C
50 brachystochrone is found in the work of Jakob Bernoulli; nowadays it would be called a mistake and marked wrong since the Greek word has an iota (i = i), not an upsilon (u = y), in the superlative degree; the upsilon appears in the positive degree bracÚj. Newton and Leibniz solved the problem posed by Jakob Bernoulli (1654–1705) and proved that the cycloid (q.v.) is the brachistochrone; they did so by assuming that the point mass falls as if it were a light ray, which moves according to Fermat’s principle, so as to minimize time. C c This is the symbol for the cardinal number of the continuum, although the Hebrew is also used. calculate The Latin word for stone is calx, calcis. The addition of the ending -ulus to the stem produces the diminutive calculus, which means a small stone or pebble. As a medical term, it is used of bladder, gall, and kidney stones, and even the gritty accumulation on the teeth. Since such pebbles were used as counters in counting, the verb calculo, calculare, calculavi, calculatus came into existence with the meaning to count. The verb calculate is derived from the fourth principal part of this verb, from which is also deduced the noun calculatio, calculationis and our noun calculation. calculus This is the Latin word for a small stone. See the previous entry. It came to be used by the late seventeenth-century mathematicians as a technical term for any theory that laid the foundations of a general method to calculate the solutions of certain types of problems and then, kat' ™xoc»n, to those theories that solved the problems of tangent lines (differential calculus) and quadrature (integral calculus). In modern times calculus is the standard introduction to the higher mathematics, and it will remain so until innovators sweep it away with everything else. 51 calendar mathematics The Greek verb kalšw means to call, and from it the Romans derived the name kalendae, -arum, the kalends, for the first day of their months. The Greeks did not use the kalends, so the expression Greek kalends came to mean a day that would never come; it is equivalent to the Hebrew expression when the Messiah comes. At the time of Julius Caesar (100–44 B.C.), it was obvious to the world that the days of the year were not occurring in the season originally intended; for example, the first day of spring was falling in June. The error was due to an ancient mistake in estimating the time required for the earth to make one revolution about the sun. The mathematician Sosigenes advised the Perpetual Dictator that the length of the solar year was 365 days and 6 hours. On the basis of this calculation, Caesar introduced in 46 B.C. the calendar that bears his name, and which continues to survive in the Orthodox Church. The advance of knowledge has since determined the length of the solar year to be 365 days, 5 hours, 48 minutes, 46 seconds. This means that Caesar’s year is 11 minutes, 14 seconds too long. The accumulated error amounts to one day every 128.1899 Julian years. As a result, if left uncorrected, Christmas would eventually be celebrated in spring rather than at the beginning of winter. The Supreme Pontiff Gregory XIII (1572–1585) determined to distinguish his pontificate by correcting the calendar of Caesar. There were two problems to be solved. First, he had to correct the accumulated error, which amounted to 12.7 days since 46 B.C. Also, it was necessary to make some change to prevent the error from accumulating again. Since the year 46 B.C. was of no importance for the Catholic religion, the pope determined to restore the situation to where it had been in A.D. 325, the year of the Ecumenical Council of Nicaea. From 325 to 1582 there had elapsed 1,257 years, and the error accumulated during those years amounted to 9.805764 days. It was determined to fix this problem by skipping the 10 days between October 4 and October 15, 1582, a period during which the ecclesiastical calendar had no vital feasts. To prevent the error from reaccumulating, it was determined to skip 3 leap years every 4 centuries, a convenient approximation to the exact error of 3 years every 384.56973 years. It was therefore decreed that centurial years [18.188.252.23] Project MUSE (2024-04-19 09:38 GMT...
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