tosyokan de ha mou sukosi tiisaku hanasite kudasai.

では here is で + は.

• で marks the place where an action happens.
• は adds a topic/contrast nuance.

So 図書館では means something like:

• in the library
• as for in the library
• at least in the library

Using は can make the sentence sound slightly more context-based or contrastive, as if the speaker is saying:

• In the library, please speak a little more quietly.

If you said 図書館で, it would still be understandable, but 図書館では feels more natural when giving a rule, reminder, or polite correction about behavior in that place.

もう少し means a little more.

In this sentence, it does not mean continue speaking for a little longer. It means:

• make it a little more quiet
• speak a bit more softly

So the idea is that the person is already speaking, but the speaker wants them to lower their voice a little further.

This is a very common pattern:

• もう少しゆっくり話してください。 = Please speak a little more slowly.
• もう少し大きく書いてください。 = Please write a little larger.

Because 小さく is the adverbial form of the い-adjective 小さい.

• 小さい = small
• 小さく = small-ly / in a small way

Japanese often turns い-adjectives into adverbs by changing い to く.

So:

• 小さい声 = a small/quiet voice
• 小さく話す = to speak quietly / in a low voice

Even though 小さい usually means small, with voices and sound it can mean quiet or soft.

Yes, it is understandable, but many learners notice that it sounds a bit literal.

Common natural alternatives include:

• もう少し静かに話してください。 = Please speak a little more quietly.
• もう少し小さい声で話してください。 = Please speak in a slightly quieter voice.

So 小さく話してください is not wrong, but 静かに話してください or 小さい声で話してください may sound more common in everyday Japanese.

話してください is:

• 話す = to speak
• 話して = the て-form
• ください = please do ...

So 話してください means please speak.

This is a standard polite request pattern:

• 見てください。 = Please look.
• 読んでください。 = Please read.
• 待ってください。 = Please wait.

In your sentence, 小さく話してください means please speak quietly/softly.

〜てください is a polite and straightforward way to ask someone to do something.

It is commonly used for:

• instructions
• requests
• reminders
• public notices

So this sentence sounds like a polite request, but it can still feel somewhat direct depending on context.

Softer alternatives exist, such as:

• 話してもらえますか = Could you speak...?
• 話していただけますか = Would you be able to speak...?

But for signs, staff instructions, or clear requests, 〜てください is very common.

The sentence is ordered like this:

• 図書館では = in the library / as for in the library
• もう少し = a little more
• 小さく = quietly / more softly
• 話してください = please speak

Japanese usually puts the verb at the end, and words that describe the action come before it.

So the structure is very normal:

[place/topic] [degree] [manner] [verb]

That is why 小さく comes before 話して.

Yes, at least a little.

図書館では can suggest something like:

• In the library, please speak more quietly.
• maybe not everywhere, but especially here

This contrast can be weak or strong depending on context. It does not always mean the speaker is directly comparing the library with another place, but it often gives that flavor.

For example, it can feel like:

• You can talk normally elsewhere, but in the library, please lower your voice.

No. In normal Japanese writing, this would usually be written without spaces:

図書館ではもう少し小さく話してください。

Spaces are often added in textbooks or beginner materials to make the parts easier to see.

So the spaces are just a learning aid, not standard written Japanese.

Yes, literally that is close to what it says, and that is why it means speak more softly/quietly.

Japanese often uses small and big for voice volume:

• 声が小さい = the voice is quiet
• 声が大きい = the voice is loud

So 小さく話す naturally connects to the idea of lowering your voice.

Yes, it is polite enough in many situations, especially if:

• a staff member is speaking to a visitor
• someone is giving a reminder
• it appears on a sign or notice

However, because it is a direct request, it may sound a little firm depending on tone and situation.

A softer spoken version might be:

• 図書館では、もう少し静かに話してもらえますか。
• 図書館では、もう少し小さい声でお願いします。

So the original sentence is polite, but not the softest possible wording.