Gemara

(Beraisa): Two witnesses do not join unless they saw the testimony together;

R. Yehoshua ben Korchah says, they join even if they saw the testimony at different times.

Sanhedrin 30b: They argue about reasoning, or a verse.

Opinion #1: They argue about reasoning. The first Tana says, if they did not see the testimony together, perhaps they testify about different loans;

R. Yehoshua ben Korchah says, in any case, both agree that he owes the money!

Answer #2: They argue about a verse, "V'Hu Ed O Ra'ah O Yada";

(Beraisa): "Lo Yakum Ed" is singular. The Torah says "Echad" to teach that "Ed" always connotes two, unless specified otherwise.

The Torah refers to two witnesses seeing testimony in the singular to teach that they must see like one (at the same time);

R. Yehoshua ben Korchah says, "V'Hu Ed O Ra'ah O Yada" - any way he knows testimony is acceptable.

R. Yochanan: Does anyone know whether or not the Halachah follows R. Yehoshua ben Korchah?

R. Yosi b'Rebbi Chanina: I heard that R. Yehoshua ben Korchah holds like R. Noson (who permits the witnesses to testify on different days).

R. Yochanan: This is obvious! The essence of testimony is seeing it. R. Yehoshua does not require them to see it together. All the more so, they need not say it together!

(R. Chiya bar Avin): The Halachah follows R. Yehoshua ben Korchah, both regarding (testimony about) land and Metaltelim.

(Ula): The Halachah follows R. Yehoshua ben Korchah regarding land, but not regarding Metaltelim.

Question (Abaye): This implies that there is an argument about land. R. Aba taught that Chachamim agree with R. Yehoshua ben Korchah regarding land!

(Rav Idi bar Avin - Beraisa): Chachamim agree with R. Yehoshua ben Korchah regarding testimony about a Bechor, land, Chazakah, and similarly in a boy or girl (one witness saw two hairs on the front, and one the back).

Answer: They are Amora'im. R. Chiya bar Aba and Ula argue with them (and say that Chachamim argue about land)!

(Rav Yosef citing Ula): The Halachah follows R. Yehoshua ben Korchah, both regarding land and Metaltelim;

(R. Zeira citing Rav): The Halachah follows R. Yehoshua ben Korchah regarding land, but not regarding Metaltelim.

(Chachamim of Neharda'a): We join (testimony of) two admissions, two loans, or one of each (in either order).

This is like R. Yehoshua ben Korchah.

Gitin 33b - Question: If a man said 'All of you (write and give a Get to my wife)', does R. Shimon ben Gamliel hold that he can cancel this in front of one of them?

Answer (Beraisa - Rebbi): If he told two people 'Give a Get to my wife,' he can cancel either individually;

R. Shimon ben Gamliel says, he can cancel them only together.

Since both must sign the Get, it is like if he said 'All (i.e. both) of you', and R. Shimon ben Gamliel argues even in this case!

Rejection (Rav Ashi): The Beraisa does not discuss writing the Get, rather, giving the Get, which even one person can do.

Support (Seifa): If he appointed each individually, he can cancel either individually.

We understand this if it discusses Sheluchim to give a Get. But if it discusses witnesses to (write and) sign a Get, their testimonies do not combine!

(Beraisa): Testimony of witnesses is joined only if they saw it together.

Rejection: Perhaps R. Shimon ben Gamliel rules like R. Yehoshua ben Korchah.

Rishonim

Rif and Rosh (Sanhedrin 9a and 3:34): The Halachah follows R. Yehoshua ben Korchah. The testimonies join whether both saw loans or admissions or one saw a loan and the other saw an admission.

Rambam (Hilchos Edus 4:2,3): In monetary cases, even if the witnesses saw one after the other their testimony joins. If David says 'I saw Shimon borrow from or admit (that he owes) to Reuven on Sunday', and Levi says 'I saw Shimon borrow from or admit to Reuven on Monday', their testimony joins.

Poskim

Shulchan Aruch (CM 30:6): In monetary cases, even if the witnesses saw one after the other their testimony joins. If David says 'I saw Shimon borrow from or admit (that he owes) to Reuven on Sunday', and Levi says 'I saw Shimon borrow from or admit to Reuven on Monday', their testimony joins.

Beis Yosef (DH Ein): Chachamim of Neharda'a conclude that the Halachah follows R. Yehoshua ben Korchah. The Rif, Rambam and Rosh rule like this. However, SMaG observes that in Gitin, Rav Ashi said that the Beraisa must discuss Sheluchim to give the Get because he holds like Chachamim. It seems that this is why Hagahos Maimoniyos, the Mordechai citing R. Chananel, and the Rashbam disqualify even an admission after an admission. I disagree. Rav Ashi did not say that the Beraisa must discuss Sheluchim to give the Get; the Stam Gemara said so. And even if he said so, we do not abandon a clear Pesak in the primary place where the Halachah was taught, due to an inference elsewhere.

SMA (20): Edus Meyuchedes is when witnesses saw the same event at once, but did not see each other. It is Pasul only for capital cases. The Tur and Shulchan Aruch did not need to say that it is Kosher for monetary cases.

Beis Yosef (DH uv'Sof and DH ul'Inyan): Regarding capital cases, Edus Meyuchedes is Pasul. What is the law when we accept witnesses in a capital case solely for the sake of monetary matters? If witnesses knew that a woman was secluded with her ex-husband, she needs a second Get. The Rif and Rosh (Gitin 35b and 6:4) cite a case from the Yerushalmi in which witnesses saw seclusion at different times, and another Get was not required. The Ran says that this is because Kidushin pertains to capital cases, therefore the witnesses must see together. However, the Mordechai says that the Yerushalmi applies the argument of R. Yehoshua ben Korchah and Chachamim to Edei Ki'ur (witnesses of circumstantial evidence of adultery). The Bavli applies the argument to Isur, i.e. establishing a man to be a Kohen (Kesuvos 26b) and signing a Get. Even though a Get affects capital cases, since now it is not a capital case they need not see at once. Perhaps we are not concerned for Kidushin when there was only one witness at a time because the man and woman knew that there was only one witness, so they did not intend for Kidushin. However, the Yerushalmi asks whether seclusion of a Safek Sotah in front of witnesses at different times is like Kidushin, or like other matters. It seems that it is unsure whether such testimony is Pasul for all Isurim, or only regarding Kidushin, because they do not intend for Kidushin. The Bavli holds that whenever we are not concerned for the capital aspect of a case, the witnesses need not see at once. We follow this.

Darchei Moshe (2): The Rivash (193 and 266) equated kidushin and divorce to monetary cases regarding witnesses who saw at different times.

Rema: The same applies to testimony about Isurim.