This article focuses on some theoretical developments prompted by the use and construction of telescopes in the first half of the seventeenth century. It argues that today's notion of "scientific instrument" cannot be used to categorize these optical devices or explain their impact on natural philosophy. The article analyzes in historical terms the construction of conceptual references for the telescope as an instrument of a new kind, which possessed capabilities and working principles unlike those of traditional "mathematical instruments." It shows that through the 1650s, in both rhetorical and explanatory terms, first-rank telescope makers, theoreticians, and astronomers found it useful to equate the telescope with the eye, suggesting that the data the telescope produced was as reliable as that obtained in naked-eye vision. Kepler's and Descartes' theory of the telescope will be shown to dovetail uncannily with this understanding of the telescope.