Berachos, chapter five, mishnah 2. This mishnah addresses the question of exactly where the various additions recited in Shemoneh Esrei are inserted, according to the seasons of the year and the various times.
Mentioning the might of the rains:
The mishnah uses the expression "gevuros geshamim" - the Holy One, blessed is He, expresses His might toward us by bringing down the rain, and by saying "mashiv haruach umorid hageshem" - a person mentions Hashem's might as it is revealed in the rain. This mention belongs in the second berachah of Shemoneh Esrei, the berachah of the resurrection of the dead, and that is where it fits in terms of its content.
The request for rain:
In contrast to the mention, the request for rain - "veten geshem livrachah" - is recited in a different berachah. Rain is inherently bound up with livelihood and food, and therefore the request was placed in the berachah in which we ask for our livelihood, the berachah of the years.
Havdalah in the tefillah:
Havdalah is added in the tefillah in order to express the distinction between the weekdays and Shabbos, and it is said at the departure of Shabbos. Its place is in the berachah of understanding - the request for knowledge and comprehension from Hashem - which is the first of the middle berachos of Shemoneh Esrei.
The Gemara explains the reason: the berachah of Havdalah is connected to the idea of entering the weekdays. The first three berachos of Shemoneh Esrei are recited in the very same wording on Shabbos as well, while the middle berachos are recited on weekdays; therefore Havdalah was placed at the very opening of the middle berachos.
The dispute among the Tannaim regarding the place of Havdalah:
Rabbi Akiva: He too holds that its place is at the beginning of the middle berachos, except that in his opinion it is not said within the berachah, but rather as a separate berachah of Havdalah standing on its own - "Baruch atah Hashem hamavdil bein kodesh lechol" - and only afterward does one begin the first of the middle berachos. The halachah does not follow his opinion.
Rabbi Eliezer: The place of Havdalah is in the berachah of thanksgiving - "Modim." The same place in which additions are inserted in that berachah is the place in which Havdalah is said on Motzaei Shabbos.
In summary: In this mishnah we learned the placement of the additions in Shemoneh Esrei - mentioning the might of the rains in the berachah of the resurrection of the dead, the request for rain in the berachah of the years in which we ask for our livelihood, and Havdalah in the berachah of understanding at the opening of the middle berachos. We also examined the opinion of Rabbi Akiva, that Havdalah is said as a separate berachah on its own, and the opinion of Rabbi Eliezer, that its place is in the berachah of thanksgiving.