Christoph Scheiner · 1617
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Refractiones coelestes addresses atmospheric refraction and the apparent elliptical — vertically flattened — shape of the Sun near the horizon. Scheiner presents observations and a geometrical account of horizontal refraction: why the low Sun looks oval, and how refraction distorts measured solar altitudes and diameters.
The argument is built as a chain of theorems rather than a narrative. Scheiner begins with preliminaries and preliminary theorems establishing which planes through the Sun are planes of refraction and which are not — no longitude plane when the Sun is outside the zenith, only the primary altitude plane always and everywhere — and works from there to the conclusion that the Sun is refracted along one dimension and not the other. That asymmetry is the whole explanation of the oval: the low Sun is lifted more at its lower limb than its upper, and so is squeezed vertically while keeping its width.
He then takes up quantity rather than direction. A series of lemmas leads to the greatest and least solar refractions and to the difficulty of the tangent ray, and thence to two consequences a working astronomer cannot ignore: the Sun’s apparent altitude exceeds its true altitude, and the Sun’s disc is contracted. The theory is checked against experiments conformable to it, and the book closes with chapters on lenses in general and in particular.
Every positional observation near the horizon is wrong until refraction is accounted for, and this is one of the first monographs to treat that correction as a subject in its own right rather than a nuisance. The flattened Sun is the visible symptom of a systematic error running through the observational record, and Scheiner’s geometry both explains the appearance and quantifies the correction. The closing turn to lenses points forward: the same optics would occupy him in the solar work of Rosa Ursina.
The translated source is the 1617 printing, opening with a dedicatory epistle to Archduke Maximilian III of Austria and a set of verses applauding the author for having discovered and explained the solar ellipse.