Roman numerals

“ According to Ball's 'Short Account of the History of Mathematics,' the arabic arithmetic was practically unknown in Europe until the end of the thirteenth century. At that date numbers were written in Roman numerals. When we see a date inscribed in Roman numerals upon the portal of a public building, we witness the persistence, in art, of the system which was in universal use for all the arithmetical purposes of the civilized world only a few centuries ago.
How simple to our minds to-day seems such a numerical problem as a determination of the number of seconds in a mean solar day. ”

“ The case of the Roman numerals in Europe furnishes a ready illustration of this symbolical language. There is nothing in the symbols 1, 2, 3, &c. by which their pronunciation can be ascertained when presented to the eye, yet they communicate meaning independent of sound, and are respectively intelligible to the inhabitants of the different countries of Europe; while, at the same time, the sounds by which a native of one country distinguishes the written symbols 1, 2, 3, &c. are unintelligible to all the rest. ”

“ The arithmetical or Arabic numerals are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Properly they should be styled Hindu or Indian numerals; for the Arabs borrowed them, along with the decimal system of notation, from the Hindus. They were probably first introduced from the East into Italy about 1202; yet they did not come into general use before the invention of printing. Accounts were kept in Roman numerals up to the sixteenth century. Figures are usually made one en thick; but of late a broader figure is cast for newspaper use, which is two-thirds or six-sevenths of an em in width. ”

“ Thus we find the numerals gradually replacing the Roman forms all over Europe, from the time of Leonardo of Pisa until the seventeenth century. But in the Far East to-day they are quite unknown in many countries, and they still have their way to make. In many parts of India, among the common people of Japan and China, in Siam and generally about the Malay Peninsula, in Tibet, and among the East India islands, the natives still adhere to their own numeral forms. ”

“ They should never be used to record the publication date of a work, even if the source uses Roman numerals. They should not be used in page names to represent volume or issue numbers, in part because the trend in modern libraries has been to shift away from Roman numerals for these purposes, and to use Arabic numerals instead. ”

“ It was the weakness and the uneven alignment of the arabic figures made for old-style fonts that compelled printers to use bolder-faced roman numerals for all title-pages, chapter headings, dedications, inscriptions, and every other part of a book that was required to be composed largely in capital letters. ”

“ I. F. Weidler, Spicilegium observationum ad historiam notarum numeralium pertinentium, Wittenberg, 1755, speaks of the "figura cifrarum Saracenicarum" as being different from that of the "characterum Boethianorum," which are similar to the "vulgar" or common numerals; see also Humboldt, loc. cit.
[254] Gerhardt mentions it in his Entstehung etc., p. 8; Woepcke, Propagation, states that these numerals were used not for calculation, but very much as we use Roman numerals. These superposed dots are found with both forms of numerals (Propagation, pp. 244-246) . ”

“ The Egyptians, for example, had three systems of writing, with a numerical notation for each; the Greeks had two well-defined sets of numerals, and the Roman symbols for number changed more or less from century to century. Even to-day the number of methods of expressing numerical concepts is much greater than one would believe before making a study of the subject, for the idea that our common numerals are universal is far from being correct. It will be well, then, to think of the numerals that we still commonly call Arabic, as only one of many systems in use just before the Christian era. ”

“ It is to be understood that where there is more than one division on a plate, as is usually the case, they will be numbered consecutively from the top downward, first, second, third, &c. In giving the numerals, the Roman represent the red or day numerals, the Arabic the black or month numbers. The red numerals usually found over the day columns will also be placed over them here. ”

“ MCM=1900. For some amounts exceeding 2000 the characters ∞, ╳, X, V, and the C inverted as Ↄ, have to be rudely made by the printer, for these characters are not provided in fonts of book type. [3] Roman numerals had to be used by the first printers because they had no arable figures. These figures were first used in 1471 by Ther Hoernen, but they did not obtain a general acceptance for many years after. They were irregular in form and bad mates for the roman capital letters. These unsymmetrical characters were bettered but slowly, still remaining
Fifteenth century. ”

“ John H. R. Smith, Jun.
Coin of Carausius.—A brass coin has lately come into my possession, bearing on the obverse the head and inscription:
"IMP. CARAVSIUS. P. P. AVG."
And on the reverse, a female figure, with spear and a branch:
"PAX. AUG. S. P. MLXXI."
I believe it to have been struck by Carausius, an usurper of the end of the third century, and my Query is as to the meaning of the letters MLXXI. Some friends assert them to be the Roman numerals, making the year 1071, and conclude it to have been struck at that date. ”

“ The Romans designed the number ten by an oblique cross X, and the Chinese by a vertical one 十. This resemblance in the forming of their numerals, so simple and natural that almost all nations have adopted it, is surely too slight a coincidence for concluding, that the people who use them must necessarily, at some period or other, have had communication together. The Doctor however seems to think so, and proceeds to observe, that the three principal Roman cyphers, I. V. X. or one, five and ten, are denoted in the Chinese language by the same sounds that they express in the Roman alphabet. ”

“ As to Germany, the fifteenth century saw the rise of the new symbolism; the sixteenth century saw it slowly [150] gain the mastery; the seventeenth century saw it finally conquer the system that for two thousand years had dominated the arithmetic of business. Not a little of the success of the new plan was due to Luther's demand that all learning should go into the vernacular. [606]
During the transition period from the Roman to the Arabic numerals, various anomalous forms found place. For example, we have in the fourteenth century cα for 104 ”

