ABA 



quented on account of its mineral waters. E. long. 1 1° 59'. 

 N. lat. 48° 53'. 



ABACINARE, or AnnAciNARE, derived either from 

 the Italian bacxno, a hafon, or lacio, a dark place, in IFrihrj 

 of the Middle Age, a ipccies of punilliment, conllfting in the 

 blinding of the criminal, by iiolding a red hot bafon, or bow, 

 before his eyes. Du-Cange. 



ABACK, in Sea Language, fignifies the fituation of the 

 fails, when their furfaces are flatted againft the mails by 

 the force of the wind. They may be brought aback, either 

 by a ludden change of the wind, or an alteration in the 

 Ihip's courie. Thty are laid aback to effeft an immediate 

 retreat, without turning either to the right or left, in order 

 to avoid fome imminent danger, in a narrow channel, or 

 when (he has advanced beyond her ftation in the line of 

 battle, or othcrwife. The fails are put in this pofition 

 by flackening their lee-braces, and hauhng in the weather- 

 ones. 



ABACOA, in Geography, one of the Bahama [[lands, 

 about 54 miles in length and 21 miles in breadth. See 

 Providence. 



ABACOOCHEE, a river of America, called alfoCoosA. 



ABACOT, a cap of llate, wrought up in the form of 

 two crowns, worn by our ancient Britifli kings. 



ABACTOR, formed of ab, from, and aclor, a driver, 

 from agere, to drive, (called by the Roman la\vyers ylbigeus 

 or Abigevus), one who drives off cattle in herds ; in contradif- 

 tinftion to one who fteals a fingle (heep, &c. only, who is 

 called a thief. Nam qui ovem unam furripiierit, ut fur coer- 

 eetur, qui gregcm ut Abaclor. The punifliment of Abigeat 

 was more fevere than that of Furtum ; viz. condemnation 

 to the mines, banifhment, or even death itfelf, according to 

 the quality of the offender. But fometimes in Spain the 

 punilliment was more fevere than elfewhere, the people there 

 being moil addifted to it. 



ABACTUS, or Abigeatus, among the Ancient Phy- 

 jicians, was ufed for a mifcarriage procured by art, or force 

 of medicines, in contvadiilinction to abortus, which is 

 natural. But the moderns know no fuch dillintlion. See 

 Abortion. 



ABACUS, among the Ancients, was a kind of cupboard, 

 or Buffet. 



The word is formed from the Greek a^o.^, which, among 

 that people, fignified the fame thing. 



Abacus, among the Mai hema/icians, was a little table 

 ftrewed over with dull, on which they di-ew their fchemes 

 and figures. 



In this fenfe, the word feems formed from the Phoeni- 

 cian piJ^j abai, dujf. 



ABACUS Pythagoriciis, a table of numbers, contrived for 

 the ready learning of the principles of arithmetic ; fo deno- 

 minated from its inventor, Pythagoras. 



Hence alfo, from an agrcemer.t in point of ufe, the 

 names Abacus and Abacj are ufcd, among Latin and Italian 

 writers, for an alphabet, or ABC, &c. 



The Abacus Pyihagoricus was, in all probability, no other 

 than what we call a multiplication-table. 



Ludolfus and Wolfius give us methods of performing 

 multiplication without the help of the Abacus ; but they 

 are too operofe in ordinaiy cafes for praftice. See Mul- 



TirLICATION. 



The Abacus for facilitating the operation of arithmetic, 

 is an inftrument almoft as ancient, and extenfive, as the art 

 of arithmetic itfelf: if it be later than the methods of com- 

 puting by the fingers, and by lapilli, or ftoues (which ob- 

 tained among the Egyptains), it is at leaft much prior to the 

 ufe of numeral letters or figures, wrought with the pen. 



We find it in ufe, under fome variations, among the 



ABA 



Greeks, Romans, Chinefe, Germans, French, &c. It 

 excels in point of facility, and neatncfs of operation, as 

 working without any llrokes or blots of the pen, or wade 

 of paper ; fome alfo give it the preference in point of ex- 

 pedition. 



The Abacus is varioudy contrived ; that chiefly ufed in 

 European countries is made by drawing any number of 

 parallel lines, at pleafure, at a diftance from each other, 

 equal to twice the diameter of a calculus, or counter. Here 

 a counter placed on the firll or lowermoil line, fignifies i ; 

 on the fecond, 10 ; on the third, 100 ; on the fourth, loco ; 

 on the fifth, 10,000 ; and fo on. In the fpaces between the 

 lines, the fame counters iignify half of what they fignify on 

 the next fuperior line ; viz. in the fpace between the firft 

 and fecond lines, 5 ; between the fecond and third, 50 ; 

 between the third and fourth, 500 ; and fo on. Thus the 

 counters on the Abacus, in the fig\irc here fubjoincd, make 

 the fum of 37392. — The Abacus is aifo divided crofs-wife 

 \x\to arcrtle, by means whereof fubtradlions ETC made. Wolf^ 

 Lex. Matlu p. 171, fcq. 



The Grecian Abacus, aSa.%, or counting-board, was an ob- 

 long frame, divided by feveral brafs-wires llretclied parallel 

 to one another, and mounted with an equal number of 

 little ivory balls, hke the beads of a necklace. By the 

 arrangement of thefe balls, dillinguifliing the numbers into 

 different claffes, and obferving the relations of the lower to 

 the upper, all kinds of computations were eafily performed. 

 Mahudel, in Hift. Acad. R. Infer, tom. iii. p. 390. 



The Roman Abacus was much the fame with the Gre- 

 cian, except that inftead of Rrings, or wires, and beads, in 

 the Roman, we find pins and groves for them to Aide in. 

 It is defcribed by feveral authors ; but notwithllanding all 

 thefe defcriptions, we (hould have had a very obfcure idea 

 of the ancient manner of reckoning, if figures of it had not 

 been found among the ancient marbles. Phil. Tranf. N'^ 1 80. 



The Chinefe Abacus confifts, like the Grecian, of feveral 

 feries of beads flrung on brafs wires, extended from the top 

 to the bottom of the inftniment, and divided in the middle 

 by a crofs piece from fide to fide ; fo that in the upper row 

 each firing has two beads, which are each reckoned for 

 five ; and in the lower row, each firing has five beads of 

 different values ; the firfl being reckoned as i ; the fecond, 

 as 10 ; the third, as 100, &c. as among us. Add, that 

 inflead of four pins for digits, or units, in the Roman 

 Abacus, the Chinefe has five beads. 



We have two different figures, and defcriptions, of the 

 Chinefe Abacus, one given by F. Martinius, who had lived 

 many years in China ; the other by Dr. Hooke, who copied 

 it from a Chinefe didlionai-y of the court-language. Sec 

 Shwan-Pan. 



AiiACUs logijlicus is a rightanglcd triangle, whofe fides, 

 forming the right angle, contain the numbers from i to 

 60 ; and its area, the produfts of each two of the op- 

 pofite numbers. This is alfo called a canon of sexage- 

 simals. 



Abacus Ss" palmult, in tlie And(nt Mufic, denote the 



machinery^ 



