Sanhedrin

Now, which view do they adopt?  If they hold that the Tekufah day  is the completion [of the previous season]: then, even if it were not so,  it will meet with the requirement neither of him who holds that the whole Festival [must be included,] nor of him who holds that only part of it [is necessary]! — 11 One must say therefore that they both hold that the Tekufah day begins [the new Tekufah]. An objection is raised: The Tekufah day concludes [the previous season]: this is R. Judah's view. R. Jose maintains that it commences [the new].  Further has it been taught: A year is not intercalated unless the [summer] Tekufah is short of completion by the greater part of the month [Tishri]. And how much is that? Sixteen days. R. Judah said: Two thirds  of the month. And how much is that? Twenty days.  R. Jose ruled: It is to be calculated thus: [If there are] sixteen [days short of completing the Tekufah] which precedes Passover,  the year is to be intercalated.  [If, however, there are] sixteen [short of completing the Tekufah] which precedes the Feast [of Tabernacles],  the year is not to be intercalated.  R. Simeon maintained: Even where there are sixteen [days short of completing the Tekufah] which precedes the Feast [of Tabernacles], the year is intercalated.  Others say [that the year is intercalated even if the Tekufah is short of completion] by the lesser part of the month. And how much is that? Fourteen days?  — The difficulty remained unsolved. The Master has said: 'R. Judah said: Two thirds of the month. And how much is that? Twenty days. R. Jose ruled: It is to be calculated [thus: if there are] sixteen [days short of completing the Tekufah] which precedes Passover, the year is to be intercalated.'  But is not this view identical with R. Judah's?  — They differ as to whether the Tekufah day completes [the previous] or begins [the new cycle]. The Master has said: '[R. Jose holds that] if there are sixteen [days short of completing the Tekufah] which precedes the Feast [of Tabernacles], the year is not intercalated.' According to R. Jose, then, only if there are sixteen [days short of completing the Tekufah] preceding the Feast [of Tabernacles is intercalation] not [permitted]; but if there are seventeen or eighteen [days short], the year is intercalated. But has he not himself said: If there are sixteen [days short of completing the Tekufah] which precedes Passover, we may intercalate, but not if less?  — But no; in neither case  may we intercalate. But seeing that he spoke of the number sixteen [with regard to the Tekufah] preceding Passover,  he gives it also [in connection with the Tekufah] preceding the Feast [of Tabernacles]. [It was stated above]: 'R. Simeon maintained:  Even where there are sixteen [days short of completing the Tekufah] which precedes the Feast [of Tabernacles], the year is intercalated.' But is not this view the same as that of the first Tanna?