in the abstract, or when nothing but the number of things is considered, will not be true when the question is limited to particular things: for instance, the number two is less than three; yet two yards is a greater quantity than three inches; because regard must be had to their different natures as well as number, whenever things of a different species are considered; for, though we can compare the number of such things abstractedly, yet we cannot compare them in any applicate sense. And this difference is necessary o be considered, because upon it the true sense, and the possibility or impossibility, of some questions depend. Number is unlimited in respect of increase; because we can never conceive a number so great but still there is a greater. However, in respect of decrease, it is limited; unity being the first and least number, below which therefore it cannot descend, except by subdivision into decimal or other parts, which may also be extended infinitely, at least in idea, if not in fact; for we cannot conceive any particle of matter so small, but that it may be supposed capable of being rendered still smaller, by divi

sion and subdivision.

NUMBER, GOLDEN. See CHRONOLOGY, Index. NUMBERS, ANCIENT. Numbers were by the Jews, as well as the ancient Greeks and Romans, expressed by letters of the alphabet: hence we may conceive how imperfect and limited their arithmetic was, because the letters could not be arranged in a series, or in different columns, convenient for ready calculation. The invention of the arithmetical figures which we now make use of, and particularly the cypher, has given us a vast advantage over the ancients in this respect. (See ARITHMETIC, Index.) The Jewish cabbalists, the Grecian conjurors, and the Roman augurs, had a great veneration for particular numbers, and the result of particular combinations of them.

NUMBERS, BOOK OF, the fourth book of the Pentateuch, taking its denomination from its numbering the families of Israel. A great part of this book is historical, relating to several remarkable passages in the Israelites' march through the wilderness. It contains a distinct relation of their several movements from one place to another, or their forty-two stages through the wilderness. But the greatest part of this book is spent in enumerating those laws and ordinances, whether civil or ceremonial, which were given by God, but not mentioned before in the preceding books. NU'MERAL, adj. Fr. numeral, numeNUMERABLE, rateur, numeration; NU'MERALLY, adv. Lat. numerus, numeNU'MERARY, adj. ratio, numerator, nuNUMERATION, n.s. merosus. Relating to NUMERATOR, n. s. numbers: numerable NUMERICAL, adj. is capable of being NUMERICALLY, adv. numbered: numerary, NU'MERIST, n.s. any thing pertaining NUMEROSITY, to a certain number: NUMEROUS, adj. numeration, the act or NU'MEROUSNESS, n. s.) art of numbering; number contained; a rule of arithmetic: a numerator is a person who numbers; or a given number, the measure of others: numerical, denoting or pertaining to numbers; identical; the

same not only in kind but number: numerist, one who deals in or reckons numbers: numerosity, the state of being numerous: numerous, many; containing many; containing musical numbers; harmonious; melodious: numerousness, the quality of being numerous; harmony. Many of our schisms in the West were never heard of by the numerous Christian churches in the east of Asia. Lesley.

Queen Elizabeth was not so much observed for having a numerous, as a wise counsel. Bacon. The blasts and undulary breaths thereof maintain no certainty in their course; nor are they numerally feared by navigators.

Browne.

NUMERAL CHARACTERS OF THE ARABS are those figures which are now used in all the operations of arithmetic in every nation of Europe. A writer in the Gentleman's Magazine thus endeavours to prove that the Arabs derived their notations from the Greeks:-'I maintain,' says he, that the Indians received their numeral chaacters from the Arabians, and the Arabians from the Greeks, as from them they derived all their learning, which in some things they improved, but for the most part have altered. The numerical figures which they received from the Greeks are proofs of this alteration; which is so great, that without particular attention one can scarcely discover in them the vestiges of their origin. But when we compare them carefully, and without prejudice, we find in them manifest traces of the Greek figures. The Greek numerical figures were no other than the letters of their alphabet. A small stroke was the mark of unity. The B, being abridged of its two extremities, produced the 2. If you incline they a little on its left side, and cut off its foot, and make the left horn round towards the left side, you will produce a 3. The A makes the 4, by raising the right leg perpendicularly, and lengthening it a little below the base, and lengthening the base on the left side. The forms the 5, by turning the lowest semicircle towards the right, which before was turned towards the left side. The number 5 forms the 6 by having its head taken off, and its body rounded. Z, by taking away the base, makes the 7. If we make the top and bottom of H round, we shall form an 8. The is the 9 with very little alteration. The cypher 0 was only a point, to which one of the figures was added to make it stand for ten times as much. It was necessary to mark this point very strongly: and, in order to form it better, a circle was made, which was filled up in the middle; but that circumstance was afterwards neglected. Theophanes, an historian of Constantinople, who lived in the ninth century, says expressly, that the Arabians retained the Greek figures, having no characters in their language to represent all the numbers. The Greeks observed in their numbers the decuple progression, which the Arabians have retained.' That this reasoning is plausible will hardly be questioned; but whether it be conclusive our readers must determine.

