Animodar method of Rectification
the Animodar method of rectification can be traced back to the work of Ptolemy and is explained in detail in several traditional works, such as Antonius de Montulmo's work on nativities and the nativities section of William Lilly's Christian Astrology. It aims to correct the degree of the ascendant once the astrologer knows which sign should be on the ascendant.
The method is based upon consideration of the degree of the previous syzygy (lunation). If the chart was preceded by a new Moon, it considers which planet has the most essential dignity at the degree of the New Moon; if it was a full Moon it considers which planet has the most essential dignity in the degree of the luminary above the earth.
According to Lilly's instruction, having identified that planet you then consider whether it is nearer to the ascendant or midheaven. If it is nearer to the ascendant you alter your ascendant to the degree position of that planet. If it is nearer the midheaven, you alter the midheaven in your chart to the degree position of that planet and then adjust your ascendant accordingly.
Galileo's chart notes for his own horoscope appear to demonstrate him attempting to rectify his birth time according to the animodar method. The planet which had most dignity in the previous New Moon was Venus and its degree position - 27°37' - is marked alongside the ascendant. If he was using the method exactly as Lilly described it he would have changed the MC to 21.37, which would have put 28.42 Leo on the ascendant instead. But this may suggest that what has been omitted from Lilly's description is the instruction that if the planet is closer to the asc-desc axis rather than the MC-IC axis you amend the ascendant degree (and change the MC if it's vice versa).