Archimedes - Arukime (English spelling)

Archimedes was an ancient Greek scientist, mathematician, and engineer. He was born in Syracuse, Sicily. He studied in Alexandria for a time, but later returned to Syracuse and continued his research with the support of his acquaintance, King Hieron II of Syracuse, and his son Gelon. At the time, the Punic Wars between Rome and Carthage were in full swing over the dominance of the Mediterranean, and Syracuse was on Carthage's side. Archimedes also contributed to his country by developing various weapons for Syracuse during the Second Punic War (218-201 BC).

Today, there remain more than ten of his mathematical and physical works, some of which are related to interesting anecdotes. One time, he boasted, "If you give me a foothold somewhere (other than the Earth), I will move the Earth." As proof of this, he used a double pulley to pull a three-masted warship that was on the coast to the shore by himself. This was because he was familiar with the "principle of the lever," and an explanation of this is written in "Equilibrium of a Plane."

When King Hieron gave a craftsman a lump of pure gold to make a crown for his king, he was accused of removing some of the gold and mixing it with silver. Archimedes was asked to solve this problem. One day, while soaking in a bathtub full of water, he discovered that the water overflowed in an amount equal to his body weight, and he became lighter. He was so happy that he ran naked through the city shouting "Herike, Herike (I've found it, I've found it)." This was discovered by placing a crown made of pure gold, pure silver, and a mixture of gold and silver, all of the same weight as the crown, in the same container of water, and measuring the amount of water overflowing. This is known as "Archimedes' principle," and fits the explanation in Book I of his book "Les Flotas."

To express large numbers, he calculated how many grains of sand there would be if the universe were filled with them, and concluded that the modern method of expressing this number is less than 10 ^{^63} , and he described this method of expressing large numbers in Counting the Grains of Sand. He also discovered the Archimedes spiral, and calculated pi, the ratio between a circle's circumference and its diameter, as follows: "The circumference of a circle is less than 220/70 of its diameter, but more than 223/71 of its diameter."

During the Second Punic War, Archimedes caused trouble for the Roman army by building large, powerful catapults and using machines like cranes to slam enemy ships into the sea. However, Syracuse fell before the Roman army could attack its food supplies. On that day, Archimedes was studying geometric figures at home when a Roman soldier came and tried to capture him. When he said, "Stay away from my figures," the soldier stabbed him to death. On the tombstone that he had entrusted to be erected after his death, there was carved the figure he had discovered: "The volume of a sphere is two-thirds the volume of the cylinder that circumscribes it."

He was a rare scientist in ancient times who believed that the combination of theory and practice was what would advance science, and in his book "Method" he candidly revealed his research methods.

[Hirata Hiroshi]

"History of Greek Mathematics II" by T. L. Heath, translated by Hiroshi Hirata et al. (1960/Reprint edition 1998, Kyoritsu Shuppan)" ▽ "The Origin of Science" by Hiroshi Hirata (1974, Iwanami Shoten)

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

古代ギリシアの科学者、数学者、技術者。シチリア島シラクサ出身。一時アレクサンドリアに遊学したが、のちシラクサに帰り、縁故のあるシラクサ王ヒエロン2世Hieron Ⅱやその子ゲロンGelōnの援助で研究に励んだ。当時は地中海の覇権をめぐってローマとカルタゴの間のポエニ戦争のさなかにあり、シラクサはカルタゴに味方していた。アルキメデスも第二次ポエニ戦争（前218～前201）ではシラクサのためにさまざまな武器を開発して祖国に尽くした。

　彼の著作は、今日、数学的、物理的なものが10編余り残っているが、そのいくつかは興味あるエピソードと関連している。あるとき、「私にどこか（地球以外の）足場を与えてくれるなら、地球を動かしてみせる」と豪語した。そしてその証拠として、海岸にあった3本マストの軍艦を、複滑車を使ってひとりで岸に引き揚げた。これは「てこの原理」に精通していたからで、その解説は『平面板の平衡』に書かれている。

　ヒエロン王が職人に純金の塊を与えて王冠をつくらせたところ、その王冠には金をいくらか抜き取って銀が混ぜてあるという告発があった。この問題の解決を頼まれたアルキメデスは、ある日、湯がいっぱい入った浴槽につかったとき、浴槽につかった自分の身体と同体積の湯があふれ出し、体重も軽くなることを発見して、喜びのあまり「ヘライカ、ヘライカ（みつけた、みつけた）」と叫びながら裸で街を走ったという。これは、王冠と同じ重さの純金、純銀、それに金と銀を混ぜたという王冠を、水を張った同じ容器にそれぞれ入れて、あふれ出る水の量で王冠の不正を見破ったわけで、「アルキメデスの原理」として知られ、彼の著作『浮体』第1巻の説明に当てはまる。

　また、大数を表すために、宇宙に砂粒をいっぱい詰めると、その砂粒の数はどれくらいになるかを計算し、現代式ではその数は10⁶³より少ないとし、この大数の表記法を『砂粒を数えるもの』のなかで述べている。このほか、「アルキメデスの螺旋(らせん)」を発見したり、円周率すなわち円周と直径との比率について「円周はその直径の70分の220より小さく、71分の223よりは大きい」と算出した。

　第二次ポエニ戦争中は、大形の強力な投石器をつくったり、起重機のような機械で敵船を海面にたたきつけたりしてローマ軍を悩ませたという。しかしローマ軍の兵糧(ひょうろう)攻めの前にシラクサも陥落した。その日、アルキメデスが家で図形を描いて研究しているところへローマの一兵卒がきて彼を捕まえようとした。「私の図形に近寄らないでくれ」といったとき、兵卒は彼を刺し殺した。死後の建立を託していた墓碑には、彼が発見した「球の体積はそれに外接する円柱の3分の2である」の図形が彫ってあった。

　理論と実際の結合こそ科学を向上させると考えた古代では珍しい科学者であり、その著『方法』では、その研究の方法まで赤裸に示している。

［平田　寛］

『T・L・ヒース著、平田寛他訳『ギリシア数学史Ⅱ』（1960／復刻版1998・共立出版）』▽『平田寛著『科学の起原』（1974・岩波書店）』

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