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It has been used 11 times so far since the enactment of the fixed calendar in 4119. It was used in 4179, 4257, 4504, 4602, 4849, 5096, 5194, 5441, 5519, 5688, and 5766. The next time it will be used is 6013 if we still have a fixed calendar then. You can read about this exceedingly rare Dechiya and its history here.


The answer is well implied in the first 2 paragraphs of the Halachot you quote, namely that we are using 24 hour days and 60 minute hours, not sha'ot z'mani'ot. Rambam KidushHachodesh 6:1 states: ...The first level of these calculations represent approximations of the time of the conjunction, and their accuracy is not great. This approximation of the ...


The source of the Rambam is the Mishna, Rosh Hashana 2:7, and Rav Ovadia MiBartenura explains (based on the combination of Rav Pappa and Rav Nachman Bar Yitzchak's opinions in the Gemara Rosh Hashana 24a) that the declaration is structured according to the verses in Vayikra 23 2 and 44. In verse 44, Moshe declares the holidays, and thus the start of the ...


The Rambam is trying to explain how the end of the year "drifts" across the days of the week. The lunar year (twelve lunar months) is roughly 354.3 days. 350 is divisible by seven (hence "groups of seven"), so the only thing that decides what day of the week the year ends on is the remainder. --- the extra 4.3 days. Thus, if the end of the previous year ...

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