A precise measurement of the cross section of the process e(+)e(-) -> pi(+)pi(-) (gamma) from threshold to an energy of 3 GeV is obtained with the initial-state radiation (ISR) method using 232 fb(-1) of data collected with the BABAR detector at e(+)e(-) center-of-mass energies near 10.6 GeV. The ISR luminosity is determined from a study of the leptonic process e(+)e(-) -> mu(+)mu(-) (gamma)gamma(ISR), which is found to agree with the next-to-leading-order QED prediction to within 1.1%. The cross section for the process e(+)e(-) -> pi(+)pi(-) (gamma) is obtained with a systematic uncertainty of 0.5% in the dominant rho resonance region. The leading-order hadronic contribution to the muon magnetic anomaly calculated using the measured pi pi cross section from threshold to 1.8 GeV is (514.1 +/- 2.2(stat) +/- 3.1(sys)) x 10(-10).
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