Ut primum amicus canitiem videt, galericulum quaerit.

Here ut primum is a fixed temporal expression meaning as soon as.

So in this sentence, ut is not introducing a purpose clause like ut veniat (so that he may come). Instead, ut primum works together as one unit and tells you when the main action happens.

A useful way to read the structure is:

• Ut primum ... videt = as soon as ... sees
• galericulum quaerit = he looks for ...

Because primum is being used adverbially, not as an adjective modifying a noun.

Latin often uses neuter singular adjective forms as adverbs. So primum here means something like first or at the first moment, which helps create the sense as soon as.

So you do not need to look for a noun that primum agrees with.

Because canitiem is the accusative singular, and it is the direct object of videt.

The friend is the one doing the seeing, and canitiem is the thing seen.

So the basic relationship is:

• amicus = subject
• videt = sees
• canitiem = direct object

This noun is from canities, a feminine fifth-declension noun.

Because Latin often uses canities as a collective singular.

English can also do something similar with words like hair:

• His hair is gray
  not usually
• His hairs are gray

So even if the idea involves many gray hairs, Latin can still use the singular noun canities to refer to gray hair or hoariness in general.

Yes.

Amicus is the subject of videt, and it is also understood as the subject of quaerit. Latin often leaves out a repeated subject when it is obvious from the context.

So the sentence is effectively:

• Ut primum amicus canitiem videt, (amicus) galericulum quaerit.

The second amicus is omitted because it would be unnecessary.

The verb ending helps a lot.

Both videt and quaerit are third-person singular forms, meaning he/she/it sees and he/she/it seeks. Since amicus has already been given as the subject, Latin does not need to repeat a separate word for he.

This is very common in Latin. English usually needs a subject pronoun, but Latin often does not.

Here galericulum is accusative singular, the direct object of quaerit.

The form ends in -um because it is a second-declension neuter noun. For neuter second-declension nouns:

• nominative singular = -um
• accusative singular = -um

So the form looks the same in both cases. You tell its function from the sentence structure:

• quaerit needs an object
• galericulum is the thing being sought

The present tense here can express a general or customary action.

So the sentence is not necessarily describing only one event happening right now. It can mean something like:

• Whenever / as soon as a friend sees gray hair, he looks for ...

Latin often uses the present in this way for vividness or general truth.

Because Latin word order is much more flexible than English word order.

English depends heavily on position:

• subject + verb + object

Latin depends much more on endings. That means Latin can move words around for emphasis, rhythm, or style.

This sentence is arranged very naturally in Latin:

• Ut primum amicus canitiem videt = first, the time-setting clause
• galericulum quaerit = then, the main action

Also, putting the object before the verb is extremely normal in Latin:

• canitiem videt
• galericulum quaerit

In this meaning, it normally takes the indicative.

That is why you see videt, not a subjunctive form.

So here:

• ut primum = temporal conjunction
• videt = indicative verb in the subordinate clause

A learner should be careful not to assume that every ut automatically leads to a subjunctive.

Quaerit comes from quaerere, which usually means to seek, look for, or try to find.

So it suggests the beginning of a search, not necessarily successful finding.

That is an important distinction:

• quaerit = he looks for / seeks
• not automatically he finds

Yes: the ending -culum is a diminutive-type ending.

That often suggests something small, or it may simply be the normal lexical form of the noun by the time it appears in actual usage. So a learner may notice that the word has a diminutive shape, even if the exact nuance is not the main point of this sentence.

In other words, the form may originally suggest something like a little version of the base noun, but context determines how strongly that idea is felt.