1. The science of projectiles, from the Greek ballo, ‘I throw’. It is Mersenne’s term for what we would call ‘mechanics’ or ‘kinematics’ — the science of impacts between moving bodies.

2. This is not Hobbes’s view. For Hobbes a motion is propagated through the medium between object and sense organ.

3. i.e. the circular motion fades away because each rise in the water level is counteracted by gravity. However, this is to overlook the fact that the energy is also dissipated by the expansion of the rings.

4. Reading clariora esse quam ubi objecta absunt for clariora quam ubi objecta abeunt.

5. Reading in qua for in quas.

6. The association between Pythagoras and a bean is that Pythagoras allegedly prohibited the eating of beans, because they might contain the souls of dead humans which had transmigrated to a lower form of life. The association between bean and fable is linguistic: the Latin for ‘bean’ is faba, and for ‘fable’ is fabula. And of course Aesop was famous for his fables.

7. This doesn’t read nearly as oddly in Latin, since discursus means the act of running all over the place. It was only in scholastic philosophy that it came to mean the sequence from one thought to the next in a piece of reasoning, which is broadly Hobbes’s sense. During the 16th century, the French discours and the English discourse acquired their modern senses of ‘conversation’, ‘lecture’, or ‘treatise’, and these sense became attached to the Latin discursus.

8. Reading aliam for alium.

9. Reading quo quis for quo si quis.

10. Reading praesentem for praecedentem. The argument seems to be as follows. We remember events happening in the order A1 . . . B1. We then experience A2, which is similar to A1. We assume the same order of events, and, treating A2 is if it were numerically identical to A1, we imagine B1 following it in the future, even though the event we are imagining actually happened in the past.

11. The first occurrence translates experimentum, the second experientia.

12. Reading quo for qui.

13. As Hobbes says elsewhere, this is also the condition of most humans.

14. Literally, ‘copulated by a verb.’ However, I am sure he is making the logical point that a proposition consists of subject and predicate joined by the copula ‘to be’, rather than the grammatical point that sentences usually have a subject, a verb, and an object.

15. Colligo means both ‘add’ and ‘conclude’.

16. Reading dicimur for dicimus.

17. I have added the word ‘science’ to indicate that he is referring to a discipline which includes deductive reasoning (e.g. the mathematical ratios between different notes).

18. Molesworth thinks the text is corrupt here, but I’m not sure.

19. These definitions of love and hatred are compressed to the point of unintelligibility (even more so in the Latin). Hobbes must surely have been summarising material he had already written for Leviathan chapter 6, 3rd paragraph.

20. Etymologically, the Latin deliberare means to weigh in the scales.

21. There is a pun on deliberationis (deliberation), libertatis (freedom), and depositio (renunciation).

22. This is Mersenne’s pun. Corpus refers both to the totality of Hobbes’s writings (virtually none of which had yet been published), and to De corpore in particular, which would probably have been of most interest to Mersenne.