total gravitational attraction of the Sun on the Earth, and of the Sun on the Moon, the difference that represents the perturbing effect on the motion of the Moon relative to the Earth. In summary, line LS in Newton's diagram as shown below represents the size and direction of the perturbing acceleration acting on the Moon in the Moon's current position P (line LS does not pass through point P, but the text shows that this is not intended to be significant, it is a result of the scale factors and the way the diagram has been built up). Shown here is Newton's diagram from the first (1687) Latin edition of the Principia (Book 3, Proposition 25, p. 434). Here he introduced his analysis of perturbing accelerations on the Moon in the Sun-Earth-Moon system. Q represents the Sun, S the Earth, and P the Moon. Parts of this diagram represent distances, other parts gravitational accelerations (attractive forces per unit mass). In a dual significance, SQ represents the Earth-Sun distance, and then it also represents the size and direction of the Earth-Sun gravitational acceleration. Other distances in the diagram are then in proportion to distance SQ. Other attractions are in proportion to attraction SQ. The Sun's attractions are SQ (on the Earth) and LQ (on the Moon). The size of LQ is drawn so that the ratio of attractions LQ:SQ is the inverse square of the ratio of distances PQ:SQ. (Newton constructs KQ=SQ, giving an easier view of the proportions.) The Earth's attraction on the Moon acts along direction PS. (But line PS signifies only distance and direction so far, nothing has been defined about the scale factor between solar and terrestrial attractions). After showing solar attractions LQ on the Moon and SQ on the Earth, on the same scale, Newton then makes a vector decomposition of LQ into components LM and MQ. Then he identifies the perturbing acceleration on the Moon as the difference of this from SQ. SQ and MQ are parallel to each other, so SQ can be directly subtracted from MQ, leaving MS. The resulting difference, after subtracting SQ from LQ, is therefore the vector sum of LM and MS: these add up to a perturbing acceleration LS. Later Newton identified another resolution of the perturbing acceleration LM+MS = LS, into orthogonal components: a transverse component parallel to LE, and a radial component, effectively ES. Newton's diagrammatic