Answer
I say, and with God's success: The minimum threshold for cattle is thirty, so there is no obligation for zakat on less than that. For thirty cattle, one must give a tabe'a or tabe'a - and the tabe'a is the male that has completed a year, and the tabe'a is its female - and for forty cattle, one must give a musin or musina - and the musin is the one that has completed two years, and the musina is its female - and for sixty, two tabe'as or two tabe'at must be given, and for seventy, one musin and one tabe'a must be given, and for eighty, two musinas must be given. Thus, the threshold for zakat changes every ten; as narrated by Mu'adh ibn Jabal (may Allah be pleased with him) who said: "The Prophet (peace be upon him) sent me to Yemen and commanded me to take from every thirty cattle a tabe'a or tabe'a, and from every forty a musina," as found in Sunan al-Tirmidhi 3: 20, which he deemed good, and in Al-Mustadrak 1: 555, and Sahih Ibn Khuzaymah 4: 19. As for what is between forty and sixty, zakat is obligatory according to Abu Hanifa based on its share, which is the only amount among the thresholds that has no exemption. For every additional one over forty, one must give one-fortieth of the value of a musina, which is called one-fourth of a tenth of a musina, and for two, half a tenth of a musina, and for three, three-fourths of a tenth of a musina, and for four, one-tenth of a musina, and so on; due to Allah's saying: {Take from their wealth a charity} (At-Tawbah: 103). Reason cannot determine the establishment of the threshold, nor is there a text regarding it, so it is obligatory. From Tawus (may Allah have mercy on him): "The Messenger of Allah (peace be upon him) sent Mu'adh ibn Jabal (may Allah be pleased with him) to Yemen and commanded him to take from every thirty cattle a tabe'a, and from every forty a musina. He was brought cattle less than that, and he refused to take anything from it, saying: I did not hear anything from the Messenger of Allah (peace be upon him) regarding it until I return to him, and the Messenger of Allah (peace be upon him) passed away before Mu'adh (may Allah be pleased with him) arrived," as found in Al-Muwatta of Muhammad 339. According to the two companions: there is nothing for the increase until it reaches sixty, which would require two tabe'as or two tabe'at. From Mu'adh ibn Jabal (may Allah be pleased with him) who said: "The Messenger of Allah (peace be upon him) did not command me regarding the intermediate cattle anything," in Musnad Ahmad 5: 230. Al-Bayhaqi and Al-Daraqutni narrated from the hadith of Baqiyah from Al-Mas'udi from Al-Hakam from Tawus from Ibn Abbas (may Allah be pleased with them): "The Messenger of Allah (peace be upon him) sent Mu'adh to Yemen and commanded him to take from every thirty cattle a tabe'a, and from every forty a musina. They asked: What about the intermediate ones? He said: The Messenger of Allah (peace be upon him) did not command me regarding them with anything, and I will ask him when I return to him. When he returned to the Messenger of Allah (peace be upon him), he asked him, and he said: There is nothing in them." This indicates that Mu'adh arrived in Medina while the Messenger of Allah (peace be upon him) was alive. It is also supported by what Abu Ya'la narrated: "When Mu'adh (may Allah be pleased with him) returned from Yemen, he prostrated to the Prophet (peace be upon him), and he said to him: O Mu'adh, what is this? He said: When I arrived in Yemen, I found the Jews and Christians prostrating to their dignitaries, and they said: This is the greeting of the prophets. He said: They lied about their prophets, and if I were to command anyone to prostrate to other than Allah, I would have commanded a woman to prostrate to her husband." This contradicts the narration of Malik and other authentic narrations, as found in the commentary of Al-Mujaddid 2: 144, and Allah knows best.