The statement "all cells come only from other living cells" is known as the Cell Theory. While it's difficult to pinpoint a single person who definitively "stated" it, Rudolf Virchow is credited with popularizing and solidifying this concept in 1855 with his famous phrase: "Omnis cellula e cellula" (Latin for "all cells come from cells").

However, it's important to note that the Cell Theory is the culmination of contributions from several scientists:

* Robert Hooke (1665) was the first to observe and name cells.

* Anton van Leeuwenhoek (1674) made further observations of cells and their structure.

* Matthias Schleiden (1838) concluded that all plants are made of cells.

* Theodor Schwann (1839) expanded this to include animals, proposing that all living organisms are made of cells.

Therefore, while Virchow's phrase popularized the concept, the Cell Theory itself is the product of many scientific minds working together over several centuries.