第14章 古埃及——奇特的尼罗河文明(5)

Wounds were treated by bandaging with raw meat， white linen， sutures， nets， pads， and swabs soaked with honey to prevent infection， while opium was used to relieve pain. Garlic and onions were used regularly to promote good health and were thought to relieve asthma symptoms. Ancient Egyptian surgeons stitched wounds， set broken bones， and amputated diseased limbs， but they recognized that some injuries were so serious that they could only make the patient comfortable until death occurred.

古埃及医学：多灾多难中的健康智慧

古埃及人的医疗问题直接来源于他们的生存环境。在尼罗河附近生活和工作，不断滋生的疟疾和血吸虫病带来的危害就是造成肝脏和肠道损伤。危险的野生动物，如鳄鱼和河马，也普遍威胁着他们的生命。在农业和建筑领域的终身劳动对脊柱和关节的压力很大，在建设和战争中负伤也重重地摧残着身体。石材地面上的砂砾和沙子磨损着牙齿，使它们更易感染脓肿（虽然龋齿是罕见的）；富裕家庭吃的糖太多，从而促进牙周病的产生。尽管刻在古墓墙上的雕像有些夸大，但是很多上层阶级的木乃伊的超重现象展示了他们的放纵生活。古埃及成人的预期寿命男人大约是35岁，女人大约是30岁，但大约1/3的人在婴儿期就死去。

古埃及医生因医术高明而在古代近东地区名声显赫，有些如印何阗这样的医生死去多年后还远近闻名。希罗多德说，埃及医生中有一批专业化程度相当高的医师，有的治疗头疼或胃病，有的是专业的眼科医生和牙医。培训医生是在“生命之屋”机构中进行的，医学记载中记录了有关解剖、损伤和实际治疗的经验知识。

他们对伤口的处理通常是用浸泡在蜂蜜中的生肉、白色亚麻、缝合线、网布、垫子、墩布进行包扎，以免伤口感染。鸦片是用来减轻疼痛的；大蒜和洋葱经常用来促进健康，人们认为它们可以缓解哮喘症状。古埃及的外科医生可以缝合伤口，拼凑碎骨或截下患肢，但他们承认，有些伤痛太严重了，他们无能为力，只是静候患者的离世。

Egyptian mathematics：The Pythagorea theorem and the golden ratio

The earliest attested examples of mathematical calculations date to the predynastic Naqada period， and show a fully developed numeral system. The importance of mathematics to an educated Egyptian is suggested by a New Kingdom fictional letter in which the writer proposes a scholarly competition between himself and another scribe regarding everyday calculation tasks such as accounting of land， labor， and grain. Texts such as the Rhind Mathematical Papyrus and the Moscow Mathematical Papyrus show that the ancient Egyptians could perform the four basic mathematical operations—addition， subtraction， multiplication， and division—use fractions， compute the volumes of boxes and pyramids， and calculate the surface areas of rectangles， triangles， and circles. They understood basic concepts of algebra and geometry， and could solve simple sets of simultaneous equations.

Mathematical notation was decimal， and based on hieroglyphic signs for each power of ten up to one million. Each of these could be written as many times as necessary to add up to the desired number； so to write the number eighty or eight hundred， the symbol for ten or one hundred was written eight times respectively. Because their methods of calculation could not handle most fractions with a numerator greater than one， they had to write fractions as the sum of several fractions. For example， they resolved the fraction two- fifths into the sum of one-third + one-fifteenth.

Ancient Egyptian mathematicians had a grasp of the principles underlying the Pythagorean theorem， knowing， for example， that a triangle had a right angle opposite the hypotenuse when its sides were in a 3–4–5 ratio. They were able to estimate the area of a circle： Area ≈ [（8/9）D]2 = （256/81）r2 ≈ 3.16r2.

The golden ratio seems to be reflected in many Egyptian constructions， including the pyramids， but its use may have been an unintended consequence of the ancient Egyptian practice of combining the use of knotted ropes with an intuitive sense of proportion and harmony.

埃及数学：勾股定理与黄金比例

数学计算最早的例子要追溯到前王朝涅伽达统治时期，它充分显示了一个先进的数字系统。在一封新王国的虚构信件中，阐述了数学对于一名有教养的埃及人的重要性，作者提出要举办一次他自己和另外一名文士之间的有关日常计算的学术竞争，如计算土地、劳动和谷物。某些作品，如《莱因德数学纸草书》和《莫斯科数学纸草书》表明，古代埃及人已经掌握四个基本的数学运算——加法，减法，乘法，除法，他们可以使用分数，计算盒子的容积和金字塔的体积，以及矩形、三角形和圆形的面积。他们还知道代数和几何的基本概念，可以解出简单的联立方程组。

数学符号是十进制，这是基于从10到100万的象形文字符号。为了达到人们期望的数字，这些数字都可能被写入其中计算多次；如果想写数字80或800，10或100的符号要写8次。因为他们的计算方法还无法处理大多数分子大于1的分数，他们只能写下几个分数的总和。例如，他们要写2/5，就得写1/3+1/15的总和。

古埃及的数学家非常精通勾股定理的基本原理，例如，一个直角三角形的直角边和斜边的长度比例为3：4：5时，他们就能够估算出圆的面积：面积≈ [（8/9）D]2=（256/81）r2≈3.16r2.

黄金比率似乎也反映在许多埃及建筑当中，包括金字塔，然而这很可能只是古埃及人在使用打结的绳索的时候结合自己的直觉上的和谐比例而产生的意外结果。