NONIUS

, or Nunez (Peter), a very eminent Portuguese mathematician and physician, was born in 1497, at Alcazar in Portugal, anciently a remarkable city, known by the name of Salacia, from whence he was surnamed Salaciensis. He was professor of mathematics in the university of Coimbra, where he published some pieces which procured him great reputation. He was mathematical preceptor to Don Henry, son to king Emanuel of Portugal, and principal cosmographer to the king. Nonius was very serviceable to the designs, which this court entertained of carrying on their maritime expeditions into the East, by the publication of his book Of the Art of Navigation, and various other works. He died in 1577, at 80 years of age.

Nonius was the author of several ingenious works and inventions, and justly esteemed one of the most eminent mathematicians of his age. Concerning his Art of Navigation, father Dechales says, “In the year 1530, Peter Nonius, a celebrated Portuguese mathematician, upon occasion of some doubts proposed to him by Martinus Alphonsus Sofa, wrote a Treatise on Navigation, divided into two books; in the first, he answers some of those doubts, and explains the nature of Loxodromic lines. In the second book, he treats of rules and instruments proper for navigation, particularly sea-charts, and instruments serving to sind the elevation of the pole; but says he is rather obscure in his manner of writing.”—Furetiere, in his Dictionary, takes notice that Peter Nonius was the first who, in 1530, invented the angles which the Loxodromic curves make with each meridian, calling them in his language Rhumbs, and which he calculated by spherical triangles.—Stevinus acknowledges, that Peter Nonius was scarce inferior to the very best mathematicians of the age. And Schottus says, he explained a great many problems, and particularly the mechanical problem of Aristotle on the motion of vessels by oars. His Notes upon Purbach's Theory of the Planets, are very much to be esteemed: he there explains several things, which had either not been noticed before, or not rightly understood.

In 1542 he published a Treatise on the Twilight, which he dedicated to John the 3d, 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 called, from him, a Nonius, a particular account of which see in the following article.—He corrected several mathematical mistakes of Orontius Finæus.—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 Arithmeticay Geometra; 1564.|

, is a name also erroneously given to the method of graduation now generally used in the division of the scales of various instruments, and which should be called Vernier, from its real inventor. The method of Nonius, so called from its inventor Pedro Nunez, or Nonius, and described in his treatise De Crepusculis, printed at Lisbon in 1542, 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 Nunez, in his treatise De Arte et Ratione Navigandi, lib. 2, cap. 6, 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 nine, the method of diagonals, first published by Thomas Digges, Esq. in his treatise Alæ seu Scalæ Mathematicæ, 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. See VERNIER.