Explanation:

The first true mechanical calculator, known as the Pascaline, was invented by Blaise Pascal in 1642. Pascal developed this device to assist his father, a tax collector, with tedious arithmetic. The Pascaline could perform addition and subtraction directly and multiplication and division through repeated operations. Option (a) Joseph Marie Jacquard is known for the Jacquard loom, which used punch cards to automate weaving patterns, a significant step in programming but not a calculator. Option (b) John Mauchley was a co-inventor of ENIAC, one of the first electronic digital computers, much later in the 20th century. Option (d) Howard Aiken developed the Harvard Mark I, an electro-mechanical computer, in the 1940s. Thus, Blaise Pascal ($ \text{c} $) is correctly credited with the first mechanical calculator.