Gemara

(Mishnah): The Shi'ur for mascara is to paint one eye.

(Rav Huna): Women who dress very modestly and leave only one eye exposed paint only one eye.

94b (Mishnah - R. Eliezer): One is liable for coloring eyes;

Chachamim forbid only mid'Rabanan.

129a (Chachamim of Neharda'a): We are not Mechalel Shabbos for a Yoledes (one who gave birth) [after seven days, but] within 30 days , but we get a Nochri to do her needs;

(Rav Ula brei d'Rav Ilai): All needs of a Choleh may be done through a Nochri on Shabbos.

(Rav Hamnuna): One may tell a Nochri to do something for a Choleh who is not in mortal danger.

141b (Mishnah): One may carry a child holding a rock.

(D'Vei R. Yanai): The case is, the child is lovesick for his father. (He will get sick if his father does not pick him up.)

(Rav Chana Bagdata'ah citing Shmuel): One may reset a broken bone on Shabbos.

Avodah Zarah 28a (Mishnah): If one's teeth hurt, he may not put vinegar in his mouth (on Shabbos).

Inference (Abaye): If he is in great pain, this is permitted.

Rejection: The Tana taught 'hurt', and this includes a great pain.

28b (Rav): If an eye is about to leave the socket, one may paint it on Shabbos.

Rabanan assumed that one may not do Melachah for this, e.g. to grind ingredients for it or carry though a Reshus ha'Rabim. Rather, it must be ready from before Shabbos.

(R. Yakov citing Rav Yehudah): One may do Melachah for this.

It is permitted because nerves connect the eye to the heart.

(Rabah bar Zutra): We may raise drooping ears on Shabbos.

29a (R. Yehoshua ben Levi): On Shabbos, we may raise Unkli (tonsils that obstruct breathing; alternatively the opening to the stomach).

Beitzah 22a: Ameimar permitted to paint eyes through a Nochri on Shabbos.

Question (Rav Ashi): The Yisrael helps, i.e. he opens and closes his eye!

Answer (Ameimar): Help is insignificant.

Rishonim

Rambam (Hilchos Shabbos 2:10): If there is no danger, we do needs of a Choleh through Nochrim. We tell Nochrim to cook for him, bake, bring medicine through Reshus ha'Rabim, paint his eyes, even though there is no danger. Things that do not require a Melachah mid'Oraisa, even Yisre'elim may do, e.g. to lift his ears or return a broken bone.

Magid Mishneh, citing the Rashba in the name of the Ramban: Shabbos 129a permits doing a Choleh's needs through a Nochri. This is only if the illness affects the entire body, e.g. a Yoledes within 30 days, or painting the eye at the end of the illness when he is bedridden, or in pain and sick from it. If he has pain, but he walks around like a healthy person, he may not transgress Shevus (Isur mid'Rabanan), even through a Nochri. Both a proper Shevus done through Yisrael, or commanding a Nochri [to do a Melachah], is permitted only for an illness that includes the entire body, but not for one limb without danger. This is why a Yisrael may not paint his eyes, even though it is only Shevus, like the Rambam says below (23:12).

Rosh (Avodah Zarah 2:10): We permit Melachah to heal an eye only because there is mortal danger. We do not permit merely due to danger to a limb. However, we may do Isurim mid'Rabanan to heal it. Even if the ingredients were ground up already, every cure is forbidden mid'Rabanan lest one grind. Similarly, one may do all needs of a Choleh through a Nochri. We do not distinguish Shevus with an act from Shevus without an act (telling a Nochri). Or perhaps loss of a limb is unlike a Choleh without danger. We find that one may not return a bandage outside the Mikdash (Eruvin 102b). Or perhaps that is not a case of illness, rather, mere pain, therefore we forbid Shevus with an act. This requires investigation.

Beis Yosef (DH v'Ika): The Tur says that the Rambam permits Shevus through Yisrael for a Choleh without danger. This is difficult. If so, why does he permit painting the eyes only through a Nochri, but not through a Yisrael? This is only mid'Rabanan! The Magid Mishneh says that the Rambam distinguishes between an illness of the entire body and of one limb. The Tur connotes that this resolves the Rosh's Safek. We permit Shevus through Yisrael only for an illness of the entire body. If so, we must say that lifting uoe or return a broken bone affect the entire body, since we permit them through Yisrael. I disagree. There is no source that the Rambam distinguishes between an illness of the entire body and of one limb. Rather, if the Shevus is close to a Torah Melachah, e.g. painting the eyes, which is like writing, or any Refu'ah with a potion, in which there is concern for grinding spices, we permit only through Nochrim. If the Shevus is not close to a Torah Melachah, it is permitted even through Yisrael. Therefore, a Yisrael may lift Unkli and ears and return a broken bone. These are not like any Melachah. They do not involve ingredients. The Rambam wrote 'needs that do not include Melachah' to permit them. This resolves the Rosh's Safek to be stringent, and not to be lenient. The Rosh and Ran permit Shevus through a Yisrael when there is danger to a limb. The Rambam would forbid if it is like a Melachah, or there is room to decree due to grinding spices.

