Answer: The historian researching the trans-Atlantic slave trade in the period 1600-1800 would find the following source most useful for determining patterns in the points of origin, the destinations, and the numbers of slaves involved in the trade:
C) Records of the cargoes of Spanish and British ships in the trans-Atlantic trade.
These records, including ship manifests, logs, and other documentation related to the slave trade, provide detailed information about the origins of enslaved individuals, the destinations to which they were transported, and the numbers of slaves involved in each voyage. These records offer valuable data for studying the trans-Atlantic slave trade, understanding its patterns, and assessing its historical impact.
While the other sources mentioned (A, B, and D) may provide valuable information about aspects of the trans-Atlantic slave trade or its consequences, they are not as directly related to determining patterns in the origins, destinations, and numbers of enslaved individuals involved in the trade.