hereupon / onto this
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hereupon / after this
Expresses a sequence in time and means 'after that' or 'subsequently.' It is mainly used in written language.
Der Redner beendete seine Einführung; hierauf begann die eigentliche Debatte.
The speaker finished his introduction; hereupon the actual debate began.
'Hierauf' is a pronominal adverb, made up of 'hier' (here) and 'auf' (on / onto). It literally means 'onto this' and can refer to a time or a place.
Zuerst kam die Theorie, hierauf folgten die praktischen Übungen.
First came the theory; after this came the practical exercises.
When 'hierauf' stands at the beginning of a sentence, the conjugated verb follows directly. This word order (inversion) is typical for adverbs in position 1.
Der Vertrag wurde geprüft. Hierauf leisteten beide Parteien ihre Unterschrift.
The contract was reviewed. Hereupon both parties provided their signatures.
In its temporal meaning ('danach' = after that), 'hierauf' belongs to formal written language. It is rarely used in spoken language.
Der Vorstand fasste den Beschluss. Hierauf wurden die Mitarbeiter informiert.
The board passed the resolution. Hereupon the employees were informed.
You can tell from context whether a temporal or spatial meaning is intended. If 'hierauf' refers to an event, it is temporal. If it refers to an object, it is spatial.
Zuerst gab es eine Warnung, hierauf folgte die Kündigung.
First there was a warning; after this came the dismissal.
afterward / after that
'danach' and 'hierauf' can both express a chronological sequence: first something happens, then something else follows. 'danach' is the normal word in everyday language and fits almost everywhere. In this use, 'hierauf' also means 'afterward' or 'after this', but it sounds more written and more formal. You are more likely to find it in reports, minutes, or narrative texts. If you want to speak naturally, 'danach' is usually the better choice.
Der Kunde unterschrieb den Vertrag; hierauf begann die Lieferung der Ware.
The customer signed the contract; after this, delivery of the goods began.
Meine Mutter kauft zuerst die Fahrkarten, danach packen wir die Koffer.
My mother buys the tickets first; after that, we pack the suitcases.