Tosafot probe the Gemara's assumption about what the mishnah proves and why the sugya needs to analyze whether there are one or two cases. They sharpen the logic behind why seeing a lost object does not itself establish acquisition.
בראיה בעלמא קנה - אע"ג דקתני במתני' (לקמן בבא מציעא דף ט:) ראה את המציאה ואמר לחבירו תנה לי דלא קנה בראיה וכן ראה את המציאה ונפל עליה (לקמן בבא מציעא דף י.) קתני נמי דלא קני מצי למדחי כיון דאמר תנה לי או שנפל עליה גלי דעתיה דלא ניחא ליה למקני עד שיגיע לידו: דבראיה בעלמא לא קני - והא דאמרי' בפרק הבית והעלייה (לקמן בבא מציעא דף קיח. ושם) הבטה בהפקר קני היינו שעשה מעשה כל דהו כגון שגדר גדר קטן: והא זה וזה קתני - איכא דוכתי דפריך כי האי גוונא ואיכא דוכתי דלא פריך: [עי' תוס' בכורות דף לא: ד"ה א"כ]:
He acquired [it] through sight. The Gemara is suggesting that if the Mishna had only written - אני מצאתיה - I found it - one might think that the litigant is claiming that I saw it first and that by seeing it, he acquires the garment. The second phrase of the Mishna - כולה שלי - it is all mine - indicates that seeing is insufficient for acquiring a lost object. One must actually lift up the garment to acquire it. Tosfos will quote two Mishnayos where it is evident that one cannot acquire a lost object by seeing it. If so, why was it necessary for our Mishna to repeat the same ruling? The Mishna on 9b: Even though the Mishna teaches (below 9b): [Ruvain] who saw a lost object and said to [Shimon] “give it to me”. The Mishna rules that Shimon who was asked to pick it up may acquire it for himself. We see that [Ruvain] did not acquire it by seeing it, since Ruvain who asked Shimon to pick it up, obviously was the first to see it and even so Shimon may lift it up for himself. It is evident that Ruvain did not acquire it by seeing it. The Mishna on 10a: So too, we learned in another Mishna: [Ruvain] saw a lost object and fell on it, but did not lift it up and Shimon comes and lifts it up, the Mishna teaches us that [Ruvain] did not acquire it since he did not make a proper act of acquisition. But Ruvain did see it first? Once again we see that seeing the lost object is not a way of acquiring it. Why does our Mishna need to stress this lesson? [The Gemara] could have deflected the proof from those Mishnayos, that seeing is not an act of acquisition, by saying, since [Ruvain] said to Shimon in the Mishna on 9b “give it to me”, or in the Mishna on 10a he fell on it, he is showing his mindset, that he is not satisfied to acquire it by any method of acquisition until it actually reaches his hand. It is only then that those Mishnayos rule that seeing the lost object is not a valid method of acquiring it. However, when one did not in any way indicate that he does not want to acquire the lost object by seeing it, it may very well be that seeing is a proper way of acquiring it. Our Mishna must therefore teach us that even when there is no indication that he is dissatisfied to acquire it by seeing, he cannot acquire it. [H]e does not acquire [it] through sight. The Mishna teaches us that by merely seeing a lost object, one does not acquire it. There seems to be a contradiction to this ruling from a Gemara later on 118a. The Gemara there quotes a Mishna in Shekalim which cites a dispute about whether those who guard the growing barley in the Shemittah year must be paid for their labor or not. The first Tanna holds that they must be paid. Otherwise, the barley they are guarding would belong to them and the barley for the Omer offering must belong to the public, not to an individual. R’ Yose holds that the guards can work for free if they so desire. The Gemara explains that the first Tanna holds that “guarding” the ownerless barley is a way of acquiring it. If the guards are not paid from public funds, they become the legal owners and the Omer offering must be owned by the public. R’ Yose holds that “guarding” the ownerless barley is not an acceptable method of acquiring it. Thus, even if the guards are not paid, the barley does not become their property and may be used for the Omer offering. The Gemara continues to suggest other ways of explaining the dispute, but they all focus around whether “guarding” the growing barley is an acceptable method of acquisition. The Gemara uses the expression הבטה which literally means looking or watching. Tosfos understands that this is the same as ראיה - seeing, of our Gemara. Thus, we have what appears to be a contradiction. That which [the Gemara] says in Perek Habayis Vehaliyah (below 118a): “watching” an ownerless item is an effective act of acquisition, that is when he did some minimal action, such as constructing a small fence around the barley. Even though he did nothing at all to the barley, “watching” or “guarding” it is an effective act of acquisition, but by merely seeing a lost object and taking no action whatsoever, one does not acquire the object. But doesn't [the Mishna] teach: this [one] and this [one]? The Gemara suggested that even though the Mishna uses the phrase אני מצאתיה - I found it, and the phrase כולה שלי - it is all mine, it is not speaking of two different cases. Each of the litigants is simply saying - I found it and it all mine. The Gemara then rejects this suggestion because the Mishna did not need to repeat the words זה אומר - this one says, twice. The Gemara then concludes that the Mishna is in fact speaking of two distinct cases. Tosfos comments: There are places throughout the Talmud, that [the Gemara] asks this question: Why did the Mishna need to repeat “this one says”? There are places where [the Gemara] does not ask this question. [See Tosfos Bechoros 31b 7-8 (ד'ה אם כן] where Tosfos elaborates on this subject and cites many more instances throughout the Talmud. Tosfos does suggest some reason for this inconsistency.