Measurement of the neutron magnetic form factor from inclusive quasielastic scattering of polarized electrons from polarized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

We report a measurement of the asymmetry in spin-dependent quasielastic scattering of longitudinally polarized electrons from a polarized $^{3}\mathrm{He}$ target. The neutron magnetic form factor ${\mathit{G}}_{\mathit{M}}^{\mathit{n}}$ has been extracted from the measured asymmetry based on recent PWIA calculations using spin-dependent spectral functions. Our determination of ${\mathit{G}}_{\mathit{M}}^{\mathit{n}}$ at ${\mathit{Q}}^{2}$=0.19 (GeV/c${)}^{2}$ agrees with the dipole parametrization. This experiment represents the first measurement of the neutron magnetic form factor using spin-dependent electron scattering.