He went in one of them, and touched טהרות, etc. - הלך באחד מהן ועשה טהרות
Summary:
The two people who walked on these ב' שבילין require טבילה והזאה to prevent any difficulties that may arise if they both touched the same person or תרומה.
There is a doubt whether it entered or not; this is the same as ‘a valley’ - ספק על ספק לא על היינו בקעה
Summary:
תוספות has two questions on the ruling that ספק על is comparable to בקעה. First that by חמץ there is a חזקת בדוק (but not by בקעה [which is a רה"י]), and second, why previously בדיקת חמץ was compared to ספק טומאה ברה"ר, and here it is compared to ספק טומאה ברה"י.
A doubt whether it entered; is טהור, etc. - ספק ביאה טהור
Summary:
A ספק ביאה is considered a ספק ספיקא. According to ר"א we can only derive from סוטה that a ספק טומאה ברה"י is טמא, not a ס"ס. However, the חכמים maintain that the תורה teaches us that any ספק in רה"י is treated as a ודאי.
It entered, he searched and did not find; this is a dispute between ר"מ and the רבנן, etc. - על ובדק ולא אשכח פלוגתא דרבי מאיר ורבנן
Summary:
According to רש"י the case of על ובדק is where the owner performed ביטול and ר"מ ורבנן agree that this is sufficient (and תוספת agrees with the ruling). According to תוספות the case is where he was not מבטל; and according to ר"מ he must be מבטל.
חולין and מעשר שני are intermingled one with the other -
חולין ומעשר שני מעורבים זה בזה
Summary:
רש"י maintains that we bring outside סלעים and are מחלל the מעות on סלעים. However תוספות argues that according to רש"י he can be מחלל the money from the מעות in the mixture. The ריב"א asks that one is not permitted to be מחלל money for money.
He placed ten and found nine; it is a dispute between רבי and the רבנן, etc. - הניח עשר ומצא תשע פלוגתא דרבי ורבנן
Summary:
רבי maintains that (in the case of הניח י ומצא ט) he needs to find but the one piece of חמץ that is missing, because רבי rules מנה הניח ומנה מוטל (therefore only one was lost) and קבר שאבד הוא קבר שנמצא (therefore the found loaf is the lost loaf. The loaves were קשורים זב"ז (otherwise the חכמים would also agree that [only] one loaf is missing) and nevertheless we assume that a קטן may have untied them.
