
zeugen
to father
For a man to biologically produce a child.
Er hat mit seiner Frau zwei Kinder gezeugt.
He fathered two children with his wife.
to father / to testify
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to father
For a man to biologically produce a child.
Er hat mit seiner Frau zwei Kinder gezeugt.
He fathered two children with his wife.

to testify to
To be evidence or a sign of something; to clearly express or show something.
Sein detailliertes Wissen zeugt von intensivem Studium.
His detailed knowledge testifies to intensive study.

to testify
To make a statement as a witness in court or before an authority.
Der Nachbar wurde vorgeladen, um in dem Fall zu zeugen.
The neighbor was summoned to testify in the case.
'Zeugen' (to father / to testify) is related to 'der Zeuge' (witness) and 'das Zeugnis' (testimony/certificate). The shared idea is bringing something forth or proving something—whether a child, a statement, or an achievement.
Seine guten Noten sind ein Zeugnis für seinen Fleiß.
His good grades are testimony to his diligence.
In the meaning 'ein Beweis sein für' (to be evidence of), 'zeugen' (to testify to) is always used with the preposition 'von' and the dative. The structure is: 'Etwas zeugt von etwas' (Something testifies to something).
Ihre schnelle Reaktion zeugt von großer Professionalität.
Her quick reaction testifies to great professionalism.
The meaning 'eine Aussage machen' (to make a statement) is found almost exclusively in a legal context. Typical formulations are 'vor Gericht zeugen' (to testify in court) or 'gegen jemanden zeugen' (to testify against someone).
Er musste vor Gericht gegen seinen ehemaligen Freund zeugen.
He had to testify in court against his former friend.
In the meaning 'ein Kind hervorbringen' (to produce a child), 'zeugen' (to father) is a rather formal or biological term. It is often used in written or formal contexts.
Laut Testament hat der Verstorbene drei Kinder gezeugt.
According to the will, the deceased fathered three children.
to book / prove / top
Belegen and von etwas zeugen can both show that a statement or situation is true. Belegen emphasizes concrete evidence for a claim, whereas etwas zeugt eher als Anzeichen oder Ausdruck davon (serves more as an indication or expression of it). For direct proof, belegen is appropriate; for recognizable traces or signs, zeugen von is more appropriate.

Die nassen Straßen zeugen von dem starken Regen.
The wet streets are evidence of the heavy rain.
Die Messwerte belegen, dass der Wasserstand stark gestiegen ist.
The measurements prove that the water level has risen sharply.