“ The Romans never used the successive letters of their alphabet for numeral purposes in the manner practiced by the Syrians, Hebrews, and Greeks, although (as we shall see) an alphabet system was at one time proposed by a late Roman writer. Before the ascendancy of Rome the Etruscans, who inhabited the country nearly corresponding to modern Tuscany and who ruled in Rome until about 500 B.C., used numeral signs which resembled letters of their alphabet and also resembled the numeral signs used by the Romans. ”

“ As men advanced in the use of numbers, they adopted a group derived from the fingers of both hands; thus ten became the base of numeration.
Notation, like numeration, began with ones, advanced to fives, then to tens, etc. Roman notation consisted of a series of signs signifying 1, 5, 10, 50, 100, 500, 1000, etc.,—a series evidently the result of counting by the five fingers and the two hands, the numbers signified being the products of continued multiplication by five and by two alternately. ”

“ In savage languages it is sometimes possible to detect these meanings, and thus to obtain possession of the clue that leads to the development, in the barbarian's rude mind, of a count scale—a number system. But in languages like those of modern Europe, the pedigree claimed by numerals is so long that, in the successive changes through which they have passed, all trace of their origin seems to have been lost. ”

“ The words we employ to designate the higher orders of units, as million, billion, trillion, etc., are appropriated bodily from the Italian; and the native words pair, tale, brace, dozen, gross, and score, can hardly be classed as numerals in the strict sense of the word. German possesses exactly the same number of native words in its numeral scale as English; and the same may be said of the Teutonic languages generally, as well as of the Celtic, the Latin, the Slavonic, and the Basque. ”

“ As it then existed the system was no better than many others, it was of late origin, it contained no zero, it was cumbersome and little used, [2] and it had no particular promise. Not until centuries later did the system have any standing in the world of business and science; and had the place value which now characterizes it, and which requires a zero, been worked out in Greece, we might have been using Greek numerals to-day instead of the ones with which we are familiar. ”

“ The use of visible signs to represent numbers and aid reckoning is not only older than writing, but older than the development of numerical language on the denary system; we count by tens because our ancestors counted on their fingers and named numbers accordingly. So used, the fingers are really numerals, that is, visible numerical signs; and in antiquity the practice of counting by these natural signs prevailed in all classes of society. In the later times of antiquity the finger symbols were developed into a system capable of expressing all numbers below 10,000. ”

“ If the strong man who had six fingers on each hand, and six toes on each foot, had invented a system of numeration, it would have gone in twelves, nearly like the duodecimals which our carpenters use; unless, indeed, he had been stupid after the manner of very strong men, and not gone beyond sixes. We see how the Romans, though they inherited from their Eastern ancestors a numeration by tens up to decem, and then beginning again undecim, &c., yet when they began to write a notation could get no farther than five—I., II., III., IV., V. ”

“ The theory that man’s primitive mode of counting was palpable reckoning on his hands, and the proof that many numerals in present use are actually derived from such a state of things, is a great step towards discovering the origin of numerals in general. Can we go farther, and state broadly the mental process by which savage men, having no numerals as yet in their language, came to invent them? ”

“ The Egyptians, in their hieroglyphic character, counted by upright strokes up to nine, and then made a special sign for ten, in this respect resembling the modern Creek Indians, and the fact that the Chinese only count 〡〢〣 in strokes, and go on with an 〤 for four, and then with various other symbols till they come to 十 or ten, does not interfere with the fact, that in three or four systems of numeration, so far as we know independent of one another, in Italy, China, and North America, more or less of the earlier numerals are indicated by counted strokes, and ten by a crossed stroke. ”

“ Occasionally there went along these routes of trade men of real learning, and such would surely have carried the knowledge of many customs back and forth. Thus at a period when the numerals are known to have been partly understood in Italy, at the opening of the eleventh century, one Constantine, an African, traveled from Italy through a great part of Africa and Asia, even on to India, for the purpose of learning the sciences of the Orient. ”

“ Sanskrit has twenty-seven, while Japanese possesses twenty-four, and the Chinese a number almost equally great. Very many languages, as might be expected, contain special numeral expressions, such as the German dutzend and the French dizaine; but these, like the English dozen and score, are not to be regarded as numerals proper.
The formation of numeral words shows at a glance the general method in which any number scale has been built up. The primitive savage counts on his fingers until he has reached the end of one, or more probably of both, hands. ”

“ A single alphabet, that which the Phœnicians extracted from one of the forms of Egyptian writing, made the tour of the Mediterranean, and served all the nations of the ancient world in turn for preserving their thoughts and the idiom of their language. A system of numerals, of weights and measures, was invented in Babylon and travelled across Western Asia to be adopted by the Greeks, and, through the mediation of the Greek astronomers and geographers, has given us the sexagesimal division which we still employ for the partition of a circumference into degrees, minutes and seconds. ”

“ Etymological research into the derivation of numeral words thus hardly goes with safety beyond showing in the languages of the lower culture frequent instances of digit-numerals, words taken from direct description of the gestures of counting on fingers and toes. Beyond this, another strong argument is available, which indeed covers almost the whole range of the problem. The numerical systems of the world, by the actual schemes of their arrangement, extend and confirm the opinion that counting on fingers and toes was man’s original method of reckoning, taken up and represented in language. ”

“ The introduction of myriads as in the Greek, and thousands as in Arabic and in modern numeration, is really a step away from a decimal scheme. So in the numbers below one hundred, in English, eleven and twelve are out of harmony with the rest of the -teens, while the naming of all the numbers between ten and twenty is not analogous to the naming of the numbers above twenty. To conform to our written system we should have ten-one, ten-two, ten-three, and so on, as we have twenty-one, twenty-two, and the like. The Sanskrit is consistent, the units, however, preceding the tens and hundreds. ”