Portal de Periódicos da CAPES

II. On the theory of probability, applied to random straight lines

1868; Royal Society; Volume: 16; Linguagem: Inglês

10.1098/rspl.1867.0054

2053-9126

Morgan William Crofton, J.J. Sylvester,

Mathematical and Theoretical Analysis

This paper relates to the Theory of Local Probability—that is, the application of Probability to geometrical magnitude. This inquiry seems to have been originated by the great naturalist Buffon, in a celebrated problem proposed and solved by him. Though the subject has been more than once touched upon by Laplace, yet the remarkable depth and beauty of this new Calculus seem to have been little suspected till within the last few years, when the attention of several English mathematicians has been directed to it, and results of a most singular character have been obtained. The problems on Local Probability which have been hitherto treated relate almost exclusively to points taken at random. The object of the present paper is to show how the Theory of Probability is to be applied to straight lines whose position is unknown, or, in other words, which are taken at random.