NUMERAL LETTERS, or NUMERALS, those letters of the alphabet which are generally used for figures; as I, one; V, five; X, ten; L, fifty; C, 100; D, 500; M, 1000, &c. It is not agreed how the Roman numerals originally received their value.. It has been supposed that the Romans used M to denote 1000, because it is the first letter of mille, the Latin for 1000; C to denote 100, because it is the first letter of centum, the Latin for 100; that D, being formed by dividing the old M in the middle, was therefore appointed to stand for 500, or half as much as the M s ood for when it was whole; or, more probably, that D stands for dimidium mille, the half of 1000 and that L, being half a C, was, for the same reason, used for fifty; that V stood for five, because it is the fifth vowel; that X stood for ten, because it contains V twice, one of them

inverted; and that I was used for one, because it is the first letter of initium, the beginning. But all these are fanciful derivations; and the following are perhaps equally so, though some think they afford the most natural account of the matter. The Romans probably put down a single stroke, I, for one; this I they doubled, trebled, and quadrupled, to express two, three, and four; thus II. IÎI. IIII. So far they could easily number the strokes with a glance of the eye. But they found that, if more were added, it would be necessary to tell the strokes one by one; they therefore expressed five by joining two strokes together in an acute angle, thus, V, which is the more probable, as the progression of the Roman numbers is from five to five, i. e. from the fingers on one hand to the fingers on the other. After they had made this acute angle V, for five, they added the single strokes to it to the number of four, thus, VI. VII. VIII. VIIII., and then, to prevent confusion, they doubled their acute angle by prolonging the two lines beyond their intersection, thus, X to denote two fives, or ten. After this they doubled, trebled, and quadrupled, this double acute angle thus, XX. XXX. XXXX. They then joined two single strokes in another form, and, instead of an acute angle, made a right angle L to denote fifty. When this fifty was doubled, they then doubled the right angle thus, L, to denote 100; and having numbered this double right angle four times, thus, EE. EEE. EEEE. when they came to the fifth number as before, they reversed it, and put a single stroke before it, thus, II, to denote 500; and, when this 500 was doubled, then they also doubled their double right angle, setting two double right angles opposite to each other, with a single stroke between them, thus, LI, to denote 1000: when this note for 1000 had been four times repeated, then they put down ICT for 5000, ELIT for 10,000, and 1 for 50,000, ELEITT for 100,000, I for 500,000, and EEEEI for 1,000,000. That the Romans did not originally write M for 1000, and C for 100, but square characters, as they are written above, we are expressly informed by Paulus Manutius; but the corners of the angles being cut off by the transcribers for despatch, these figures were gradually brought into what are now numeral letters. When the corners of EIT were made round, it stood thus, CIO, which is so near the Gothic n, that it soon deviated into that letter: so I having the corner made round, it stood thus, I, and then easily deviated into D. E also became a plain C by the same means; the single rectangle which denoted fifty was, without alteration, a capital L the double acute angle was an X; the single acute angle a V consonant; and a plain single stroke the letter I; and thus these seven letters, M, D, C, L, X, V, I, became numerals.-See ARITHMETIC.

NUMIDA, in ornithology, a genus belonging to the order gallinæ. On each side of the head there is a kind of colored fleshy horn; and the beak is serrated near the nostrils.

N. cristata, the crested guinea-hen, a species mentioned by Latham, inhabiting Africa. Perhaps it may have some relation to the crested

sort which Marcgrave mentions to have seen, and which came from Sierra Leone. This had a kind of membranous collar about the neck, was of a bluish-ash color, and had a large roundish black crest. Buffon, who describes it at great length, calls it la peintade. Linnæus and Gmelin call it numida meleagris, &c. Ray and Willoughby call it gallus and gallina Guineensis, &c. Mr. Pennant contends, and seems to prove, that the pintadoes had been early introduced into Britain, at least prior to the year 1277. But they seem to have been much neglected, on account of the difficulty of rearing them; for they occur not in our ancient bills of fare. They have a double caruncle at the chaps, and no fold at the throat. N. meleagris, the Guinea hen, is a native of Africa. It is larger than a common hen. Its body is sloped like that of a partridge, and its color is all over a dark gray, very beautifully spotted with small white specks; there is a black ring round the neck; its head is reddish, and it is blue under the eyes. They naturally herd together in large numbers, and breed up their young in common; the females taking care of the broods of others, as well as of their own. Barbut informs us, that in Guinea they go in flocks of 200 or 300, perch on trees, and feed on worms and grasshoppers; that they are run down and taken by dogs; and that their flesh is tender and sweet, generally white, though sometimes black. They breed very well with us. Mr. Latham observes that the native place of this bird is without doubt Africa, and that it is the meleagris of old authors. It is supposed originally to have come from Nubia, and was esteemed in the Roman banquets. It has been met with wild, in flocks of 200 or 300, by various travellers. Dampier found them in numbers in the island of Mayo; and Forster speaks of them as numerous at St. Jago; but they have been transported into the West Indies and America, and are now in a wild state in those places as well as domesticated.' The white-breasted one is a mere variety, of which there are many: it is mostly found in Jamaica.

