In this chapter I take a close look at the early lineage thinking of paleontologists and their attempts to infer evolution from stratigraphic sequences of fossils. Linear thinking with fossils emerged as a core component of the traditional paleontological method in the second half of the nineteenth century. It was taken to extremes by orthogeneticists, and I use the late-nineteenth-century debate between Franz Hilgendorf and Alpheus Hyatt about the famous freshwater Miocene Steinheim snails as a case study for looking at competing forms of lineage thinking. But it was in fact the straight-thinking orthogeneticist Othenio Abel who helped resolve the conundrum of how branching evidence can shed light on the evolution of linear lineages.