ANOBON, a small island in Africa, on the east coast of Loango, belonging to the Portuguese. It lies in long. 5. 30. E. lat. 1. 32. S., and receives its name from being discovered on the new year's day. According to Pyrard, it is about five or six French leagues in circuit; Braudrand makes it ten leagues. It contains two high mountains, having their tops continually enveloped in clouds, and thus occasioning frequent rains. Off the south-east of the island are two rocks, one of which is low, and upon a level with the surface of the sea; the other higher and larger, but both dangerous to shipping in the night: between them the channel is deep and clear. On the same side of the island is a convenient watering place; but the road ANNUITIES.
The doctrine of Compound Interest and Annuities—certain is too simple ever to have occupied much of the attention of mathematicians; inquiries into the values of interests dependent upon the continuance or the failure of human life, being more interesting and difficult, have occupied them more, but yet not so much as their importance would seem to demand; the discoveries both in Pure Mathematics and Physics, especially those of Newton, which distinguished the close of the seventeenth century, having provided them with ample employment of a more interesting kind, ever since the subjects of this article were submitted to calculation.
Fermat, Pascal, and Huygens, by laying the foundation of the doctrine of probabilities, about the middle of that century, first opened the way to the solution of problems of this kind. The earliest mathematical publication on probabilities, the little tract of Huygens, *De Ratiociniis in Ludo Aleae*, appeared in 1658; and in 1671 his celebrated countryman John de Witt published a treatise on Life-Annuities in Dutch. (Montucla, *Hist. des Math.* tome iii. p. 407.) This, however, appears to have been very little known or read, and to have had no sensible influence on the subsequent progress of the science, the origin of which may be properly dated from the publication of Dr Halley's paper on the subject, in the *Philosophical Transactions* for the year 1693 (No. 196). That celebrated mathematician there first gave a table of mortality, which he had constructed from observations made at Breslaw, and showed how the probabilities of life and death, and the values of annuities and assurances on lives, might be determined by such tables; which, he informs us, had till then been only done by an imaginary valuation. Besides his algebraical reasonings, he illustrated the subject by the properties of parallelograms and parallelopipeds; there are, perhaps, no other mathematical inquiries, in the prosecution of which algebra is entitled to so decided a preference to the elementary geometry as in these, and this example of the application of geometry has not been followed by any of the succeeding writers.
In the year 1724 M. de Moivre published the first edition of his tract entitled *Annuities on Lives*. In order to shorten the calculation of the values of such annuities, he assumed the annual decrements of life to be equal; that is, that out of a given number of persons living at any age, an equal number die every year until they are all extinct; and upon that hypothesis he gave a general theorem, by which the values of annuities on single lives might be easily determined. This approximation, when the utmost limit of life was supposed to be 86 years, agreed very well with the true values between 30 and 70 years of age, as deduced from Dr Halley's table; and the method was of great use at the time, as no tables of the true values of
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1 Hardly any terms are made use of in this article which may properly be considered technical. But since it is desirable that the reader should have perfectly clear and well-defined ideas of the terms that are employed, in the demonstrative part, which follows the historical, a few have been defined in the paragraphs where they are first introduced; and we here give those terms in alphabetical order, with the numbers of the paragraphs in which their definitions are given:
| Term | Paragraph | |-----------------------|-----------| | Annuity | | | Annuity, Certain | | | Annuity, Deferred | | | Annuity, Life | | | Annuity, Temporary Life | | | Annuity on any Life or Lives | | | Assurance on any Life or Lives | | | Mortality, Table of Years' Purchase, No. of, that an Annuity is worth | |
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ANNOVA, in *Roman Antiquity*, denotes provision for a year of all sorts, as of flesh, wine, &c. but especially of corn. Annona is likewise the allowance of oil, salt, bread, flesh, corn, wine, hay, and straw, which was annually provided by the contractors for the maintenance of an army.