
der Ausspruch
saying
A noteworthy, often quoted statement or well-known sentence by a person.
Der berühmte Ausspruch „Der Würfel ist gefallen“ wird Julius Cäsar zugeschrieben.
The famous saying 'The die is cast' is attributed to Julius Caesar.
saying / pronouncement
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saying
A noteworthy, often quoted statement or well-known sentence by a person.
Der berühmte Ausspruch „Der Würfel ist gefallen“ wird Julius Cäsar zugeschrieben.
The famous saying 'The die is cast' is attributed to Julius Caesar.

pronouncement
In a legal context, the formal announcement of a judgment or decision by a court.
Alle warteten gespannt auf den Ausspruch des Richters in diesem komplizierten Fall.
Everyone waited anxiously for the judge's pronouncement in this complicated case.
'Der Ausspruch' (the saying / pronouncement) is the nominalization of the verb 'aussprechen' (to pronounce / to say). It therefore refers to something that was said or pronounced publicly or formally.
Der Zeuge weigerte sich, den Namen des Täters auszusprechen.
The witness refused to say the perpetrator's name.
The meaning depends strongly on the context. If the topic is history, literature, or a famous person, it usually means a quoted statement. In connection with 'Gericht' (court), 'Richter' (judge), or 'Urteil' (judgment), it refers to the legal decision.
„Ich bin ein Berliner“ ist ein berühmter Ausspruch von John F. Kennedy.
'Ich bin ein Berliner' is a famous saying by John F. Kennedy.
When referring to a quoted statement, 'Ausspruch' (saying) is often combined with adjectives such as 'berühmt' (famous), 'bekannt' (well-known), or 'historisch' (historic). You can also say 'einen Ausspruch machen' (to make a statement / saying).
Auf ihrer Reise machte sie einige denkwürdige Aussprüche.
On her trip, she made several memorable remarks.
In the meaning 'Urteilsverkündung' (pronouncement of judgment), 'Ausspruch' (pronouncement) is a technical term, specifically from legal language. In everyday life, you will rarely hear this word in this context.
Der schriftliche Ausspruch des Urteils wird den Anwälten zugestellt.
The written pronouncement of the judgment will be sent to the lawyers.
judgment / verdict
Urteil is the court's legal decision as a whole. In a legal context, Ausspruch refers to its formal pronouncement. Urteil fits when the content and outcome of the proceedings are at issue; when the act of pronouncing the decision is the focus, Ausspruch is more appropriate.

Am Freitag erfolgte der Ausspruch des Urteils öffentlich.
The verdict was formally pronounced in public on Friday.
Am Freitag traf das Gericht sein Urteil.
The court reached its verdict on Friday.