N. mitrata, is a different and not a common species: it inhabits Madagascar and Guinea. Pallas seems to think that it may be the bird mentioned by Columella as differing from the common one; and will account for Pliny's having thought the numida and meleagris to be different birds.

NUMIDIA, an ancient kingdom of Africa, bounded on the north by the Mediterranean Sea; on the south by Gætulia, or part of Libya Interior; on the west by the Mulucha, a river which separated it from Mauritania; and on the east by the Tusca, another river that bounded it in common with Africa Propria. Dr. Shaw has rendered it probable that the river formerly named Malva, Malvana, Mulucha, or Molochath, is the same with that now called Mullooiah by the Algerines; in which case the kingdom of Numidia must have extended upwards of 500 miles in length; its breadth, however, cannot be so well ascertained; but, supposing it to have beeu the same with that of the present kingdom of Algiers, in the narrowest part it must have been at least forty miles broad, and in the widest

upwards of 100. This country included two districts, one inhabited by the Massyli, and the other by the Masæsyli; the latter being also called in after times Mauritania Cæsariensis, and the former Numidia Propria. The country of the Massyli, or, as some call it, Terra Metagonitis, was separated from the proper territory of Carthage by its eastern boundary, the river Tusca, and from the kingdom of the Masæsyli, or Mauritania Cæsariensis, by the river Ampsaga. It seems to correspond with that part of the province of Constantina, lying between the Zaine and the Wed al Kibeer, which is above 130 miles long, and more than 100 broad. The seacoast of this province is for the most part mentioned as rocky, answering to the appellation given to it by Abulfeda, viz. El Edwaa, the high or lofty. It is far from being equal in extent to the ancient country of the Masæsyli, which Strabo informs us was yet inferior to the country of the Massyli. Its capital was Cirta, a place of very considerable note among the ancients. The most celebrated antiquarians think that the tract extending from the isthmus of Suez to the lake Tritonis was chiefly peopled by the descendants of Mizraim, and that the posterity of his brother Phut spread themselves all over the country between that lake and the Atlantic Ocean. Herodotus countenances this; for he tells us, that the Libyan Nomades, whose territories on the west were bounded by the Triton, agreed in their customs and manners with the Egyptians; but that the Africans, from that river to the Atlantic Ocean, differed in almost all points from them. Ptolemy mentions a city called Putea, near Adrametum; and Pliny, a river of Mauritania Tingitana, known by the name of Fut, or Phut; and the district adjacent to this river was called Regio Phutensis, which plainly alludes to the name of Phut.

The history of Numidia, during many of the early ages, is buried in oblivion. It is probable, however, that, as the Phoenicians were masters of a great part of the country, these transactions had been recorded, and generally known to the Carthaginians. Jarbas, or Hiarbas, probably reigned here as well as in Africa Proper, if not in Mauritania, and other parts of Libya, when Dido began to build Byrsa. Justin says that, about the age of Herodotus, the people of this country were called both Africans or Libyans, and Numidians. He likewise intimates that about this time the Carthaginians vanquished both the Moors or Mauritanians, and Numidians; in consequence of which they were excused from paying the tribute which had hitherto been demanded of them. After the conclusion of the first Punic war the African troops carried on a bloody contest against their masters the Carthaginians; and the most active in this rebellion, according to Diodorus Siculus, were a part of the Numidian nation named Micatanians. This so incensed the Carthaginians, that, after Hamilcar had either killed or taken prisoners all the mercenaries, he sent a large detachment to ravage the country of those Numidians. That detachment executed his orders with the utmost cruelty, plundering the district, and crucifying all the prisoners without distinction. This filled

