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This paper considers geometric perspective in relation to devotional requirements in Italian religious painting from about 1250 to about 1450. The content of the altarpiece consisted in antithetical elements--the graphic exposition of Christian dogmatics, and a dramatis personae increasingly to be identified in empathetic terms. The one-point perspective system that was invented towards the end of that period, then, presented an opportunity and a difficulty. It enabled the creation of a naturalistic space, aiding empathetic identification with psycho- logically plausible individuals in the pictured world. On the other hand, whilst superficially the space marked out by the geometry of the vanishing point coincided with that of Christian hierarchy, it threw dogmatics into crisis, as it set picture space against picture plane. In addition to a humanistic imperative, the method was driven by a mathematical one, consideration of which allows us to see it as the last stage in a process of simplification of the conditioning geometry governing representation within the altarpiece. The paper shows that, despite first impressions, the earlier mathematical perspective systems were systematic. It demonstrates that, as there was a stand-off between dogma and empathy, there was one between iconic stability and mobile perspective in the earlier perspective methods, and one between static viewpoint and imaginative mobility in the invention. From within these antitheses came the necessity for very devious negotiations of the timeless and the historical--all compromising one another in one way or another--and, after the invention of the one-point system, the proposition of an expanded mental life both in those depicted and in those observing. [ABSTRACT FROM AUTHOR]