Galileo, the diagram, and the physical object

Around 1598-1600, Galileo Galilei composed a compact and elegant treatise on mechanics for his pupils at Padua; from fol.16r from his manuscript at the BCN Firenze, Ms.Gal.72, we have the simplest example I could think of to illustrate the contemporary tension between his diagrams and drawings. At the top right, we have a crosshatched cube of shadowed stone atop a triangular fulcrum and plank of wood, which sits in stasis, and seems to occupy space. Below, the lever is abstracted into a geometric diagram, in two sequential states. As Galileo explains: Impero che, ripigliando la med(esima) [linea] BCD, della quale sia C il sostegno, e la distanza CD pogasi…per essempio quintupla alla distanza CB, e mossa la lieva sin che pervenga al sito ICG. That is, for again assuming the…[lever] BCD, with fulcrum C, let the distance CD be taken to be five times the distance CB, and move the lever to position ICG. In that time the the force will have moved through space DI, and the weight will have moved from B to G. Because the distance DC was five times that of CB, it is clear that the weight placed in B may be five times greater than the force applied in D. In the pages of this manuscript, Galileo would fuse mathematical and physical arguments in the same way he linked geometrical diagrams (which would begin to depict spatial and temporal changes) to drawings of physical objects. But at this point, the tension is still evident.

Of course, one should refer to Michael Mahoney’s lucid critique of Samuel Edgerton et al. (Diagrams and Dynamics) before reading a lasting revolution into the marginal strokes of Galileo’s illustrations alone: the emergence of analysis cannot be ignored.