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Lambert projections:
Fully 7.5° of overlap from either side of declination 45° has deliberately been created between the projections. Thus the stars from declination 37.5° to 52.5° will appear on both the azimuthal and the cylindrical charts.
The PDFs were created in a Mathematica notebook.
Understanding the distorted salmon-colored circles:
A sphere cannot be flattened without distortion. The “indicatrices” show what circles on the sphere have been crushed into.
My version of two finished charts with connecting lines in the constellations. Also with the addition of the Orion Nebula, the Andromeda Galaxy, and the Pleiades dotted in around Alcyone:
From the Flamsteed-Fortin Atlas, 1795 edition (scanned and graciously placed on the web by G. M. Caglieris):
From Uranometria, 1603: