The History of Mathematics: A Brief Course

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  1. WHAT WAS COUNTED? 123


reason for noticing it. Like all stars, Sirius gains about four minutes per day on the
Sun, rising a little earlier each night until finally it rises just as the Sun is setting.
Then for a while it cannot be seen when rising, since the Sun is still up, but it
can be seen setting, since the Sun will have gone down before it sets. It goes on
setting earlier and earlier until finally it sets just after the Sun. At that point it
is too close to the Sun to be seen for about two months. Then it reappears in the
sky, rising just before the Sun in the early dawn. It was during these days that
the Nile began its annual flood in ancient times^8 Thus the heliacal rising of Sirius
(simultaneous with the Sun) signaled the approach of the annual Nile flood. The
Egyptians therefore had a very good basis for an accurate solar calendar, using the
heliacal rising of Sirius as the marker of the year.
The Egyptians seem originally to have used a lunar calendar with 12 lunar
cycles per year. However, such a calendar is seriously out of synchronicity with the
Sun, by about 11 or 12 days per year, so that it was necessary to add an extra
"intercalary" month every two or three years. All lunar calendars must do this, or
else wander through the agricultural year. However, at an early date the Egyptians
cut their months loose from the Moon and simply defined a month to consist of 30
days. Their calendar was thus a "civil" calendar, neither strictly lunar nor strictly
solar. Each month was divided into three 10-day "weeks" and the entire system
was kept from wandering from the Sun too quickly by adding five extra days at
the end of the year, regarded as the birthdays of the gods Osiris, Horus, Seth, Isis,
and Nephthys. This calendar is still short by about £ day per year, so that in
1456 years it would wander through an entire cycle of seasons. The discrepancy
between the calendar and the Sun accumulated slowly enough to be adjusted for,
so that no serious problems arose. In fact, this wandering has been convenient for
historians, since the heliacal rising of Sirius was recorded. It was on the first day of
the Egyptian year in 2773 BCE, 1317 BCE, and 139 CE. Hence a document that
says the heliacal rising occurred on the sixteenth day of the fourth month of the
second season of the seventh year of the reign of Senusret III makes it possible to
state that Senusret III began his reign in 1878 BCE (Clayton, 1994, PP- 12-13).
On the other hand, some authorities claim that the calendar was adjusted by the
addition of intercalary days from time to time to keep it from wandering too far.
When the Greeks came to Egypt, they used the name Sothis to refer to Sopdit.
Consequently, the period of 1456 years is known as the Sothic cycle.


The Julian calendar. In a solar calendar, the primary period of time being tracked
is the solar year, which we now know to be 365.2422 mean solar days long. Taking
365.25 days as an approximation to this period, the Julian calendar (a solar calen-
dar) makes an ordinary year 365 days long and apportions it out among the months,
with January, March, May, July, August, October, and December each getting 31
days, while April, June, September, and November each get 30 days and February
gets 28 days. For historiographical purposes this calendar has been projected back
to the time before it was actually created. In that context it is called the proleptic
Julian calendar. In a solar calendar the month is not logically necessary, and the
months have only an approximate relation to the phases of the Moon.


The floods no longer occur since the Aswan Dam was built in the 1950s.
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