  We report the first precision measurement of the proton electric to magnetic
form factor ratio from spin-dependent elastic scattering of longitudinally
polarized electrons from a polarized hydrogen internal gas target. The
measurement was performed at the MIT-Bates South Hall Ring over a range of
four-momentum transfer squared $Q^2$ from 0.15 to 0.65 (GeV/c)$^2$.
Significantly improved results on the proton electric and magnetic form factors
are obtained in combination with previous cross-section data on elastic
electron-proton scattering in the same $Q^2$ region.