Notwithstanding this success, Masinissa being apprehensive that he should be obliged to sustain a war against Syphax, he offered to treat Lacumaces with as many marks of distinction as his father Gala had Desalces, provided that prince would put himself under his protection. He also promised Mezetulus pardon, and a restitution of all the effects forfeited by his treasonable conduct, if he would make his submission to him. Both of them readily complied with the proposal, and immediately returned home; so that the tranquillity and repose of Numidia would have been settled upon a solid and lasting foundation, had not this been prevented by Asdrubal, who was then at Syphax's court. He insinuated to that prince, that he was greatly mistaken, if he imagined Masinissa would be satisfied with his hereditary dominions: that he was a prince of much greater capacity and ambition than either his father Gala, his uncle Desalces, or any of his family. And that, in fine, unless this rising flame was extinguished before it came to too great a head, both the Masæsylian and Carthaginian states would be infallibly consumed by it.' Syphax, alarmed by these suggestions, advanced with a numerous body of forces into a district then in possession of Masinissa. This brought on a general action between these two princes; wherein the latter was totally defeated, his army dispersed, and he himself obliged to fly to the top of mount Balbus, attended only by a few of his horse. Such a decisive battle at this juncture, before Masinissa was fixed on the throne, could not but put Syphax into possession of the kingdom of the Massyli. Masinissa in the mean time made nocturnal incursions from his post upon mount Balbus, and plundered all the adjacent country, particularly that part of the Carthaginian territory contiguous to Numidia. This district he not only thoroughly pillaged, but likewise laid waste with fire and sword, carrying off an immense booty, which was bought by some merchants, who had put into one of the Carthaginian ports for that purpose. In fine, he did the Carthaginians more damage, not only by committing such dreadful devastations, but by massacring and carrying into captivity vast numbers of their subjects on this occasion, than they could have sustained in a pitched battle, or one campaign of a regular war. Syphax, at the pressing and reiterated instances of the Carthaginians, sent Bocchar, one of his most active commanders, with a detachment of 4000 foot, and 2000 horse, to reduce this pestilent gang of robbers, promising him a great reward if he could bring Masinissa either alive or dead. Bocchar, watching an opportunity, surprised the Massylians, as they were straggling about the country without any

Gala dying, whilst his son Masinissa was acting at the head of the Numidian troops sent to the assistance of the Carthaginians in Spain, his brother Desalces, according to the rules of succession in Numidia, took possession of the Massylian throne. That prince dying soon after, Capusa his eldest son succeeded him. But he did not long enjoy his high dignity; for one Mezetulus a person of the royal blood, but an enemy to the family of Gala, excited a great part of his subjects to revolt. A battle soon took place between him and Capusa, in which the latter was slain, with many of the nobility, and his army entirely defeated. But, though Mezetulus thus became possessed of the sovereignty, he did not think proper to assume the title of king, but styled himself guardian to Lacumaces, the surviving son of Desalces, whom he graced with the royal title. To support himself in his usurpation he married the dowager of Desalces, who was Hannibal's niece, and consequently of the most powerful family in Carthage. To attain the same end, he sent ambassadors to Syphax, to conclude a treaty of alliance with him. In the mean time Masinissa, receiving advice of his uncle's death, and his cousin's slaughter, and of Mezetulus's usurpation, immediately passed over to Africa, and went to the court of Bocchar, king of Mauritina, to solicit succours. Bocchar, sensible of the great injustice done Masinissa, gave him a body of 4000 Moors to escort him to his dominion. His subjects, having been apprised of his approach, joined him upon the frontiers with a party of 500 men. The Moors, in pursuance of their orders, returned home as soon as Masinissa reached the confines of his kingdom. Notwithstanding which, and the small body that declared for him, having accidentally met Lacumaces at Thapsus with an escort going to implore Syphax's assistance, he drove him into the town, which he carried by assault, after a faint resistance. However, Lacumaces, with many of his men, escaped to Syphax. The fame of this exploit gained Masinissa so great credit that the Numidians flocked to him from all parts, and, amongst the rest, many of his father Gala's ve terans, who pressed him to make a speedy and vigorous push for his hereditary dominions. Lacumaces having joined Mezetulus with a reinforcement of Masæsylians, which he had prevailed upon Syphax to send to the assistance of his ally, the usurper advanced at the head of a VOL. XVI.

