To treat or not to treat hopelessly ill patients? Not to treat, Plato answers in The Republic, since for this decision it is sufficient that the doctor knows his patient as incurable. To treat, says Aristotle in The Rhetoric, since for this decision it is sufficient that the doctor knows of the possibility to return his patient's health. The authors show that these Plato's and Aristotle's explicit answers reflect their positions only partly, and under certain conditions they imply the opposite answers, too. The authors discuss the issue of passive euthanasia as the doctor's refusal to treat hopelessly ill patients from two angles: from the viewpoint of this practice in ancient societies, and from that of practical argumentation regarding actions by means of which the decisions over patients' euthanasia are justified. As concerns euthanasia practices, there are three features characterizing ancient societies: such decisions rest on the epistemic grounds, they employ a paternalistic approach to doctor-patient relations and a functional view on what health is. Therefore, the goal of medical treatment is solely the return of health, and no palliative care corresponds to it; it is his knowledge that enables the doctor to euthanize, and no patient's consent is required. In its full-fledged form, Plato's answer is: not to treat, if and only if the doctor knows about the incurable condition of the patient, and to treat if the doctor knows that the patient can be cured. Since the conclusions in practical arguments are plausible and defeasible, they amplify the rigid framework of the dichotomy in Plato's argument "from virtue" which erects doctor's knowledge to a professional virtue understood as his contribution to the well-being of society performed by treating those who deserve that and refusing to do so with those hopelessly ill. Doctor's knowledge is essential in Aristotle's argument "from patient", according to which a hopelessly ill patient has to be treated if and only if the doctor considers his treatment possible, and not treated if he thinks otherwise. The doctor determines the possibility of treatment with the help of a practical syllogism, outlined by Aristotle in The Nicomachean Ethics. In this reasoning the doctor determines a line of conduct with respect to the goal of returning health to his patient, and he has to refrain from treating the patient if no such line can be determined.