In response to your scratching post: you're right about the alignment of the Sun-Earth-Moon being in a straight line. The point is that while the Earth may be in different orientations during different eclipses, its shadow is indifferent to orientation.
The partial phase of a lunar eclipse is always delimited by a circular arc on the Moon; this is true whether the shadow is on the N, E, S, or W portion of the Moon, and is true no matter where the Moon is in the sky - rising, south, or setting.
Therefore, if we assume that the shadow on the Moon is actually the Earth's shadow, the Earth must be round in all directions, ie a sphere.
This logic is traditionally ascribed to Pythagoras ca 580 BC. Reference