Hello Cathy,
I did some research on these names. But I cannot answer your questions, but I found their official bann (intention) to marriage on December 17, 1639 in Amsterdam.
I cannot even read the record, because it is very old Dutch.
The only I can read is the age of Abraham. He was on that date, 29 years old.
On the top of this record you see the date: 17 December 1639.
After the intention to go marry, the official marriage was about 2 weeks later. That correspondents with your date, January 4, 1640.
The second part is the intention of their marriage.
Abraham de Beek and Geertruijt Gerrits.
The image is attached.
Regards,
Robert A. van Duuren
The Netherlands