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, an Arabian author, who is supposed to have lived about the fourth century, and is styled the son of Seirim, wrote a book “On the interpretation of Dreams, according to the doctrine of the Indians, the Persians, and the Egyptians,” which, with all its absurdities, has been translated into Greek and Latin, and published, together with “Artemidorus on Dreams and Chiromancy,” by M. Rigault in Paris, 1603, 4to. The original is lost.

In 1542 he published a treatise on the twilight, which he dedicated to John III. king of Portugal; to which he added what Alhazen, an Arabian author, has composed on the same subject. In this work he describes the method or instrument erroneously called, from him, a Nonius. He corrected several mathematical mistakes of Orontius Finasus. But the most celebrated of all his works, or that at least he appeared most to value, was his “Treatise of Algebra,” which he had composed in Portuguese, but translated it into the Castilian tongue when he resolved upon making it public, which he thought would render his book more useful, as this language was more generally known than the Portuguese. The dedication to his former pupil, prince Henry, was dated from Lisbon, Dec. 1, 1564. This work contains 341 pages in the Antwerp edition of 1567, in 8vo. The catalogue of his works, chiefly in Latin, is as follows: 1. “De Arte Navigandi, libri duo,” 1530. 2. “De Crepusculis,” 1542. 3. “Annotationes in Aristotelem.” 4. “Problema Mechanicum de Motu Navigii ex Remis.” 5. “Annotationes in Planetarum Theorias Georgii Purbachii,” &c. 6. “Libro de Algebra en Arithmetica y Geometra,” 1564. We have said that his name was erroneously given to the method of graduation now generally used in the division of the scales of various instruments; for Vernier was the real inventor The method of Nonius, described in his treatise “De Crepusculis,” consists in describing within the same quadrant, 45 concentric circles, dividing the outermost into 90 equal parts, the next within into 89, the next into 88, and so on, till the innermost was divided into 46 only. By this means, in most observations, the plumb-line or index must cross one or other of those circles in or very near a point of division: whence by calculation the degrees and minutes of the arch might easily be obtained. This method is also described by him in his treatise “De Arte Navigandi,” where he imagines it was not unknown to Ptolomy. But as the degrees are thus divided unequally, and it is very difficult to attain exactness in the division, especially when the numbers, into which the arches are to be divided, are incomposite, of which there are no less than uine, the method of diagonals, first published by Thomas Digges, esq. in his treatise “Alae seu Scaloe Mathematicae,” printed at Lond. in 1573, and said to be invented by one Richard Chanseler, a very skilful artist, was substituted in its stead. However, Nonius’s method was improved at different times; but the admirable division now so much in use, is the most considerable improvement of it.