Taz (7): I do not understand the Safek of the Rosh and Tur. In Beitzah 22a, Ameimar permits painting eyes through a Nochri on Shabbos. Even though the Yisrael helps, help is insignificant. This shows that a Yisrael may not paint eyes. The Rosh and Tur rule like this! The Ran answered that Ameimar discusses illness without danger to a limb. In Avodah Zarah, we permit if the ingredients were already ground, in any case when there would be danger to a limb. However, the Rosh holds that perhaps we permit a Yisrael even without any danger to a limb. If so, why did Ameimar permit only through a Nochri? Do not say that it was a mere pain without illness. The Gemara compares it to a Choleh without danger! Do not say that Ameimar discusses grinding the spices on Yom Tov, for he permits on Yom Tov Sheni of Rosh Hashanah. Surely he would not permit grinding on Yom Tov Sheni! Rather, the Beis Yosef's answer is correct.

Ohr Same'ach: Painting the eyes is only mid'Rabanan! This is clear from Shabbos 94b. The Rambam himself (23:12) says that it is like writing. He permits only through a Nochri, but not through a Yisrael. The Magid Mishneh distinguishes between an illness that includes the entire body, and one that affects only one limb. The Rambam does not mention this. Rather, a Shevus that applies only to a Choleh without danger, such as returning a broken bone or lifting Unkli or ears, is permitted through Yisrael. People paint eyes also for cosmetic reasons, therefore we permit only through a Nochri, just like carrying in Reshus ha'Rabim and cooking. If one is only slightly sick or in pain, one may tell a Nochri to do Shevus, for this is Shevus of Shevus, but not to do a proper Melachah.

Ran (Shabbos 39b DH umi'Ha): If there is no danger to a limb, just mere illness, Nochrim may do even Melachos mid'Oraisa for his needs, but Yisre'elim may not transgress even Shevus for him.

Poskim

Rema (OC 328:3): If one's tooth hurts and he wants to extract it, he tells a Nochri to extract it.

Beis Yosef (DH Kasuv b'Orchos): Orchos Chayim (Shabbos 334) says so, for when there is no danger, one tells a Nochri to do his needs.

Magen Avraham (3): We must say that his entire body is sick due to the tooth, like the Rema says in Sa'if 17. Extracting a tooth is a Melachah mid'Oraisa, i.e. wounding for the sake of Refu'ah.

Kaf ha'Chayim (17): If the entire body is not sick, one may tell a Nochri only to do Shevus.

Kaf ha'Chayim (18): According to the opinion that exempts Melachah she'Ein Tzerichah l'Gufah (it is not needed for the same purpose as in the Mishkan), extracting a tooth is not a Melachah mid'Oraisa, so one may tell a Nochri even if the entire body is not sick.

Mishnah Berurah (11): Even though he must open his mouth, many Acharonim hold like the Shulchan Aruch, that help is insignificant.

Shulchan Aruch (17): If one is bedridden due to illness, and there is no danger (Rema - or he has a pain, and due to it his entire body is sick), we tell a Nochri to make a cure for him, but we are not Mechalel Shabbos through an Isur mid'Oraisa, even if there is danger to a limb.

Magen Avraham (12): If there is no danger to a limb, one does through a Nochri, like Ameimar's case, if there is some illness. For a mere pain, it is forbidden even through Nochrim.

Mishnah Berurah (46): If there is no need to do it on Shabbos itself, one waits until Motza'ei Shabbos. If there is danger, one may not wait.

Kaf ha'Chayim (99): If one is bleeding, we tell a Nochri to anoint, tie a bandage and put on flax, egg white or other creams.

Rema: One may tell a Nochrim to cook a food for a child who does not have what to eat. Stam needs of a child are like a Choleh without danger.

Gra (DH Mutar): We learn from 141b that Shevus through Shinuy is permitted for needs [of a child, which is like illness]. All permit through a Nochri. The Ran says that we permit through a Shinuy because it cannot be done through a Nochri. The Ramban agrees that it is more lenient through a Nochri, for it is Shevus without an action. It is permitted for every Choleh.

Magen Avraham (15): Food that the Nochri cooked is Muktzeh. If one can feed the Choleh only through a Yisrael, it is permitted.

Mishnah Berurah (58): The Pri Megadim connotes that a Shinuy is required [for a Yisrael to feed Muktzeh to a Choleh]. The Chayei Adam says that one must be careful not to put the food in the pot, for [even though the Nochri puts it on the fire], the Yisrael is exempt, but it is forbidden.

Kaf ha'Chayim (114): Similarly, if a [Nochri] doctor needs to write a prescription, one may give to him a stylus, ink and paper, if there is no alternative. One should do so through a Shinuy if possible.

Rema (ibid.): What a Yisrael may not do, the Choleh himself may not do it. When a Nochri does things, the Choleh may help a little, for help is insignificant.

Magen Avraham (16): The Yisrael may help only if the Nochri could do it by himself, just not as well, e.g. opening and closing his eye helps the dye enter better. The same applies to a Melachah mid'Oraisa.

Kaf ha'Chayim (112): The Magen Avraham connotes that if it is possible through a Nochri, this is better.

Mishnah Berurah (59): It is permitted not only for the Choleh, rather, also for others. The Shulchan Aruch discusses a typical case.

Mishnah Berurah (100): For a mere discomfort, one may not tell a Nochri to do even Shevus. If it is a great pain and the entire body is weakened, he may tell him to do even a Melachah mid'Oraisa.