C

order or discipline; so that he took many prisoners, dispersed the rest, and pursued Masinissa himself, with a few of his men, to the top of the mountain where he had before taken post. Considering the expedition as ended, he not only sent many head of cattle, and the other booty that had fallen into his hands, to Syphax, but likewise all the forces, except 500 foot and 200 horse. With this detachment he drove Masinissa from the summit of the hill, and pursued him through several narrow passes and defiles, as far as the plains of Clupea. Here he so surrounded him, that all the Massylians except four, were put to the sword, and Masinissa himself, after having received a dangerous wound, escaped with the utmost difficulty. As this was effected by crossing a rapid river, in which at tempt two of his four attendants perished in the sight of the detachment that pursued him, it was rumored all over Africa that Masinissa also was drowned. For some time he lived undiscovered in a cave, where he was supported by the two horsemen that had made their escape with him. But having cured his wound, by the application of some medicinal herbs, he boldly began to advance towards his own frontiers. In his march he was joined by about forty horse, and, soon after his arrival among the Massyli, so many people flocked to him from all parts that out of them he formed an army of 6000 foot and 4000 horse. With these forces he not only reinstated himself in the possession of his dominions, but likewise laid waste the borders of the Masæsyli. This so irritated Syphax that he immediately assembled a body of troops, and encamped very commodiously upon a ridge of mountains between Cirta and Hippo. His army he commanded in person; and detached his son Vermina, with a considerable force, to take a compass, and attack the enemy in the rear. In pursuance of his orders, Vermina set out in the beginning of the night, and took post in the place appointed him, without being discovered by the enemy. In the mean time Syphax decamped, and advanced towards the Massyli, to give them battle. When he had possessed himself of a rising ground that led to their camp, and concluded that his son Vermina must have formed the ambuscade behind them, he began the fight. Masinissa being advantageously posted, and his soldiers distinguishing themselves in an extraordinary manner, the dispute was long and bloody. But Vermina unexpectedly falling upon their rear, and thus obliging them to divide their forces, which were scarcely able before to oppose the main body under Syphax, they were soon thrown into confusion, and forced to betake themselves to a precipitate flight. All the avenues being blocked up, partly by Syphax and partly by his son, such a dreadful slaughter was made of the unhappy Massyli, that only Masinissa himself, with sixty horse, escaped to the Lesser Syrtis. Here, he remained betwixt the confines of the Carthaginians and Garamantes, till the arrival of Lælius and the Roman fleet on the coast of Africa, when he Joined with the Romans; and by the assistance of Lælius, at last reduced Syphax's kingdom

See ROME. According to Zonoras, Ma

sinissa and Scipio, before the memorable battle of Zama, deprived Hannibal by stratagem of some advantageous posts; which greatly contributed to the victory the Romans obtained. At the conclusion, therefore, of the second Punic war, he was amply rewarded by the Romans for the important services he had done them. As for Syphax, after the loss of his dominions, he was kept in confinement for some time at Alba; whence being removed to grace Scipio's triumph, he died at Tibur in his way to Rome. Zonoras adds, that his corpse was decently interred; that all the Numidian prisoners were released; and that Vermina, by the assistance of the Romans, took peaceable possession of his father's throne. However, part of the Masæsylian kingdom had been before annexed to Masinissa's dominions, to reward that prince for his singular fidelity and attachment to the Romans. A short time before the beginning of the third Punic war he again attacked the Carthaginians, and by drawing a line of circumvallation around their army, posted upon an eminence, under the command of Asdrubal, Massinissa cut off all manner of supplies from them; which introduced both the plague and famine into their camp. As the body of Numidian troops employed in this blockade was not near so numerous as the Carthaginian forces, the line here mentioned must have been extremely strong, and the effect of great labor and art. The Carthaginians, finding themselves reduced to the last extremity, concluded a peace upon the following terms, which Masinissa dictated:-1. That they should deliver up all deserters. 2. That they should recal their exiles, who had taken refuge in his dominions. 3. That they should pay him 5000 talents of silver within fifty years. 4. That their soldiers should pass under the yoke, each carrying off only a single garment. As Masinissa himself, though between eighty and ninety years of age, conducted the whole enterprise, he must have been extremely well versed in fortification, and other branches of the military art. Soon after, the consuls landed an army in Africa, in order to lay siege to Carthage, without imparting to Masinissa their design. This not a little chagrined him, as it was contrary to the former practice of the Romans; who, in the preceding war, had communicated their intentions to him, and consulted him on all occasions. When, therefore, the consuls applied to him for a body of his troops to act in concert with their forces, he answered, 'that they should have a reinforcement when they stood in need of it.' It could not but be provoking to him, that after he had extremely weakened the Carthaginians, and even brought them to the brink of ruin, his pretended imperious friends should come to reap the fruits of his victory, without giving him the least intelligence of it. However, his mind soon returned to its natural bias in favor of the Romans. Finding his end approaching, he sent to Emilianus, then a tribune in the Roman army, to desire a visit from him. What he proposed by this visit, was to invest him with full powers to dispose of his kingdom and estate as he should think proper, for the benefit of his children. The high