The invention that allowed sailors to plot their positions at sea by looking at the stars is the sextant.

Here's why:

* Measuring Angles: The sextant is a precision instrument that measures the angle between two objects, in this case, a celestial body (like a star) and the horizon.

* Celestial Navigation: By knowing the precise time and the angle of a star above the horizon, sailors could use nautical almanacs to calculate their latitude and longitude.

While other tools like the astrolabe and quadrant were used for celestial navigation before the sextant, the sextant was a significant advancement due to its accuracy and portability.