Plain astronomy. Manuscript volume of notes on practical astronomy and mathematics.

A fascinating manual of astronomy, written in English, particularly as it relates to the form of the motions of the heavens, dating from the period 1780-1825, probably from the beginning of that range. It is written in a single hand (with the exception of one page), though with some variations indicating that different parts of the MS were written at different times. The MS could have been prepared for personal use or as part of public tuition (probably the former). The writer summarizes the subject matter of the manual on the first leaf: "Astronomy is that part of Natural Philosophy which treats of the Phenomena of the heavenly Bodies. It is divided into 2 Parts, Physical and Plain: by the latter we discover their Motions from the Apparent Motions; by the former the Causes of these real Motions." The manuscript comprises three parts, with distinct subject matter. The first part covers the motion of the earth around the sun, and its rotation about its axis, with the consequences for the apparent motions of the sun and the heavens; with the moon and its phases and motion; and with lunar and solar eclipses. There are several references to John Keill’s An introduction to the true astronomy (London, 1721 or later editions). The second part principally discusses section 11 of Newton’s Principia (1713 or later editions), in particular as it relates to the motion of the moon. This part ends with a short section on algebra, particularly polynomials, which seems to have been composed more haphazardly than the remainder of the text. The third part, which runs backwards starting from the end of the notebook, gives demonstrations of various results in Book I of Principia, notably the theorem that the orbits of the bodies in the solar system do not precess if and only if the central attractive force operating on them is exactly inverse-square. This is an important result not only for Newton’s system of universal gravitation but also for the observational astronomy of the solar system which is discussed in the opening section of the book. Between the end of the second part and that of the third there are a few blank leaves, and others have been torn out, but the text appears to be complete.The manuscript appears to work through at least two different texts, beginning with Keill’s on astronomy. There is a section devoted to what is called the precession of the equinoxes (the westward drift of the points where the ecliptic and equator intersect, due to the precession of the earth’s axis) - the author notes that "Sir Isaac Newton has demonstrated that it arises from the broad spheroidal figure of the earth." The author then turns to sunspots and the arguments for and against their being on the surface of the sun. Then comes a long discussion of the planets: the planes and periods of their orbits, phases, conjunctions, retrograde motions, apparent brightness, and their distances from the sun. The second and third parts are notably more mathematical in nature than the first.The third part of the manuscript consists of a reading of various sections of Newton’s Principia (1713 or later editions). Again, it appears to work through and in some cases repeat Newton’s proofs, rather than representing a translation or paraphrase. It is not based on Motte’s translation nor does it correspond with Thorp’s partial translation and edition. It does not appear to be based on any other intermediary between Newton and the writer (such as Pemberton) but to rely on Newton’s Latin original, here rendered in places pretty exactly into English. It renders propositions 43 to 59 of section 9 of book 1 of the Principia, which concern the motion of bodies in moveable orbits and the motion of the apsides. This topic remains of considerable interest to astronomers and historians of astronomy. The manuscript hand remains fairly constant throughout the book: some variations more likely indicate the same writer at a different times or with a different pen than a different wr.…