How we cite our quotes: Citations follow this format: (Book.Chapter.Paragraph)
Quote #7
No man, one sees, can understand and estimate the entire structure or its parts – what are its frailties and what its repairs, without knowing the nature of the materials. (2.15.8)
Part of Lydgate's ambition is to discover the basic tissue of all life. He believes that in order to understand the "structure," you first have to know "the nature of the materials" that make it up. This could perhaps be paralleled to the way Eliot shows us the "nature" or personality of her characters in order to clarify their actions. It's impossible to understand a person's actions without first having a glimpse of their inner life.
Quote #8
And he counted on quiet intervals to be watchfully seized, for taking up the threads of investigation – on many hints to be won from diligent application, not only of the scalpel, but of the microscope, which research had begun to use again with new enthusiasm of reliance. (2.15.8)
In order to carry out his ambition of scientific discovery, Lydgate will use the "microscope" as well as the "scalpel." For a long time, scientists relied more on dissection of samples than on examining them under microscopes. Lydgate plans on using both techniques – he'll look at things up close, on a micro level, as well as from a macro level. Again, Eliot suggests that it's beneficial to combine the micro and the macro, or the particular with the general, in order to understand something thoroughly.
Quote #9
henceforth he would take a strictly scientific view of women, entertaining no expectations, but such as were justified beforehand. (2.15.25)
Here's yet another passage suggesting that women can be understood scientifically. The assumption, of course, is that you can make generalizations about all women. Lydgate's tendency to apply scientific observation and objectivity to his personal relationships is part of why his relationship with Rosamond crumbles.