埃及国家的形状狭长,ref: Eratosthenes, Syene, and Alexandria



所有跟贴·加跟贴·新语丝读书论坛http://www.xys.org/cgi-bin/mainpage.pl

送交者: xj 于 2005-1-12, 18:29:30:

回答: 同时不是关键,同经才是. 由 outsider 于 2005-1-12, 18:07:47:

偶把synene 的英文给猜出来,古狗一牵出来,不牛不行:-)
================================

Eratosthenes was born in Cyrene (now Shahhat, Libya) around 276 B.C. and after studying in Alexandria and Athens he became the third director of the Library of Alexandria. He is presently referred to as the father of geodesic science and the first man to measure the earth, but in his own day his nickname was Beta, which means second. Eratosthenes' works have been lost although the titles of his major works have come down to us from secondary sources, such as his treatise On the Measurement of the Earth.

Eratosthenes heard (or read) that at noon on the summer solstice the sun shined directly into a deep well near the southern border of ancient Egypt in the city of Syene, marking the latitude of Syene as the Tropic of Cancer. Eratosthenes reported that Syene and the Tropic of Cancer were located at 23° 51' north latitude. He also reported that in Alexandria at noon on the summer solstice the sun cast a shadow with an angle of 7° 12'. This led Eratosthenes to believe that Alexandria was 7° 12' north of Syene, at 31° 03' north latitude. Eratosthenes understood that 7° 12' is 1/50th of 360°, thus 1/50th of the circumference of the earth, so he concluded that the distance from Syene to Alexandria was 1/50th of the circumference of the earth.

Eratosthenes reported that Syene was due south of Alexandria on the same meridian, and he reported that the distance from Syene to Alexandria was 5,000 stadia. The stadia that Eratosthenes referred to is in dispute. The most widespread view is that he was referring to a Greco/Roman stadia of 600 Roman feet. This stadia times 5,000 times 50 is about 15% longer than the actual circumference of the earth, which most commentators regard as a good estimate for Eratosthenes' day.

Syene is actually located at 24° 06' north latitude. The Tropic of Cancer was located at 23° 51' north latitude during the dynastic period of ancient Egypt, but by the time of Eratosthenes the tropic had moved down to 23° 45' north latitude. The sun shines directly down on an area of the earth covering one-half of one degree of latitude. When the Tropic of Cancer was at 23° 51' N, the northern edge of the sun at noon on the summer solstice would have shined directly down into the well at Syene, one-quarter of one degree north of the Tropic of Cancer. In Eratosthenes' day, the tropic had moved too far south for the sun to shine directly down into the well at Syene.

Alexandria is actually located at 31° 12' north latitude. Since the tropic was at 23° 45' north latitude in Eratosthenes' day and since the northern edge of direct downward sunlight is an additional one-quarter of one degree north, the northern edge of direct downward sunlight on the summer solstice in Eratosthenes' day would have been at 24° 00' north latitude and the angle of the shadow cast by the northern edge of the sun at noon on the summer solstice in Alexandria would have been 7° 12', just as Eratosthenes reported.

Syene is actually almost three full degrees of longitude east of Alexandria The distance from Syene to Alexandria is not 5,000 stadia regardless of what stadia is employed, because Syene is so far east of Alexandria. The reason Eratosthenes got the latitude for Alexandria wrong was because he was basing the difference on an incorrect assumption about the latitude of Syene, an incorrect assumption about the latitude of the tropic and because he was unaware that the sun shines directly down on an area one-quarte of one degree north of the tropic.

Although the distance from Alexandria to Syene is not equal to 1/50th of the circumference of the earth, the distance from the latitude of Alexandria to the latitude of Philae, six minutes south of Syene at the southern border of ancient Egypt, is equal to 1/50th of the circumference of the earth (7° 12'). According to Livio Stecchini, the ancient Egyptians employed a stadia of 300 cubits, although this measure was not in use during Eratosthenes' day. The ancient Egyptian cubit of 20.62 inches, times 300, times 5,000 equals 488 miles. The distance due north-south from the latitude of Alexandria to the latitude of Syene is 488 miles.

Modern scholars say it is a happy coincidence that all of Eratosthenes' errors tended to cancel out, resulting in a fairly accurate measure of the circumference of the earth, even though most of his data and calculations were wrong. All of this suggests that Eratosthenes did not stray too far from accurate conclusions because he already knew from fragmentary records in the Library of Alexandria that the boundaries of ancient Egypt had originally been set at 1/50th of the circumference of the earth and that the distance from the latitude of Alexandria to the latitude of Syene was 1,500,000 cubits or 5,000 ancient Egyptian stadia. If Eratosthenes acknowledged this, it could explain the loss of all of his works even though other Greek works from before, during and after his time have survived.





所有跟贴:


加跟贴

笔名: 密码(可选项): 注册笔名请按这里

标题:

内容(可选项):

URL(可选项):
URL标题(可选项):
图像(可选项):


所有跟贴·加跟贴·新语丝读书论坛http://www.xys.org/cgi-bin/mainpage.pl