[en] We present a new measurement of the cross section for the process e⁺e^- → e⁺e^-π⁺π^- at center-of-mass energy 29 GeV for invariant pion pair masses M_φφ between 350 MeV/c² and 3.5 GeV/c². For M_ππ above 2.1 GeV/c², we find approximate agreement with the hard-scattering prediction of Brodsky and Lepage. In the low mass region, we observe the f₂(1270), and measure its radiative width to be 3.15 ± .04 ± .39 keV. We also observe an enhancement in the π⁺π^- spectrum near 1 GeV. We hypothesize that it is the f₀(975) and determine it's radiative width to be 0.29 ± .07 ± .12 keV. 48 refs