Origin and history of testudinal

late 14c., teste, "small vessel used in assaying precious metals," from Old French test, from Latin testum "earthen pot" (in Medieval Latin especially "earthen vessel in which metals are tried"); which is related to testa "shell of shellfish," testudo "tortoise." In Watkins, etc., this is derived from PIE root *teks- "to weave," also "to fabricate." But de Vaan (2008) writes, "Derivation from the root *tek- 'to build' is unlikely for semantic reasons," and "The word testa is probably a loanword, as words for vessels often are." 

The sense of "trial or examination to determine the correctness of something" is recorded from 1590s (Nashe, making a figure from the metallurgical sense); hence "any critical trial or examination." The comparison is to ascertaining the quality of a metal by melting it in a pot. By Johnson's day (1755) test could mean "means of trial" generally.

In mechanics, "action meant to establish the physical properties of materials or constructions" with an eye to durability, safety, etc. (as in crash-test), by 1877. To test-drive (v.) an automobile is by 1954.

The sense of "procedure for determining and measuring academic accomplishment, native intelligence, etc." is by 1905, "in academic and similar contexts usu. implying a simpler, less formal procedure than an exam" [OED, 1989].

With verb put (put to the test) by 1778 and this form was common from early 19c.; earlier the phrase was bring to the test (Shakespeare).

In law, test case is by 1841. In reference to nuclear weapons development, test-ban is by 1958. In English history Test Act was given to various laws meant to exclude Catholics and Nonconformists from office (especially that of 1673, repealed 1828) by requiring oaths of supremacy and allegiance, subscription to doctrines, or reception of sacraments obnoxious to their faiths.