A decimal system of numeration was used, with numbers going up to io,000.
Other Methods of Numeration and Notation.
At present, both in N and B, Hebrews is placed after 2 Thess., but in B there is also a continuous numeration of sections throughout the epistles, according to which I to 58 cover Romans to Galatians, but Ephesians, the next epistle, begins with 70 instead of 59, and the omitted section numbers are found in Hebrews.
The numeration was in the denary scale, so that it did not agree absolutely with the notation.
This seems to be in part due to a difference in numeration, but the state suffered heavily from famine in 1896-1897 and 1899-1900.
The principle of subtraction from a higher number, which appeared in notation, also appeared in numeration, but not for exactly the same numbers or in exactly the same way; thus XVIII was two-from-twenty, and the next number was onefrom-twenty, but it was written XIX, not IXX.
The medieval Arabians invented our system of numeration and developed algebra.
Discrepancies between Numeration and Notation.
With Regard To The Numeration Of The Years Previous To The Commencement Of The Era, The Practice Is Not Uniform.
1 It may be added that the double system of accentuation ofthe Decalogue in the Hebrew Bible seems to preserve traces of the ancient uncertainty concerning the numeration.
In numeration, indeed, uniformity was not attained till at least the 2nd century of the Christian era.
Numeration was at a low level, based on counting fingers on one hand only, so that the word for man (puggana) stood also for the number 5.
Arithmetic is supposed to deal with cardinal, not with ordinal numbers; but it will be found that actual numeration, beyond about three or four, is based on the ordinal aspect of number, and that a scientific treatment of the subject usually requires a return to this fundamental basis.
The representation of numbers by spoken sounds is called numeration; their representation by written signs is called notation.
The systems adopted for numeration and for notation do not always agree with one another; nor do they always correspond with the idea which the numbers subjectively present.
This may have been due to one or both of two causes; a primitive tendency to refer numbers, in numeration, to the nearest large number (§ 24 (iv)), and the difficulty of perceiving the number of a group of objects beyond about three (§ 22).
The use of the denary scale in notation is due to its use in numeration (§ 18); this again being due (as exemplified by the use of the word digit) to the primitive use of the fingers for counting.
The number ten having been taken as the basis of numeration, there are various methods that might consistently be adopted for naming large numbers.
- Although numeration and notation are both ostensibly on the denary system, they are not always exactly parallel.
(iv) Even beyond twenty, up to a hundred, the word ten is not used in numeration, e.g.
(v) The rule that the greater number comes first is not universally observed in numeration.
In other words, the denary scale, though adopted in notation and in numeration, does not arise in the corresponding mental concept until we get beyond too.
Addition is the process of expressing (in numeration or notation) a whole, the parts of which have already been expressed; while, if a whole has been expressed and also a part or parts, subtraction is the process of expressing the remainder.
C. Conant, The Number-Concept (1896), gives a very full account of systems of numeration.
Here we must bear in mind that Hebrew numeration always includes the day which is the terminus a quo as well as that which is term.
simple numeration is expanded to " abstract " mathematics by metaphorical projections from our sensory-motor experience.
The original numeration will be used solely as a guide, and the numbers will not necessarily be rigidly adhered to.
This method of numeration dates from the time of Guzman Blanco, but the common people adhere to the names bestowed upon the city squares in earlier times.
We can now see how long and laborious was the process by which the Greeks attained to uniformity in writing and in numeration.
(iii) Names might be given to the successive powers of ten, up to the point to which numeration of ones is likely to go.
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