Tesserae triangulae ad limbum aptantur.

Here tesserae is nominative plural feminine and is the subject of the sentence.

A learner often notices that tesserae could also be genitive singular in isolation, but in this sentence that would not make sense. The clue is the verb aptantur, which is third person plural, so the subject must be plural: the tiles.

Because triangulae is an adjective modifying tesserae, and Latin adjectives must agree with the nouns they describe in:

• gender
• number
• case

So:

• tesserae = feminine plural nominative
• triangulae = feminine plural nominative

Together they mean triangular tiles.

Aptantur is the present passive indicative, third person plural, of aptare.

So its basic sense is:

• they are fitted
• they are joined
• they are adapted
• they are arranged

depending on context.

The ending -ntur is the key sign here: it shows third person plural passive in the present tense.

The passive is used because the sentence focuses on the tiles as the things being acted on, not on the person doing the action.

So:

• Tesserae triangulae ad limbum aptantur = Triangular tiles are fitted to the border

If you wanted an active sentence, you would need to name the doer, for example:

• Artifex tesseras triangulas ad limbum aptat = The craftsman fits triangular tiles to the border

Notice that in the active version tesseras triangulas becomes accusative, because it is now the direct object.

Because the preposition ad takes the accusative case.

So:

• limbus = nominative singular
• limbum = accusative singular

That is why Latin says ad limbum.

With ad, the sense is usually to, toward, up to, or sometimes at depending on context. Here it means something like to the border/edge.

Literally it means to the border or to the edge.

In context, it suggests that the triangular tiles are being fitted along the edge or up against the border of something, such as a mosaic or decorative design.

So although ad often literally means to/toward, English may translate the phrase more naturally as:

• to the border
• at the border
• along the edge

depending on the situation.

We know this from both case and verb agreement.

• tesserae triangulae is in the nominative plural
• aptantur is third person plural

Those match perfectly, so tesserae triangulae must be the subject.

By contrast, limbum cannot be the subject because it is accusative, required by the preposition ad.

Latin word order is much more flexible than English word order because the endings show the grammar.

This sentence has a very natural Latin arrangement:

• Tesserae triangulae = subject first
• ad limbum = prepositional phrase in the middle
• aptantur = verb at the end

Putting the verb at the end is very common in Latin. English usually depends more on word order, but Latin often uses endings instead.

So the sentence could be rearranged in other ways without changing the basic meaning, though the emphasis might shift.

Triangulae comes from triangulus, -a, -um, a first-and-second-declension adjective.

That means it declines like:

• masculine: similar to servus
• feminine: similar to puella
• neuter: similar to bellum

Here the feminine plural nominative form is triangulae, because it agrees with tesserae, which is feminine plural.

So this is a good example of a very common Latin pattern: a noun and adjective matching exactly in case, number, and gender.