ץחי
What is the secret of splitting the matzah, half to be used for the motzi and half for the Afikoman? In the sefer Nachlas Yaakov (154) he brings in the name of Menachem Mendel from Rimanov that splitting of the matzah is symbolic of the procedure and ritual of making a bris such as the Bris Bein Habasarim between Hashem and Avraham Avinu. It was there that Avraham cut the animal and made a pathway between the pieces of meat and walked though them. See Rashi on the passuk ךרבעל בברית ה' אלקיך (Devarim 29) The Baal Hatecheilis from Ishbitz writes that the symbolism of the bris is that each partner in the Bris has to commit to work on cutting up his נפש הבהמית in order that the bris will work. Without such a commitment of avodah it will be doomed to failure.
The source for such a comparison are two pessukim ושמרתם את המצות that one needs shmurah matzah and the passuk ושמרתם את בריתי . So too when one splits the matzah in half one half is hidden behind one's pillow upon which he reclines and the other is left on the ויהי table and the person is between them both similar to the Bris Bein Habesarim.
This pshat goes well with the Mechilta that says that the Bris Bein Habasrim was on the 15th of Nissan (Rashi Shmos 12,41 בעצם היום הזה).
With the above explanation we can say that the Baal Haggadah fixed 15 Simanim for the Seder. The reason being that many events of Pesach happened on the 15th as this Rashi points out. On Pesach the malachim came to visit Avraham and they told him and Sarah about their giving birth to Yitzchak. Yitzchak played a special role in being the catalyst for Yisrael to be redeemed earlier that the decreed 400 years. As the Panaiach Razah writes that the word וארא which begins the parsha of redemption is gematriah יצחק . For Yitzchak was willing to lessen the gematriah of his name ישחק to יצחק missing 210. That is why Yisrael were only there in bondage for 210 years. So the news of Yitzchak's birth of Pesach was also relevant to the 15th of Pesach because his new born child was going to make the geulah from Mitzrayim possible on that future Pesach.
The second even of the 15h of Pesach was the Bris Bein Habasraim which included the galus and the geulah in and from Mitzrayim. Because of these three events on the 15th of Nissan and all the other historical events that happened and which are elaborated in the Siman of Nirtza יצחב יהיו הלילה the Baal Haggadah made 15 Simanim to commemorate this special day of Nissan the 15th ליל שימורים .
