He holds: A fetus is considered as its mother’s thigh, i.e., a part of its mother’s body, and it is as though the master transferred ownership of one of her limbs to her. Since the maidservant is pregnant, the child is considered to be a part of her, and it is as though he emancipated a portion of her body. Gittin 23b
Yebamot 69b
If she is found pregnant, until the fortieth day it is only a mere fluid
.Mishnah Niddah 3:7
(7) If she miscarries on the fortieth day [since her prior immersion], she need not be concerned that it was a fetus.
(ו) הָאִשָּׁה שֶׁהִיא מַקְשָׁה לֵילֵד, מְחַתְּכִין אֶת הַוָּלָד בְּמֵעֶיהָ וּמוֹצִיאִין אוֹתוֹ אֵבָרִים אֵבָרִים, מִפְּנֵי שֶׁחַיֶּיהָ קוֹדְמִין לְחַיָּיו. יָצָא רֻבּוֹ, אֵין נוֹגְעִין בּוֹ, שֶׁאֵין דּוֹחִין נֶפֶשׁ מִפְּנֵי נָפֶשׁ:
(6) If a woman is having trouble giving birth, they cut up the child in her womb and brings it forth limb by limb, because her life comes before the life of [the child]. But if the greater part has come out, one may not touch it, for one may not push aside one person's life in favor of another life.
§ Rav Huna says: If a minor was pursuing another person in order to kill him, the pursued party may be saved with the pursuer’s life. That is to say, one is permitted to save the pursued party by killing the minor who is pursuing him, and one does not say that since the minor lacks halakhic competence, he is not subject to punishment. The Gemara explains: Rav Huna maintains that a pursuer, in general, does not require forewarning, and there is no difference with regard to this matter between an adult and a minor…Sanhedrin 72b:13-16
איתיביה רב חסדא לרב הונא יצא ראשו אין נוגעין בו לפי שאין דוחין נפש מפני נפש...
Rav Ḥisda raised an objection to Rav Huna: [once] its head has emerged [during the birthing process], it may not be harmed [in order to save the mother], because a life may not be pushed aside in favor of another life...
יצא ראשו - באשה המקשה לילד ומסוכנת וקתני רישא החיה פושטת ידה וחותכתו ומוציאתו לאברים דכל זמן שלא יצא לאויר העולם לאו נפש הוא וניתן להורגו ולהציל את אמו אבל יצא ראשו אין נוגעים בו להורגו דהוה ליה כילוד ואין דוחין נפש מפני נפש.
Its head has emerged: With a women that is experiencing difficulty giving birth and is in [mortal] danger. And it is taught in the first section [of this teaching], "the midwife extends her hand and cuts it up and extracts [the pieces];" as the entire time that that it has not gone out into the air of the world, it is not [considered] a soul/life, and [so] it is possible to kill it and to save its mother. But when its head came out, we cannot touch it to kill it, as it is like a born [baby]; and we do not push aside one life in favor of another life.
אַף זוֹ מִצְוַת לֹא תַּעֲשֶׂה שֶׁלֹּא לָחוּס עַל נֶפֶשׁ הָרוֹדֵף. לְפִיכָךְ הוֹרוּ חֲכָמִים שֶׁהָעֻבָּרָה שֶׁהִיא מַקְשָׁה לֵילֵד מֻתָּר לַחְתֹּךְ הָעֵבָּר בְּמֵעֶיהָ בֵּין בְּסַם בֵּין בְּיָד מִפְּנֵי שֶׁהוּא כְּרוֹדֵף אַחֲרֶיהָ לְהָרְגָהּ. וְאִם מִשֶּׁהוֹצִיא רֹאשׁוֹ אֵין נוֹגְעִין בּוֹ שֶׁאֵין דּוֹחִין נֶפֶשׁ מִפְּנֵי נֶפֶשׁ וְזֶהוּ טִבְעוֹ שֶׁל עוֹלָם:
One is prohibited to spare the life of a pursuer. Therefore the Sages decreed that when a pregnant woman has difficulty delivering, one is permitted to abort the pregnancy in her abdomen, whether by drugs or by hand [with a tool], because the child is understood as a pursuer intent on killing the mother. But if the head has already emerged, we don't harm it further, because we do not push aside one life in favor of another life, and this is the way of the world [that birth can be risky].
Arakhin 7a:15-16
The mishna teaches: With regard to a woman taken to be executed who sat on the travailing chair in the throes of labor, the court waits to execute her until she gives birth. The Gemara asks: What is the reason for delaying the execution in this case? The Gemara answers: Once the fetus uproots from its place and begins to leave the woman’s body, it is considered an independent body and may not be killed together with the mother.
