In all other cases recourse must be had to a map, a globe or mathematical formula.

Dodgson periodically published mathematical works - An Elementary Treatise on Determinants (1867); Euclid, Book V., proved Algebraically (1874); Euclid and his Modern Rivals (1879), the work on which his reputation as a mathematician largely rests; and Curiosa Mathematica (1888).

But later experimental researches have shown that the simple assumption of constant coefficients of conductivity and emissivity, on which the mathematical theory is based, is in many respects inadequate, and the special mathematical methods developed by J.

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For the mathematical investigation see Spherical Harmonics and for tables see Table, Mathematical.

He corresponded with some of the most eminent scholars of his time on mathematical subjects; and his house was generally full of pupils from all quarters.

Munich has long been celebrated for its artistic handicrafts, such as bronze-founding, glass-staining, silversmith's work, and wood-carving, while the astronomical instruments of Fraunhofer and the mathematical instruments of Traugott Lieberecht von Ertel (1778-1858) are also widely known.

Placed at the university of Cracow in 1491, he devoted himself, during three years, to mathematical science under Albert Brudzewski (1445-1497), and incidentally acquired some skill in painting.

Before applying the solution to a mathematical investigation of the present question, it may be well to consider the matter for a few moments from a more general point of view.

The publication of these discoveries led to a series of controversies which lasted for several years, in which Newton had to contend with the eminent English natural philosopher Robert Hooke; Lucas, mathematical professor at Liege; Linus, a physician in Liege, and many others.

English translations of the mathematical chapters of the Brahma-siddhanta and Siddhanta-ciromani by H.