Today classicists are provided with a great number of digital tools which, in turn, offer possibilities for further study and new research goals. In this paper we explore the idea that old Greek handwriting can be machine-readable and consequently, researchers can study the target material fast and efficiently. Previous studies have shown that Handwritten Text Recognition (HTR) models are capable of attaining high accuracy rates. However, achieving high accuracy HTR results for Greek manuscripts is still considered to be a major challenge. The overall aim of this paper is to assess HTR for old Greek manuscripts. To address this statement, we study and use digitized images of the Oxford University Bodleian Library Greek manuscripts. By manually transcribing 77 images, we created and present here a new dataset for Handwritten Paleographic Greek Text Recognition. The dataset instances were organized by establishing as a leading factor the century to which the manuscript and hence the image belongs. Experimenting then with an HTR model we show that the error rate depends on the century of the image.