Botany was greatly stimulated by the appearance of the first "modern" text book, Matthias Schleiden's Grundzüge der Wissenschaftlichen Botanik, published in English in 1849 as Principles of Scientific Botany. Schleiden was a microscopist and an early plant anatomist who co-founded the cell theory with Theodor Schwann and Rudolf Virchow and was among the first to grasp the significance of the cell nucleus that had been described by Robert Brown in 1831. In 1855, Adolf Fick formulated Fick's laws that enabled the calculation of the rates of molecular diffusion in biological systems.
Is there an answer to this question (If it cannot be answered, say "unanswerable"): What was the first modern text book?
Grundzüge der Wissenschaftlichen Botanik