英译汉-206词-关于数学方面的
我会选一个翻译得比较好的,下面是维基百科对几何级数的一段解释.
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BooksVIIIandIXofEuclid'sElementsanalyzegeometricprogressionsandgiveseveraloftheirproperties.
Ageometricprogressiongainsitsgeometriccharacterfromthefactthattheareasoftwogeometricallysimilarplanefiguresarein"duplicate"ratiototheircorrespondingsides;furtherthevolumesoftwosimilarsolidfiguresarein"triplicate"ratiooftheircorrespondingsides.
Themeaningofthewords"duplicate"and"triplicate"inthepreviousparagraphisillustratedbythefollowingexamples.Giventwosquareswhosesideshavetheratio2to3,thentheirareaswillhavetheratio4to9;wecanwritethisas4to6to9andnoticethattheratios4to6and6to9bothequal2to3;sobyusingthesideratio2to3"induplicate"weobtaintheratio4to9oftheareas,andthesequence4,6,9isageometricsequencewithcommonratio3/2.Similarly,givetwocubeswhosesideratiois2to5,theirvolumeratiois8to125,whichcanbeobtainedas8to20to50to125,theoriginalratio2to5"intriplicate",yieldingageometricsequencewithcommonratio5/2.
也可以查看维基百科Geometric_progression中
RelationshiptogeometryandEuclid'swork一段。