When the verb "exemplify" is used in the active participle form, "exemplifying", the example, the single case, is the noun modified, and the general category is the object of the participle. When it is used in the passive participial form, "exemplified", the general case is the noun modified, and the example is the object of the preposition "by." In this sentence, "the philosopher-king" is the the general case, not the specific example, so we need the passive form, "is exemplified ..." with the specific example, Solon, in the "by" prepositional phrase.