BIANCHINI (Francis)

, a very learned Italian philosopher and mathematician of the 17th century, was born at Verona the 13th of December 1662. He was much esteemed by the learned, and was a member of several academies; and was even the founder of that at Verona, called the Academy of Aletofili, or | Lovers of Truth. He went to Rome in 1684; and was made librarian to cardinal Ottoboni, who was afterwards Pope by the name of Alexander the 8th. He entered into the church, and became canon of St. Mary de la Rotondo, and afterward of St. Lawrence in Damaso.

Bianchini was author of several learned and ingenious dissertations. In 1697 he published La Istoria universale provata con monumenti, & figurata con simboli de gli antichi. In 1701 pope Clement the 11th named him secretary of the conferences for the reformation of the calendar; and he published in 1703, De Calendario & Cyclo Cæsaris, ac de Canone Paschali fancti Hyppoliti, Martyris, Dissertationes duæ. Bianchini was employed on the construction of the large gnomon in the church of the Chartreux at Rome, upon which he published an ample dissertation intitled, De Nummo & Gnomone Clementino. The research concerning the parallax and the spots of Venus occupied him a long time; but his most remarkable discovery is that of the parallelism of the axis of Venus in her orbit. He proposed to trace a meridian line through the whole extent of Italy. He was admitted a foreign Associate in the Paris Academy of Sciences, in 1706; and he had many astronomical dissertations inserted in their Memoirs, particularly in those of the years 1702, 1703, 1704, 1706, 1707, 1708, 1713, and 1718.—Bianchiui died the 2d of March 1729, in the 67th year of his age.

BIMEDIAL Line, is the sum of two Medials. Euclid reckons two of these bimedials, in pr. 38 and 39 lib. X; the first is when the rectangle is rational, which is contained by the two medial lines whose sum makes the bimedial; and the second when that rectangle is a medial, or contained under two lines that are commensurable only in power.

BINARY Number, that which is composed of two units.

Binary Arithmetic, that in which two figures or characters, viz, 1 and 0, only are used; the cipher multiplying every thing by 2, as in the common arithmetic by ten: thus, 1 is one, 10 is 2, 11 is 3, 100 is 4, 101 is 5, 110 is 6, 111 is 7, 1000 is 8, 1001 is 9, 1010 is ten; being founded on the same principles as common arithmetic.—This sort of arithmetic was invented by Leibnitz, who pretended that it is better adapted than the common arithmetic, for discovering certain properties of numbers, and for constructing tables; but he does not venture to recommend it, for ordinary use, on account of the great number of places of figures requisite to express all numbers, even very small ones. Jos. Pelican of Prague has more largely explained the principles and practice of the binary arithmetic, in a book entitled Arithmeticus Perfectus, qui tria numerare nescit; 1712. And De Lagni proposed a new system of logarithms, on the plan of the binary arithmetic; which he finds shorter, and more easy and natural than the common ones.