Sifrei Devarim 268

כי יקח איש אשה. מלמד שהאשה נקנית בכסף. שהיה בדין - ומה אמה העבריה שאין נקנית בבעילה, נקנית בכסף; אשה שנקנית בבעילה, אינו דין שתהא נקנית בכסף! יבמה תוכיח, שנקנית בבעילה ואינה נקנית בכסף; אף אתה אל תתמה על האשה, שאע"פ שנקנית בבעילה, לא תהא נקנית בכסף! ת"ל כי יקח איש אשה, מלמד שהאשה נקנית בכסף.

(Devarim 24:1) "If a man take a woman": We are hereby taught that a woman is acquired (as a wife) by money. For (without this verse) it would follow otherwise, viz.: If a Hebrew handmaid, who is not acquired by cohabitation is acquired by money, then a woman, who is acquired by cohabitation, how much more so should she be acquired by money! — (No,) this is refuted by the instance of a yevamah (leviratess), who is acquired by cohabitation, but is not acquired by money. Do not wonder, then, if a woman, who, though she is acquired by cohabitation were not to be acquired by money. It must, therefore, be written "If a man take a woman," to teach that a woman is acquired by money.

ובעלה. [מלמד שהאשה נקנית בבעילה.] שהיה בדין - ומה יבמה שאין נקנית בכסף, נקנית בבעילה; אשה שנקנית בכסף, אינו דין שנקנית בבעילה! אמה העבריה תוכיח, שנקנית בכסף ואין נקנית בבעילה; אף אתה אל תתמה על האשה, שאע"פ שנקנית בכסף, שלא תהא נקנית בבעילה! ת"ל ובעלה, מלמד שהאשה נקנית בבעילה.

"and he cohabit with her." We are hereby taught that a woman is acquired by cohabitation. For (without this verse) it would follow otherwise, viz.: If a yevamah, who is not acquired by money, is acquired by cohabitation, then a woman, who is acquired by money, how much more so should she be acquired by cohabitation! — (No,) this is refuted by the instance of a Hebrew handmaid, who is acquired by money, but is not acquired by cohabitation. Do not wonder, then, if a woman, who, though she is acquired by money, were not to be acquired by cohabitation. It must, therefore, be written "and he cohabit with her," to teach that a woman is acquired by cohabitation.

ומנין אף בשטר? ודין הוא - ומה כסף שאינו מוציא, הרי הוא קונה; שטר שהוא מוציא, אינו דין שיהא קונה! לא, אם אמרת בכסף, שקונה הקדש ומעשר שני; תוכיח בשטר, שאין קונה הקדש ומעשר שני! ת"ל וכתב לה ספר כריתות ונתן בידה ויצאה מביתו [וגו']. מקיש הויתה של זה ליציאתה של זה - מה יציאתה (מזה) בשטר, אף הויתה (מזה) בשטר.

And whence is it derived that she is also acquired by a writ (shtar)? It follows, viz.: If money, which does not release (a woman from marriage), acquires, then shtar (a writ [of divorce]), which does release a woman, how much more so should it acquire! (No,) this may be true of money, which acquires hekdesh (consecrated property) and second tithe, but not with shtar, which does not acquire hekdesh and second tithe. It must, therefore, be written (Ibid.) "then he shall write for her a scroll of divorce, and he shall place it into her hand, and he shall send her from his house. This one's coming in (to marriage) is compared to her going out (viz. Ibid. 2). Just as her going out is with a shtar (i.e., a get), so, her coming in.