It's tricky to pinpoint an exact date for the discovery of plant and animal cells because the understanding of cells evolved gradually over time. Here's a breakdown:

Early Observations:

* 1665: Robert Hooke first observed and named "cells" while examining a thin slice of cork under a microscope. He saw empty compartments, but he didn't know what they were or their function.

* 1674: Antonie van Leeuwenhoek observed living cells (like bacteria and red blood cells) using a more powerful microscope. He described these as "animalcules."

Development of the Cell Theory:

* 1838: Matthias Schleiden proposed that all plants are made up of cells.

* 1839: Theodor Schwann extended this idea to animals, suggesting that all living things are composed of cells.

* 1858: Rudolf Virchow added the crucial concept of cell division, stating that all cells come from pre-existing cells.

So, while Hooke's observations were the first step, it was the combined work of Schleiden, Schwann, and Virchow that established the Cell Theory, which is the foundation of modern biology.

Therefore, we can say that the discovery of plant and animal cells took place gradually between the 17th and 19th centuries.