Syzygy, revisited

To take my brain-breaks while working for the last few days, I have taken to flicking through Newton’s Principia. Imagine my surprise, after coming across the (gorgeous) term syzygy last week in my CATAM, to discover it on the first page of Newton I read. Very little further reading was needed to discover a host of equally fun words which were apparently common in seventeenth-century writing, including subtense, sagitta, and (my favourite) sesquiplicate, the last being genuinely frequent.

The Latin is very regular and relatively easy to translate compared to humanities, but there are so many barriers to understanding the meaning already that I would not recommend trying it. In fact, even in translation the Principia is another of those great books which no-one who claims to have read can possibly have done so. The notation is obscure, inconsistent, the equations written in words or phrased in ratios, and almost everything that is formulated purely in the style of classical Euclidean geometry.

If there are parts worth reading, I would recommend most the scholium at the end, and the introductions to the books which outline the thinking behind the work, which is well worth spending a bit of time to appreciate. There is only one modern translation in would seem, that of I.B. Cohen and Anne Whitman (reviewed in The British Journal for the History of Science, vol. 33, no. 2 [JSTOR]). Though the very complex philosophical nature of the book makes it understandably hard to represent in modern English, there is much fascinating thought to grapple with at any rate. In any case, regardless of its accuracy as a translation, Cohen provides several hundred pages of guide, an extremely helpful tool.

Finally, as a demonstration that these words are really quite accessible after all, and as guide for using syzygy in your next hand-in, consider this extract:

Liber Tertius. Propositio XXVIII. Problema IX.

Invenire diametros Orbis in quo Luna, ſine eccentricitate, moveri deberet

Curvatura Trajectoriæ, quam mobile, ſi ſecundum Trajectoriæ illius perpendiculum trahatur, deſcribit, eſt uc attractio directè &t quadratum velocitatis inversè. Curvaturas linearum pono eſse inter ſe in ultima proportione Sinuum vel Tangentium angulorum contactuum ad radios æquales, ubi radii illi in infinitum diminuuntur. Attractio autem Lunæ in Terram in Syzygiis eſt exceſsus gravitatis ipſius in Terram ſupra vim Solarem 2PX quâ gravitas acceleratrix Lunæ in Solem ſuperat gravitatem acceleratricem Terra in Solem vel ab eâ ſuperatur. In Quadraturis autem attractio illa eſt ſumma gravitatis Lunae in Terram &t vis Solaris KT, quâ Luna in Terram trahitur.

That is,

To find the diameters of the orbit in which the moon would have to move, if there were no eccentricity

The curvature of the trajectory that a moving body describes, if it is attracted in a direction which is everywhere perpendicular to that trajectory, is as the attraction directly and the square of the velocity inversely. I reckon the curvatures of lines as being among themselves in the ultimate ratio of the sines or of the tangents of the angles of contact, with respect to equal radii, when those radii are diminished indefinitely. Now, the attraction of the moon toward the earth in the syzygies is the excess of its gravity toward the earth over the solar force 2PK (as in the figure to prop. 25), by which force the accelerative gravity of the moon toward the sun exceeds the accelerative gravity of the earth toward the sun or is exceeded by it. In the quadrature that attraction is the sum of the gravity of the moon toward the earth and solar force KT (which draws the moon toward the earth).