Final answer:
Archimedes is portrayed as a problem-solver using his intellectual prowess during the Siege of Syracuse to create defensive war machines and running through the city exclaiming 'Eureka!' after discovering the Archimedes' principle. The Sand Reckoner illustrates his devotion to intellectual pursuits during conflict, with no clear expression of his wartime feelings.
Step-by-step explanation:
In both "Archimedes and the Siege of Syracuse" and The Sand Reckoner, Archimedes made significant contributions to his city during wartime, though his attitudes were not explicitly detailed in the provided passages. In the context of history, during the Seige of Syracuse, Archimedes applied his genius to invent war machines to defend his city against the Romans. While not directly about his feelings toward war, it can be inferred that he was focused on the problem-solving aspect, using his knowledge of physics and engineering to impact the situation. His legendary exclamation 'Eureka!' after discovering a method to determine the purity of gold, as mentioned in the provided text, shows his passion for problem-solving and intellectual discovery, rather than a direct reaction to wartime.
The Sand Reckoner is a work that dealt with the mathematical calculation of the grains of sand to fit in the universe, which does not directly relate to his wartime experiences or views on war. However, it does demonstrate his dedication to intellectual pursuits even during periods of conflict. There's no direct evidence of his feelings about the war in this text either.
In conclusion, while the challenges of wartime influenced Archimedes' work, the provided texts focus more on his intellectual endeavors and problem-solving abilities rather than his personal sentiments on war. Both passages illustrate Archimedes' dedication to his work and city during wartime but do not clearly articulate any changes in his attitudes towards war.