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We use weak lensing data from the  Hubble Space Telescope  COSMOS survey to measure the second‐ and third‐order moments of the cosmic shear field, estimated from about 450 000 galaxies with average redshift .  We measure two‐ and three‐point shear statistics using a tree‐code, dividing the signal in E, B and mixed components. We present a detection of the third‐order moment of the aperture mass statistic and verify that the measurement is robust against systematic errors caused by point spread function (PSF) residuals and by the intrinsic alignments between galaxies. The amplitude of the measured three‐point cosmic shear signal is in very good agreement with the predictions for a 7‐yr  Wilkinson Microwave Anisotropy Probe  ( WMAP 7) best‐fitting model, whereas the amplitudes of potential systematics are consistent with zero.  We make use of three sets of large Lambda cold dark matter ( ΛCDM ) simulations to test the accuracy of the cosmological predictions and to estimate the influence of the cosmology‐dependent covariance.  We perform a likelihood analysis using the measurement of  〈 M  3  ap 〉 (θ)  and find that the  Ω m −σ 8   degeneracy direction is well fitted by the relation:  σ 8 (Ω m /0.30) 0.49 = 0.78 +0.11  −0.26   which is in good agreement with the best‐fitting relation obtained by using the measurement of  〈 M  2  ap 〉 (θ) :  σ 8 (Ω m /0.30) 0.67 = 0.70 +0.11  −0.14  .  We present the first measurement of the more generalized three‐point shear statistic  〈 M  3  ap 〉 (θ 1 , θ 2 , θ 3 )  and find a very good agreement with the  WMAP 7 best‐fitting cosmology. The cosmological interpretation of  〈 M  3  ap 〉 (θ 1 , θ 2 , θ 3 )  gives  σ 8 (Ω m /0.30) 0.46 = 0.69 +0.08  −0.14  . Furthermore, the combined likelihood analysis of  〈 M  3  ap 〉 (θ 1 , θ 2 , θ 3 )  and  〈 M  2  ap 〉 (θ)  improves the accuracy of the cosmological constraints to  σ 8 (Ω m /0.30) 0.50 = 0.69 +0.07  −0.12  , showing the high potential of this combination of measurements to infer cosmological constraints.

Weak lensing from space: first cosmological constraints from three‐point shear statistics ★