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Heartbeat stars are a subclass of binary stars with short periods, high eccentricities, and phase-folded light curves that resemble an electrocardiogram. We start from the $\text{𝐺𝑎𝑖𝑎}$catalogs of spectroscopic binaries and use $\text{𝑇𝐸𝑆𝑆}$photometry to identify 112 new heartbeat star systems. We fit their phase-folded light curves with an analytic model to measure their orbital periods, eccentricities, inclinations, and arguments of periastron. We then compare these orbital parameters to the $\text{𝐺𝑎𝑖𝑎}$spectroscopic orbital solution. Our periods and eccentricities are consistent with the $\text{𝐺𝑎𝑖𝑎}$solutions for 85 $\%$of the single-line spectroscopic binaries but only 20 $\%$of the double-line spectroscopic binaries. For the two double-line spectroscopic binary heartbeat stars with consistent orbits, we combine the $\text{𝑇𝐸𝑆𝑆}$phase-folded light curve and the $\text{𝐺𝑎𝑖𝑎}$velocity semi-amplitudes to measure the stellar masses and radii with $\text{𝙿𝙷𝙾𝙴𝙱𝙴}$. In a statistical analysis of the HB population, we find that non-giant heartbeat stars have evolved off the main sequence and that their fractional abundance rises rapidly with effective temperature.