"I constantly felt (as I suppose many an ambitious girl has felt) a thumping from within unanswered by any beckoning from without"

In this quote, Anna Julia Cooper is revealing her individual experience as an ambitious woman. She describes a feeling of restlessness and drive, represented by the word "thumping," that comes from within her. This internal inspiration is not met any external opportunities or motivation, represented by the absence of "beckoning from without." Cooper suggests that this is a common experience for enthusiastic ladies, who may feel a strong desire to attain and succeed, but are not provided the exact same chances or support as their male equivalents. This quote highlights the difficulties and barriers faced by enthusiastic women in a society that often restricts their capacity.