Rif Succah 18b {Succah 37b continues; 38a}

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18b

{Succah 37b continues}
Mishna:
And when does he shake {the lulav in Hallel}?
In Hodu la-Hashem ki tov at the beginning and end, and in Ana Hashem Hoshi'a Na. These are the words of Bet Hillel.
Bet Shammai say: Also by Ana Hashem Hatzlicha Na.

Rabbi Akiva said: I looked at Rabban Gamliel and Rabbi Yehoshua and saw that the entire nation was shaking their lulavim and they only shook by Ana Hashem Hoshi'a Na.

Gemara:
How should he shake? Just as we say over there regarding the shtei halechem {two loaves} and the two sheep of Atzeret {Shavuot}: What does he do? He places the two loaves atop the two sheep and places his hand underneath them, and he waves fro and to {away from himself and near}, raises up and lowers down.

Rabbi Chiyya bar Abba cited Rabbi Yochanan: Fro and to - to He Who the four directions are His. Raises up and lowers down - to He Who the heavens and earth are His.

In the West {=Eretz Yisrael} they taught it as follows: Rabbi Chama beRabbi Akiva {our gemara: Ukva} cited Rabbi Yossi beRabbi Chanina: He brings fro and to in order to prevent the evil winds {ruchot = winds, sometimes spirits, but likely winds here. also note it means direction}. He raises up and lowers down -- to prevent bad dews.

{Succah 38a}
Rava said: And also the lulav. {just like the two loaves and the two sheep}

And so is the custom.

And there is one who says that one is required to shake three times {side-to-side} as he brings it away and towards himself, besides {=during} the movement of fro and to, up and down. And he learns it from the gemara of the residents of the West {from the Yerushalmi}, for we learn there: Rav Chiyya bar Ashi in the name of Rav: One who gets up early to go on the road, they bring him a shofar and he blows; a lulav and he shakes; a megillah and he reads it, etc. They learnt {tna}: He needs to shake it three times on each and every davar {thing}.
Rabbi Zera inquired: Is this {away} one and this {towards} one {such that away needs three and towards needs three}? Or perhaps this and this are {a single} one.

That is to say: Is the bringing away from himself {=fro} one and the bringing towards himself {to} one, or do the bringing away from himself and the bringing near to himself together form one?
Thus, "shaking" is a separate thing from fro and to, up and down.

Mishna:
One who is travelling on the road and does not have a lulav in hand - when he reaches his home, he should take on his table {before he eats}.