We present results of a large area CCD survey for low surface brightness galaxies ( LSBs ) that reaches central surface brightnesses of 25 { mag / arcsec ^ { 2 } } in V . We have analyzed 17.5 { degree } ^ { 2 } of transit scan data , and identified a statistical subset of 7 pure disk LSB ’ s with central surface brightnesses fainter than \mu _ { 0 } = 23 V { mag / arcsec ^ { 2 } } and with angular exponential scale lengths larger than \alpha = 2.5 \arcsec . The LSB detection is entirely automated , and the selection efficiency of the survey is well-quantified . After correcting for the selection efficiency , we find a surface density of 4.1 ^ { +2.6 } _ { -2.1 } { galaxies / degree ^ { 2 } } for LSBs in the considered range of \mu _ { 0 } and \alpha ( 90 % confidence levels ) , with the largest correction being due to the area lost behind bright stars , and the difficulty in detecting LSBs with small angular sizes . We have measured redshifts to the final sample of LSBs , and find them to be at distances comparable to those probed by large galaxy catalogs , and to have intrinsic scale lengths of 1.7 - 3.6 { h } _ { 50 } ^ { -1 } { kpc } , also comparable to normal galaxies . We use the redshifts and the selection efficiency to calculate the number density in LSBs with 23 < \mu _ { 0 } < 25 V { mag / arcsec ^ { 2 } } and find { \cal N } = 0.01 ^ { +0.006 } _ { -0.005 } { galaxies h _ { 50 } ^ { 3 } Mpc ^ { -3 } } , with 90 % confidence . The measurement of the absolute number density of LSBs probably represents a lower limit , due to very strong biases against LSBs with bulges or edge-on LSBs in our sample . Comparing the LSB number density to the number density of normal galaxies with either similar scale lengths or similar luminosities , we find that the number density of LSBs with 23 < \mu _ { 0 } < 25 V { mag / arcsec ^ { 2 } } is comparable to or greater than the number density of normal galaxies . The luminosity density in LSBs is comparable to the luminosity density of normal galaxies with similar luminosities , but is a factor of 3-10 smaller than the luminosity density of normal galaxies with similar scale lengths . The relative LSB number density and luminosity density agree well with the theoretical predictions of Dalcanton et al . ( 1997 ) . The redshift-space distribution of the LSBs suggests that the trend for low surface brightness galaxies to have weak small-scale correlations may continue to the fainter surface brightnesses covered in this survey .