Resources for Beitzah daf 23

1.        The גמרא says that there is no prohibition of הבערה on cooking spices used as a fragrance. רש"י explains this is so because it is only a הבערה כלאחר יד. See תוספות ד"ה על גבי חרס who quotes the ריב"א who disagrees and says that it is a real הבערה, but nevertheless is still מותר since we are following רבי יוסי who holds that הבערה was ללאו יצאת (taken out of the פּסוק of לא תעשה כל מלאכה to be just a לאו and not a מלאכה). Therefore, it is not forbidden on יו"ט since there is only a לאו on שבת, not on יו"ט. Even though we don’t pasken like רבי יוסי, the ריב"א that תוספות quotes has far reaching implications. See the שו"ת חתם סופר או"ח סימן קנ"ב who says that based on this פּסוק we can allow שביתת בהמתו on יו"ט since it is not one of the 39 מלאכות, and therefore not forbidden on יו"ט.  Another proof to this idea is as follows: our גמרא says that רבי אלעזר בן עזריה allowed his cow to go out carrying something between its horns while the חכמים did not allow that. רש"י comments that this must have been on Shabbos. See the קובץ שיעורים on our דף who says that this is because רש"י holds that there is no issue of שביתת בהמתו on יו"ט. However, see the טור או"ח סימן תקי"ב who brings this הלכה by יו"ט as well. See the ב"ח סימן תצ"ה ד"ה ומ"ש בשם ר"י who wants to prove that even the רמב"ם agrees that there is no איסור of שביתת בהמתו on יו"ט since he writes that the only issue with having an animal carry a load on יו"ט is that it is כדרך חול.

2.        The גמרא says that רבי אלעזר בן עזריה had 13,000 cows of מעשר each year. See תוספות תליסר ד"ה who asks how he could be giving מעשר בהמה after the חורבן?  תוספות has several answers. See theריטב"א, שבת דף נ"ד: ד"ה הא דאמרינן who says an astounding חידוש in our גמרא. He says that while it was given as מעשר בהמה, he did not actually call it מעשר but rather just gave it to the כהנים so as not to appear as one who isמשייר אצלו מתנות כהונה. There are two חידושים here: 1) While the Torah never says so explicitly, according to almost all ראשונים, מעשר בהמה is notמתנות כהונה (see רש״י ויקרא כז. לב, תוספות בבא מציעא דף ז ד"ה מפריש  and also the רמב''םבפרק ו מהלכות : בכורות הלכה ד). It is simply brought as a שלמים and eaten by the בעלים. The ריטב"א clearly disagrees and holds that it is מתנות כהונה. 2) רבי אלעזר בן עזריה was himself a כהן! There is a discussion in the ראשונים as to whether a כהן is חייב in מעשר בהמה, as well as whether one כהן must give another כהן his מתנות כהונה. The ריטב"א seems to hold the answer to both questions is yes.

3.        The גמרא says that רבי יהודה allowed a person to push a wagon on dirt since it is not considered חפירה because the dirt is just pressed and not dug up. See the שמירת שבת כהלכתה, פּרק כ"ח הערה צ"ט who says that even though we pasken this way, we could question whether one is allowed to turn a stroller on dirt to the left or to the right since the pivot of the wheel might cause some dirt to be dug up. (בפּשטות, one would think this must be allowed since the גמרא does not make any qualifications about not turning the wagon). He says in the name of Rav Shlomo Zalman Auerbach זצ"ל that it is permitted since it is at most a פּסיק רישא דלא ניחא ליה, מקלקל, with a חפירה כלאחר יד. He also mentions that it may not be a פּסיק רישא at all - ע"ש.

4.        The גמרא mentions that one cannot make clothes smell nice on יו"ט due to the prohibition of מוליד ריחא. See the ט"ז סימן תקי"א ס"ק ח who says that there is a מנהג to add a nice smelling substance to the water that the כהנים use to wash their hands on יו"ט and he says that this should not be allowed. See the חכם צבי סימן צ"ב who disagrees and says that we only find מוליד ריחא by clothes and houses. It does not apply to humans or food.