This essay argues that the eighteenth-century emergence of algebraic and arithmetic methods that require only numeric operators and that do not base their claims to truth upon Euclidean axiomatic geometric magnitudes and relations (lines, angles, proportions) transformed the ontological status of lines. For classicist geometers, the points and magnitudes of Euclid had a status akin to the Longinian sublime: the classical line is not simply a symbol mediating an absent truth; rather, the classical line should be understood as the thing itself. After arithmetization, however, the line is only an inscription, another symbol among many, subject to the gulf between signifier and signified. It is also relegated to an effect of, rather than the organizing principle of, motion, and hence enters... history. Aesthetic theorists contribute significantly to the reconceptualization of lineation. From William Hogarth’s infinite variety, to Edmund Burke’s insensible deviation, to Laurence Sterne’s digressive progression and William Gilpin’s easy line, aesthetic orthodoxies arise that are founded in deviation from rigid prescription and from prior axiomatic models. Aesthetically and politically, a positively construed but semantically empty notion of deviation helps to generate the fantasy of subjects in relationships to spectacles and institutions that are not mediated by any ideological structures other than personal affective sensation. Precisely because the Burkean/Gilpinesque subject/spectator recognizes himself as deviant (which is to say ungoverned by doctrine, fanaticism, or standards imposed against the grain of his own intuitions), his participation in the frame of polity and the spectacle of nation can be understood as wholly natural and volitional, not to say homogeneous. At the same time, the aesthetics of deviation can be seen as key to the modernist avant-garde, preserving a close parallel between its premises and the supposedly radically distinct values of bourgeois aesthetics.