Using a summary curve of two eigen vectors of solar magnetic field oscillations derived with Principal Components Analysis (PCA) from synoptic maps for solar cycles 21-24 as a proxy of solar activity, we extrapolate this curve backwards three millennia revealing 9 grand cycles lasting 350-400 years each. The summary curve shows a remarkable resemblance to the past sunspot and terrestrial activity: grand minima - Maunder Minimum (1645-1715 AD), Wolf minimum (1280-1350 AD), Oort minimum (1010-1050 AD) and Homer minimum (800-900 BC); grand maxima - modern warm period (1990-2015), medieval warm period (900-1200 AD), Roman warm period (400-10 BC) and others. We verify the extrapolated activity curve by the pre-telescope observations of large sunspots with naked eye, by comparing the observed and simulated butterfly diagrams for Maunder Minimum (MM), by a maximum of the terrestrial temperature and extremely intense terrestrial auroras seen in the past grand cycle occurred in 14-16 centuries. We confirm the occurrence of upcoming Modern grand minimum in 2020-2053, which will have a shorter duration (3 cycles) and, thus, higher solar activity compared to MM. We argue that Sporer minimum (1450-1550) derived from the increased abundances of isotopes 14C and 10Be is likely produced by a strong increase of the terrestrial background radiation caused by the galactic cosmic rays of powerful supernovae.