No teaching appears in more traditions, more independently, than the rule of reciprocity. It is not a modern harmonising invention — the formulations are ancient, canonical, and easy to cite. Here they are in their own words.
The formulations
Judaism. Asked to teach the whole Torah while a listener stood on one foot, the sage Hillel answered: "What is hateful to you, do not do to your fellow: this is the whole Torah; the rest is commentary — go and learn it" (Talmud, Shabbat 31a, c. 1st century BCE). Behind it stands Leviticus 19:18: "love your neighbour as yourself."
Christianity. In the Sermon on the Mount: "In everything, do to others what you would have them do to you, for this sums up the Law and the Prophets" (Matthew 7:12). Jesus states it positively — act, not merely refrain — and names it a summary, exactly as Hillel had.
Islam. From the forty hadith of an-Nawawi (no. 13), the Prophet: "None of you truly believes until he loves for his brother what he loves for himself." Here reciprocity is placed inside faith itself — a condition of belief, not merely of ethics.
Hinduism. The Mahabharata, Anushasana Parva (13.113.8): "One should never do to another what one regards as injurious to one's own self. This, in brief, is the rule of dharma." The epic, like Hillel, calls it the summary — "all else proceeds from desire."
Buddhism. The Dhammapada reasons it out rather than decreeing it: "All men tremble at punishment, all men fear death; remembering that thou art like unto them, do not strike or slay" (verse 129, Müller's translation — read it in the Study Hall). The rule is derived from shared vulnerability.
Jainism. The Sutrakritanga (1.11.33): a person should treat all creatures as they themselves would be treated — extended, characteristically for Jainism, beyond humans to all beings.
Confucianism. Asked for one word to guide a whole life, Confucius offered shu — reciprocity: "What you do not want done to yourself, do not do to others" (Analects 15.24).
The Tao. The Tao Te Ching pushes past reciprocity into something stranger: "To those who are good, I am good; and to those who are not good, I am also good — and thus all get to be good" (chapter 49, Legge's translation).
The differences are the interesting part
Lined up, the versions disagree fruitfully. Hillel and Confucius state it negatively (do not harm); Jesus and the hadith positively (actively give). The Dhammapada grounds it in empathy, the Mahabharata in dharma, the hadith in faith, the Analects in social order — four different answers to why be good to each other, converging on the same behaviour. And the Tao quietly questions the whole frame: goodness that waits for reciprocity is still a transaction.
That convergence-with-difference is this site's whole method: not that the traditions say the same thing, but that they answer the same questions — and are most illuminating exactly where they diverge. See the same method applied to anger, death and happiness.
Related
When the world is at war: what the traditions counsel · One question, five traditions · The Study Hall