Ok, so we have Rome and we have jaguars. There's stone nearby and I followed obsolete's suggestion to have a go at the Pyramids, so I switched to Masonry. I also straightaway decided that we should get the cities connected. For this, Antium had to fall.
I wondered if it was a good deciscion to keep Antium as all roads were leading to Rome, but it became a decent hybrid city (hammers and commerce) later on.
I did not make peace with Rome and took more cities for gold mainly as tech pace was rather slow. I did take my time to snatch a lot of workers. In the screenshot below there were 2 workers on the same tile as the Roman archer, which I captured the same turn.
I used my Great General to create a super-Jaguar city raider, although settling him would have been better with Representation. Rome was building walls in the remaining cities, so I thought I needed such a super-unit.
I made sure to settle towards the south soon enough and first settled near the corn/pigs/ivory on the river. Without sailing and roads it still was connected right away. I don't understand the mechanics behind it, but I guess it has something to do with being connected through cultural borders?
I liked how I timed it as Frederick was settling northwards. I settled another city to the southeast. I though a long time on it's exact location, but decided to make it a coastal city to have at least 1 coastal city.
I continued snagging Roman workers with woodsman II jaguars and razing cities for gold.
The captured workers were sent to help chop the Pyramids, which I finished in Rome at 525 BC (turn 94).
After Pottery and Writing I went for Alphabet. Only later did I realize I should have gone for Fishing - Sailing first for the trade routes with Frederick (or build roads to the south). I mistakenly though that trade routes are always a two-way street
Alphabet was taking too long for my taste and I grew impatient and I decided to finish of Rome for more gold (I played until this point before reading Dhoomstriker's suggestions).
I guess I should have kept Julius alive, but at least I got 7 workers from him.
I started to lay down some cottages and finished Alphabet at 150 BC (turn 109). Hinduism also spread to me and I switched right away. I love the spiritual trait as you don't have to worry about anarchy.
After Alphabet I went for Mathematics. Frederick wasn't going to trade anything useful, so I decided that I would take it another way. I noticed Frederick was researching Construction, so I sent a spy to one of his cities and left him there a couple of turns to do this:
With the help of the espionage slider I had just enough points to steal Construction. With running a lot of scientists I teched Fishinh and Sailing both in 1 turn and continued with Currency. After that came Code of Laws and I build Markets and Sacrificial Altars in most cities, while also settling 2 more cities near the German border.
As Frederick was spreading Hinduism in all my cities I took a detour into Polytheism - Monotheism - Priesthood before finishing Code of Laws. Priesthood wasn't really needed and I mainly wanted to switch to Organized Religion, but the cheap temples might be needed later.
I also researched Horseback Riding and Calendar and this is where I am now.
I have scouted the German lands and it looks like I have a monopoly on Ivory. I guess war elephants and catapults next could be good to take on Frederick.