EMB140 FO RPTS OVERSHOOTING RWY 17C ONTO RWY 17R CTRLINE DURING VISUAL APCH TO DFW.

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WHEN ON THE APCH INTO RWY 17C AT DFW; WE WERE ON A 320 DEG HDG WHEN WE RECEIVED A TCAS ALERT (TA). IT WAS TFC LNDG ON RWY 17L. AT THE TIME OF THE ALERT; WE WERE 4400 FT AND DSNDING TO 4000 FT. PROB WAS THAT THE TCAS SHOWED THE TFC TO BE ONLY -1100 FT BELOW US. SO I REALIZED THAT IF I CONTINUED THE DSCNT TO 4000 FT THEN WE WOULD ONLY HAVE 700 FT SEPARATION. I SLOWED THE DSCNT BY MANUALLY FLYING THE PLANE TO THE POINT OF ALMOST LEVELING OFF. I LOOKED OUT MY 'DV' WINDOW AND LOCATED THE TFC WHICH WAS GOING RIGHT BENEATH US ON APPROX 220-240 DEG HDG. I HAD THE ACFT IN SIGHT FOR JUST A SHORT PERIOD WHEN IT WAS ON THE R SIDE OF THE ACFT; BUT LOST IT WHEN THEY CROSSED RIGHT BELOW US. I TOLD THE CAPT THAT I SAW THE TFC. I MEANT I HAD IT IN SIGHT FOR TCAS PURPOSES NOT FOR VISUAL APCH PURPOSES. ABOUT THAT TIME ATC GAVE US A HDG 270 DEGS OR 280 DEGS. THE CAPT ACKNOWLEDGED THE CLRNC AND ALSO TOLD ATC WE HAD TFC IN SIGHT. THEY THEN CLRED US FOR THE VISUAL APCH WHEN I HAD REALLY NO IDEA WHERE THE OTHER ACFT WAS (BTWN THE 2 DIVERGING COURSES AND THE FACT THAT I WAS ON THE R SIDE OF THE ACFT WITH TFC GOING AWAY FROM US). I WAS BEING CAUTIOUS WHEN I DECIDED TO TURN IN TOWARDS THE RWY 17C BECAUSE I WASN'T REALLY SURE WHERE THE ACFT WAS EXCEPT FOR THE TCAS DISPLAY. WHEN I STARTED THE TURN FOR RWY 17C; THE LOC WAS NOT EVEN 'ALIVE' YET. BTWN TURNING SLOWLY AND LOOKING FOR TFC; OUR TURN WAS COMPLETE WHEN WE WERE APPROX CTRLINE FOR RWY 17R. A FEW SECONDS AFTER STARTING OUR TURN. APCH ASKED US IF WE HAD STARTED OUR TURN YET AND BY THAT POINT WE WERE 50 DEGS INTO OUR TURN FROM W.