Progress direction of the Aldebaran occultation by the moon

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EnigmaticField
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We are experiencing a regular series of the Aldebaran occultations by the moon now. I read this in the article http://www.skyandtelescope.com/observing/moon-covers-bright-star-aldebaran/. What puzzle me are the advancing directions of the occultations across the moon described in the article.

It said when the occultation occurs as the moon is in the waxing gibbous phase, Aldebaran would disappear behind the moon's dark limb and afterwards reappear from behind the moon's bright limb (such as the occultation on Dec. 23, 2015), and when the occultation occurs as the moon is in the waning gibbous moon, Aldebaran would disappear behind the moon's bright limb and afterwards reappear from behind the moon's dark limb (such as the occultation on Oct. 18, 2016).

But I think according to the revolving direction of the moon the advancing directions should be opposite to the above statement. The moon is revolving Earth in the counterclockwise direction, so I think in its waxing gibbous phase, it advances with its bright limb as the front and dark limb as the back, so that its bright limb would cover Aldebaran followed by the emergence of Aldebaran from behind its dark limb, and in its waning gibbous phase, it advances with its dark limb as the front and bright limb as the back, so that its dark limb would cover Aldebaran followed by the emergence of Aldebaran from behind its dark limb.

So where am I wrong to deduce the advancing directions opposite to those described by the article?
 
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When waxing the moon is illuminated on the right side and therefore is dark on the left side, and since the moon is moving to the left relative to the background stars I would say the article is correct.

[Reworded using a proper screen and keyboard instead of my mobile]
 
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Filip Larsen said:
Wien waxing the moon is illuminated on the right side and is dark on the left, and since it is moving to the left relative to the background I would say the article has is correct.

Thank you for your enlightening me. I probably have been disentangled from my puzzle. I think your statement can be understood by the following diagram. I previously thought wrong about the lit part of the moon so deduced wrong.

moon_phases_diagram.jpg
 
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