The cosmic ray record for the interval 1428-2005 has been inverted using the method of Caballero-Lopez et al. (2004) to estimate the annual averages of the heliomagnetic field (HMF) near Earth. There is good agreement with the results obtained by others using two independent methodologies based upon the sunspot and geomagnetic records. This provides confidence in the overall validity of all three methods and supports the use of the cosmogenic record to investigate the HMF prior to the commencement of the sunspot record. There is disagreement with another method based on the geomagnetic record that remains to be resolved. Throughout the similar to 580-year interval studied here, the estimated HMF increased by a factor of similar to 4.5 from an 11-year average of similar to 1.5 nT during the Spoerer Minimum (1420-1540) to similar to 7 nT since 1950. Between the several Grand Minima, it exhibits increasing "floor" values similar to the lower asymptote of similar to 5.2 nT evident in satellite data since 1965. The cosmogenic cosmic ray data exhibit a similar to 2300-year periodicity, and it is proposed that the steadily increasing HMF since the 15th century represents the first quarter cycle of an associated similar to 2300-year periodicity in the HMF. Recent theoretical studies of the origin of the open magnetic field are used to infer that the total magnetic flux of the Sun has increased by a factor of similar to 4.5 since the Spoerer Minimum and might increase further over the next similar to 500 years. In more recent time, the sunspot minimum estimates for the Dalton minimum (1810-1820) and Gleissberg minimum (1889-1901) are similar to 2.5 nT, rising to similar to 4 nT in the vicinity of 1850. The amplitude of the 11-year cycle throughout the Gleissberg cycle (1810-1900) is estimated to be similar to 2 nT. The estimated field is similar to 3.5 nT for each of the sunspot minima 1911-1944, increasing in a stepwise fashion to similar to 5.2 nT between the minima of 1944 and 1954. The cosmic ray and satellite data indicate that the field strength then approximated 5.2 nT for the four sunspot minima, 1965-1996.
