Cetvelin kenarına biraz yapıştırıcı bulaşmış; ataşı çıkarırken fark ettim.

This is a standard Turkish possession pattern:

• cetvel-in = of the ruler
• kenar-ı = its edge
• kenar-ı-na = to its edge

So cetvelin kenarına literally means to the ruler’s edge.

Turkish often marks both parts of this kind of relationship:

• the possessor gets the genitive: cetvelin
• the possessed noun gets a possessive suffix: kenarı

Then the case ending is added after that: kenarına.

Because bulaşmak commonly takes the dative case for the thing or surface that something gets onto.

So:

• kenarına bulaşmak = to get onto the edge
• kenarında = on/at its edge

In other words, -a / -e here marks the target surface. Turkish treats this idea more like getting onto something than simply being on something.

A rough contrast:

• Cetvelin kenarında yapıştırıcı var. = There is glue on the edge of the ruler.
• Cetvelin kenarına yapıştırıcı bulaşmış. = Glue has gotten onto the edge of the ruler.

Bulaşmak means things like:

• to get on
• to smear onto
• to rub off onto
• to become stuck/smeared on

So biraz yapıştırıcı bulaşmış means some glue has gotten on / got smeared on.

It is not the same as deliberately applying glue. It suggests accidental contact or transfer.

The ending -mış often gives a sense of:

• discovery after the fact
• inference from visible evidence
• apparently / it turns out

That fits this sentence well: the speaker notices the glue later, while removing the paperclip.

So bulaşmış is like:

• it turns out some glue got on it
• some glue had gotten on it
• apparently some glue got smeared on it

If you used bulaştı, it would sound more like a plain, direct past statement: some glue got on it.

Because yapıştırıcı here is a mass noun, like glue or adhesive in English.

After biraz, Turkish normally uses the singular:

• biraz su = a little water
• biraz para = a little money
• biraz yapıştırıcı = a little glue

So plural would sound wrong here unless you were talking about different kinds of adhesives.

Here it is a noun: glue / adhesive.

But yes, yapıştırıcı can also be an adjective in other contexts, meaning something like adhesive or sticking.

In this sentence, because it comes after biraz and functions as the thing that got smeared on the ruler, it is clearly a noun.

Ataş means paperclip.

The form ataşı is:

• ataş
  • -ı (definite accusative)

So it means the paperclip as a specific direct object.

That makes sense because the speaker is talking about removing a particular paperclip, not just any paperclip in general.

Compare:

• ataş çıkarmak = to remove a paperclip / paperclips in general
• ataşı çıkarmak = to remove the paperclip

It comes from çıkarmak, which means to take out / remove.

çıkarırken means:

• while taking out
• while removing
• as (someone) was removing

The ending -ken means while / when doing. In this form, it attaches to a present-habitual type base, giving çıkarırken.

So:

• ataşı çıkarırken = while removing the paperclip

Yes, in this sentence the understood subject is the same as in fark ettim: I.

So the meaning is:

• I noticed it while I was removing the paperclip.

Turkish often leaves subjects unstated when they are clear from context.

If the subject of çıkarırken were different, Turkish would normally make that clearer.

Because Turkish usually drops subject pronouns when the verb already shows the person.

• fark ettim = I noticed

The -im ending already tells you the subject is I, so ben is unnecessary unless you want emphasis or contrast.

For example:

• Ben fark ettim. = I noticed / I was the one who noticed.

Without emphasis, just fark ettim is more natural.

Because fark etmek is a compound verb:

• fark = difference / distinction
• etmek = to do, to make

Together, fark etmek means to notice / realize.

In Turkish, many common verbs are built this way, and the second part is the one that gets conjugated:

• fark ettim = I noticed
• fark ediyor = he/she is noticing
• fark edecek = he/she will notice

So this is normal and very common.

A rough breakdown is:

• Cetvelin = of the ruler
• kenarına = to its edge
• biraz yapıştırıcı = a little glue
• bulaşmış = has apparently gotten smeared / got on
• ataşı çıkarırken = while removing the paperclip
• fark ettim = I noticed

So the Turkish structure is roughly:

To the ruler’s edge, a little glue had gotten on; I noticed while removing the paperclip.

That sounds awkward in English, but it shows how the Turkish sentence is built.