Twenty-second Amendment to the United States Constitution
As worded, the primary focus of the 22nd Amendment is on limiting individuals twice elected to the presidency from being elected again. Due to this, several issues could be raised regarding the amendment's meaning and application, especially in relation to the 12th Amendment, ratified in 1804, which states, "But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States". While it is clear that under the 12th Amendment the original constitutional qualifications of age, citizenship, and residency apply to both the president and vice president, it is unclear whether someone who is ineligible to be elected president could be elected vice president. Because of this apparent ambiguity, there may be a loophole in the 22nd Amendment whereby a two-term former-president could be elected vice president and then succeed to the presidency as a result of the incumbent's death, resignation, or removal from office (or even succeed to the presidency from some other stated office in the presidential line of succession).
I do not choose to run
Some feel that Coolidge was honoring the two-term tradition set by President Washington. While Coolidge held the opinion that a vice president who succeeded to part of another president's term would not violate the rule by then running twice for election in his own right, this tradition was continued through him and in 1952 and 1968, by Presidents Harry S. Truman and Lyndon B. Johnson when the latter chose not to seek another term after disappointing showings in the New Hampshire primary. Both had succeeded to the presidency after the death of their predecessors and had been elected only once. Theodore Roosevelt also did not run in 1908 after his succession to the presidency in 1901 and his election in 1904. However, he ran unsuccessfully in 1912, against his successor, William Howard Taft.