Joseph-Juste Scaliger, the celebrated philologist, was born at Agen in
1540, and died at Leyden in 1609. His _Cyclometrica elementa_, to which De
Morgan refers, appeared at Leyden in 1594.

[35] The title is: _In hoc libra contenta.... Introductio i
geometri[=a].... Liber de quadratura circuli. Liber de cubicatione sphere.
Perspectiva introductio_. Carolus Bovillus, or Charles Bouvelles (Boueelles,
Bouilles, Bouvel), was born at Saucourt, Picardy, about 1470, and died at
Noyon about 1533. He was canon and professor of theology at Noyon. His
_Introductio_ contains considerable work on star polygons, a favorite study
in the Middle Ages and early Renaissance. His work _Que hoc volumine
contin[=e]tur. Liber de intellectu. Liber de sensu_, etc., appeared at
Paris in 1509-10.

[36] Nicolaus Cusanus, Nicolaus Chrypffs or Krebs, was born at Kues on the
Mosel in 1401, and died