I will simply repeat what I said on the previous page: The words door, na, alvorens, om, in plaats van and zonder can mark the beginning of a short subclause. If they do, the subclause always contains a "te + infinitive" construction. You can read more about this under short subclauses.
The word 'om' is a special case and was discussed on the previous page. We will now look at alvorens, door, in plaats van, na and zonder.
alvorens prior to
| door by
| in plaats van instead of
| na after
| zonder without
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Alvorens, door, in plaats van, and zonder
The construction is very simple: After the prepositions mentioned above follows 'te' + infinitive.
| Alvorens te beginnen, moet men de stekker in het stopcontact steken.
| Prior to starting (on it), one has to put the plug in the socket.
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| Door elke ochtend een half uurtje te lopen, zag hij er tien jaar jonger uit.
| By walking ten minutes every morning, he looked ten years younger.
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| In plaats van te helpen, maakten ze het hem juist moeilijker.
| Instead of helping (out), they just made it more difficult for him.
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| Ze staken de straat over zonder uit te kijken.
| They crossed the street without looking out.
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Na
A short subclause that begins with na always has a perfect tense. This means that we are dealing with a 'te + infinitive + past participle' construction. See also past participle.
In other words, we do not use the construction 'after dining with our neighbours', but only 'after having dined with our neighbours'.
| De timmerman kwam thuis na daar te hebben gewerkt.
| The carpenter came home after having worked there.
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| Na een uur te hebben rondgelopen, gingen we..
| After having walked around for an hour, we went... (lit)
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