How to properly reference the century one lived in when their lives cross from B.C. to A.D
Something seems wrong with this question. If someone's life spans over two different centuries, why would you ask how to reference "the century" one lived in?
Anyway, sorry if that was a petty quibble. I do understand your question. You can say Shakespeare lived during the 16th and 17 centuries, but what do you say when referring to a period overlapping both Common Era and before Common Era.
Well as far as I've seen writers probably either avoid it or have no reason for such an expression, as they will probably say something like "He lived from 59 BC to 17 AD."
However if you really want to use the construction "He lived during the X and Y centuries", though I'm not sure I'm recommend it, you could say:
- "He lived during the first centuries BC and AD."
Quotes:
... writings of the two great Jewish scholars Hillel (1st century BC)
and Philo of Alexandria (1st centuries BC and AD), and in the Analects
of Confucius (6th and 5th Centuries BC).
Believers and Brothers:
A History of Uneasy Relationship, 2009
In the 1st centuries BC and AD, terracotta lamps were mainly produced
in Italy and were mass-exported.
Handbook to Life in Ancient
Rome, 2004
... the six Dacian Fortresses of the Orăștie Mountains, in Romania,
were created in the 1st centuries BC and AD as protection against
Roman conquest,...
Dacian Fortresses of the Orăștie Mountains
(Wikipedia article)
Orlo bifido pans were common in the 1st centuries B.C. and A.D., but
their popularity declined thereafter;
Hellenistic Pottery: The
Plain Wares, 2006
If you search yourself for this construction, there is no shortage of it in use, both generally on the net and in book publications. As I said though, I'm not particularly recommending it.