I think the math is OK, but the usual convention is to measure voltage relative to ground, and indeed this is what the Arduino does. So it would measure the voltage across the RTD, that is, the voltage between the top of RTD in the schematic and ground. So if the fixed resistor is R1 and the RTD is R2, then
R2 = R1 / ( Vin/Vout - 1)
See also: Voltage divider - Wikipedia