The law of multiple proportions asserts that if two elements form more than' one compound, then the weights of the one element Law of which are found combined with unit weight of the other multiple in the different compounds, must be in the ratio of two propor or more whole numbers.
Fortunately, the compounds at first examined by the chemists engaged in verifying these laws were comparatively simple, so that the whole numbers referred to above were small.
The Liber abaci, which fills 459 printed pages, contains the most perfect methods of calculating with whole numbers and with fractions, practice, extraction of the square and cube roots, proportion, chain rule, finding of proportional parts, averages, progressions, even compound interest, just as in the completest mercantile arithmetics of our days.
Coast-line.The following table shows the numbers, the lengths of coast-line, and the areas of the various groups of islands, only those being indicated that have a coast-line of at least I ri (23/4 m.), or that, though smaller, are inhabited; except in the case of Formosa and the Pescadores, where the whole numbers are given Length of Area Number.
Recorde published several works upon mathematical subjects, chiefly in the form of dialogue between master and scholar, viz.: - The Grounde of Artes, teachinge the Worke and Practise of Arithmeticke, both in whole numbers and fractions (1540); The Pathway to Knowledge, containing the First Principles of Geometry.