What an amazing find the illustration shows. It is part of the Metropolitan Museum of Art Collection. Artists, architects and craftsman have been using grids for a very long time. The illustrated work dates back to 7000 BC. Grids are still used today and are very much alive in computer programs and on many digital cameras as an aid to composition.
When drawing a life model I think of a grid spread over the paper (and imagine another projected on to the model) even if I no longer actually draw one on the sheet. It imposes a kind of regular order on the chaotic mess of lines that are supposed to add up to a figure.
By relating one part of the grid to the actual figure, you can more easily position it in your drawing. It’s critically important that you stand in exactly the same position and use only one eye to look through the imaginary grid at the model.
There are plenty of examples of artists using mechanical aids to do exactly this. They usually consisted of wooden frames with a grid of string stretched systematically across the frame. This frame was placed in front of the model or still life. An identical grid was then drawn on the paper.
A big improvement was a fixed position spy hole that always kept the artist’s eye in the same position relative to the grid superimposed on the model. Very accurate work can be done with this simple equipment. The example below is the work of Albert Durer.
Eventually the spy hole was improved by adding a simple lens. People then started to think how clever it would be if the image could be captured on the paper without having to draw by hand.
A simple extension of this idea is to make the size of each square on the paper larger that those projected over the subject. This allows small drawings to be easily enlarged by hand.