Galileo’s Manuscripts: Still Learning the Lesson

When I studied history of science, my teachers — especially Ken Manders and Paolo Palmieri — hammered two principles like drill sergeants:

  1. Always read the original manuscripts;
  2. Always pay attention to the diagrams.

Okay, that seems obvious. We’ve known that since the mid-20th century. Yes, these lessons are easy to under-estimate — until you realize how many historians still haven’t learned them.

Here’s an example. Galileo’s personal notebooks on mechanics have survived the last four centuries. I recently took interest in one famous page among them, in which Galileo did very early work on acceleration in freefall. It’s distinguished title is Folio 152r of Manuscript 72, written sometime between 1604 and 1610. The Max Planck institute has done us the extraordinary service of putting the whole manuscript online.

I first spent a few days assembling my own interpretation of this manuscript page. Then I took a look at how other people interpreted it. Surprisingly, two features of the manuscript that I thought were significant seem to have been completely ignored by scholars. And no wonder — it turns out that the only available English reproductions of the document omit a signficant portion of the diagram.

Compare the following. Here’s Drake’s (1973) English reproduction — click to enlarge it:

Damerow et al. (1992) later spruced things up with a nicer type-face:

Finally, here’s the original. Can you see what’s missing?

Two important things. First: the little upside-down triangular diagram in the middle. (The circle visible near it is actually printed on the back of the page.) Both triangular diagrams represent distance along the vertical, and velocity along the horizontal. So, if this is small triangle is a scaled-down copy of the larger one, then the scaling rule will actually indicate which rule of freefall Galileo was considering. (It turns out to be the incorrect “double-distance” rule, which says that velocity in freefall is proportional to the square of the distance fallen.)

Second: the languages used. While the top-left, top-middle, and bottom-most paragraphs are all written in Italian, the rest of the text is written in Latin. Galileo wrote comfortably in both, but his train of thought probably only followed one language at time. That suggests a connection between these three paragraphs, which might not have otherwise been apparent, given their physical separation on the page.

So, here’s the way a translation of 152r should look:

Ah, yes. Isn’t that better with the diagram restored? Over a hundred years reading Galileo’s manuscripts, and we’re still learning this lesson!

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5 thoughts on “Galileo’s Manuscripts: Still Learning the Lesson

  1. Jonathan Livengood

    Very nice! But what was your interpretation of the page? And how does it differ from the interpretations offered by Drake and others?

  2. Bryan

    Well, it takes a bit to write it all down. In short, I think Galileo was refuting one law of freefall (the one that says time in freefall is proportional to distance fallen), and considering the consequences of two others. Maybe I’ll write another post to explain, or give a short WIP talk on it next month.

    Drake had a very different take, that Galileo was actually *discovering* the time-squared law in this passage — but his view is widely disagreed with now. Damerow et al. tell a more compelling and subtle story, in which they suggest Gaileo is mostly just considering the time-squared law and its consequences. But I think I read fewer implicit assumptions into the text, and can account for more of it.

  3. Jonathan Livengood


    I noticed that there are what appear to be construction lines intersecting the main triangular shape (the one reproduced by Drake). These are not the same as the circle that you note is actually written on the other side of the folio page. Are the construction lines also just bleeding through, or are they actually something Galileo used to construct the main triangle on the page? If the latter, then are they important?

  4. Jonathan Livengood

    Looking at the page from the Max Planck Institute, it looks like some (at least) of the lines are bleed over from the verso side, but I can’t tell whether it all is or only part of it. Do you have a regular method of deciding which bits are bleed through and which are not in fuzzy cases like this one?

  5. Bryan

    You can just look at the back of the page to figure out what’s a bleed through. That website is really fantastic.

    The “construction lines” are interesting — perhaps they should be put in the reproduction. The main thing about them, I think, is that they show more precisely how the point f was drawn in.

    What’s really interesting is to take a ruler and start measuring different parts of this diagram. For example, the ratio of AC to AB in the diagram isn’t 9 to 4 (i.e., (3/2) squared), as Galileo suggests in the text. Rather, it’s 4 to 8. So he may originally have been using the large diagram to represent v ~ d (the “incorrect” that the would later rebuke in the To New Sciences).

    All these kinds of things should be worked into the interpretation of the document!