Back in 2011 I started a project--using my Galileoscope, I wanted to reproduce some of the sketches that Galileo published in his landmark treatise Sidereus Nuncius, published in 1610. Eight years later, I've gotten most of them (see here in my Galileoscope sketches) and last night finally caught up with Orion.
[Note: Independently, Jef De Wit started doing sketches of some of these same objects using a small refractor and called his postings "In the footsteps of Galileo" so I have borrowed his title when I post my sketches. ]
Now, my plastic Galileoscope has much better optics than what Galileo used and a field of view bigger than his telescope (although still small--about 1 degree). But I found this observation and sketch to be *very* difficult to do. The belt and sword area is 3-4 degrees wide and 4-5 degrees long. I could only see a little bit of it at a time--it was hard to get the correct spacing between stars and the correct placement of their relative positions.
Galileo wrote that he originally planned to sketch the entire constellation of Orion (!) but was overwhelmed by the enormity of the task so he decided to focus on the belt and sword. He sized the stars according to magnitude and made the 9 or so visible since antiquity the largest. He was able to see and plot the positions of about 80 stars that he could see with his telescope (I plotted about 60 before I gave out).
He did not record the Orion nebula (M42). Some speculate that he could not see it with his telescope but I don't agree--I could see it--but not in detail. Since he had already shown that nebula known since ancient times like the Praesepe (M44) were actually collections of stars when seen through the newly invented telescope, I agree with those who say he decided to wait to explore the nebula until he had a more powerful telescope (but I don't think he ever got to it).
Here is a link to Galileo's drawing. And here is mine: