The rhetoric studies art of well-reasoned and convincing speech since antique times. In the article, a rhetoric phenomenon is viewed as certain method in Cicero’s philosophy of education. He considered a semantic component as a basis of the speaker speech. From the point of view of a rhetoric demand in teaching mathematics of various levels, modern interpretation of rhetorical skill does not come down to eloquence only. The rhetoric is still methodological means for strengthening the convincing influence of mathematical arguments (...) at a statement of difficult mathematical terminology or at proving theorem. Article underlines a role of the good speaker’s rhetoric of the live speech. Rhetoric gives the required words and ‘colors‘ that are essential for the live speech. From the point of teaching mathematics, the convincing speech art is especially demanded for understanding of mathematics at various justification levels. The rhetoric studies art of the convincing and reasoned eloquence. Sometimes, addressing to non-mathematician audience, mathematicians allow themselves to substitute arguments by unreasoned rhetorical means, but it is necessary to amplify the pragmatical aspect of rhetoric at lectures on mathematics. It provides the means for communication with the student audience of any level of mathematical knowledge. (shrink)