Mathematical Disquisitions by Christopher M. Graney

Author:Christopher M. Graney
Language: eng
Format: epub
Publisher: University of Notre Dame Press
Published: 2017-10-05T04:00:00+00:00

Such has been the opinion of philosophers both ancient and new. See Caesar Germanicus in the Phenomena of Aratus, toward the end; see Cleomedes; see Vitellius’s Principles of Optics ‹book 4, paragraph 77›; see the Optics of Fr. Francois d’Aquilon ‹book 5, proposition 56›;158 and so forth. “The moon,” says Macrobius in On Scipio’s Dream, book 1, chapter 19, “though of a denser substance than the other celestial bodies, it is still much purer than the earth, and it permits the light to penetrate to such a degree that it sends it forth again.”159

This opinion is supported primarily by experience. When the moon is a very young waxing crescent or a very old waning crescent, the non-illuminated part shines forth much, especially at the edge. Likewise, when the moon is eclipsing the sun, the edge shines forth, as Vitellius and Reinhold testify. Indeed, many here in Ingolstadt perceived this most brilliantly in the recent eclipse of the sun on 29 May of the year 1612, when the lunar ring shone forth mightily.160

This opinion is also supported by reason. The secondary light is neither from any star, nor from the moon itself, nor from Earth. Therefore it is from the sun. Those things which are observed to happen are consistent with, and their causes can be reasonably attributed to, this. And indeed, as is shown in [Figure 27-1], the solar rays AB and CD drawn through and near the lunar center are longer than ray GH, drawn through the lunar edge. Hence the former are weakened more, while the latter passes through with more strength retained. Thus these edge rays form that brighter ring on the lunar extremity [in Figure 26-1], while the other rays account for the weak secondary light in general. The reason for the little points of light [in Figure 26-1] that shine forth is that there are parts within the moon more permeable to the sun’s light (that these are not from the glass of the optic tube is determined by moving the tube across to other parts of the moon and observing that the points do not follow). In an eclipse of the sun, a ring is observed at the edge of the moon in that part of the moon that passes in front of the sun, and not observed in that part that is outside the sun; the reason is that in the former the solar rays are directed toward our eyes, and in the latter they are not.

From all these are established a number of conclusions.

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