Herodotus Halicarnassus, quæ quum cæteris de rebus, tum de caussa bellorum Græcos inter Barbarosque gestorum, perquirendo cognovit, ea his libris consignata in publicum edit;
MAIN CLAUSE
Herodotus Halicarnassus:哈利卡那苏斯的希罗多德。
ea: 宾语,id的宾格复数。
his libris: hic liber夺格复数,表方式, in the books.
consignata: consignare的完成时被动态分词。被记录下的。
in publicum: publicly
edit: edere的单三,发布(作品)。这个我本以为是编辑、编写,不过看词典有bring up和publish the writings的意思。
核心意思即Herodotus of Halicarnassus publishes these things (ea) having been recorded (consignata) in these books (his libris) publicly (in publicum).