Jewish tradition is sensitive to the sanctity of life, and does not permit abortion on demand. However, it sanctions abortion under some circumstances because it does not regard the fetus as an autonomous person. This is based partly on the Bible (Exodus 21:22-23), which prescribes monetary damages where a person injures a pregnant woman, causing a miscarriage. The Mishnah (Ohalot 7:6) explicitly indicates that one is to abort a fetus if the continuation of pregnancy might imperil the life of the mother. Later authorities have differed as to how far we might go in defining the peril to the mother in order to justify an abortion. The Rabbinical Assembly Committee on Jewish Law and Standards takes the view that an abortion is justifiable if a continuation of pregnancy might cause the mother severe physical or psychological harm, or when the fetus is judged by competent medical opinion as severely defective. The fetus is a life in the process of development, and the decision to abort it should never be taken lightly. Before reaching her final decision, the mother should consult with the father, other members of her family, her physician, her spiritual leader and any other person who can help her in assessing the many grave legal and moral issues involved.
Peninei Halakhah, Simchat Habayit U'Virkhato 9:12:4
In such a case, some poskim rule that even those who adopt the restrictive approach would permit abortion, since mental illness can be life-threatening and cause one to become suicidal .
Peninei Halakhah, Simchat Habayit U'Virkhato 9:4:6
Once a fetus is viable, that is, that it could survive on its own if it were born, it is almost impossible to permit abortion, even according to those who take the permissive approach....However, if it is clear that the fetus would not live for more than thirty days even if it were born naturally, then in certain cases some of those who rule permissively would permit abortion.
Mishneh Torah, Murderer and the Preservation of Life 2:6
(6) Whether a man killed an adult or an infant of one day, male or female, he must be executed if he committed deliberate murder, or exiled if he killed unwittingly. And for a child that was born premature- If it was born in less than nine months, it is not viable until it lives thirty days. If it is killed within the thirty days, it is not considered murder.
Rabbi Jacob Emden Responsa She’elat Ya”vetz 1:43 (1739-1759)
The questioner asks about an adulterous married woman (who is pregnant) is a good question. It appears to me to permit her (to abort)...And even in the case of a legitimate fetus there is reason to be lenient if there is a great need, as long as the fetus has not begun to emerge; even if the mother’s life is not in jeopardy, but only so as to save her from an evil associated with it that would cause her great pain…
Rabbi Eliezer Waldenberg, Tzitz Eliezer 9:51.3 (1967)
If there is a danger to the mother from continuing the pregnancy, one should permit abortion without hesitation. Also, if her health is poor and to cure her or to relieve her from great pain it is necessary to abort the fetus, even if she is not in actual danger, there is room to permit it, based on the halachic authority’s evaluation of the situation.
“Killing a fetus is prohibited until the doctors have great reason, close to certainty, that the mother will die. Since the permission is due to the fetus’s status as a pursuer, it must be near-certain that he is a pursuer.” Rabbi Moshe Feinstein
Havot Yair 31:9
For it is no better than a case of masturbation, which is considered to be a “slaughtering of children.” And masturbation is considered a grave offense, and the reason is because every drop of semen has the potential to create holy progeny. And one cannot say that the prohibition of masturbation is because of auto-eroticism… Thus even women are prohibited from …]wasting seed [and destroying potential life.
When Does Life Begin?
And Antoninos said to Rabbi Yehuda HaNasi: From when is the soul placed in a person? Is it from the moment of conception or from the moment of the formation of the embryo, forty days after conception? Rabbi Yehuda HaNasi said to him: It is from the moment of the formation of the embryo. Antoninos said to him: That is inconceivable. Is it possible that a piece of meat could stand for even three days without salt as a preservative and would not rot? The embryo could not exist for forty days without a soul. Rather, the soul is placed in man from the moment of conception. Rabbi Yehuda HaNasi said: Antoninos taught me this matter, and there is a verse that supports him, as it is stated: “And Your Providence [pekudatekha] has preserved my spirit” (Job 10:12) indicating that it is from the moment of conception [pekida] that the soul is preserved within a person.
(7) If she miscarries on the fortieth day [since her prior immersion], she need not be concerned that it was a fetus. If [she miscarries] on the forty-first day, she should sit [for the required number of days] for a male and for a female, and for [being] a niddah. Rabbi Yishmael says: on the forty-first day she should sit for [the required number of days for one who gives birth to] a male and for [being] a niddah. On the eighty-first day she should sit for a male and for a female and for [being] a niddah, because [the formation of] a male is completed in forty-one [days], and a female in eighty-one. And the Sages say: this and that [are both completed] in forty-one.