We have used the Faint Object Spectrograph on the Hubble Space Telescope to observe the spectra of SN 1987A over the wavelength range 2000 -- 8000 AA on dates 1862 and 2210 days after the supernova outburst. Even these pre-COSTAR observations avoid much of the contamination from the bright stars nearby and provide a very useful set of line strengths and shapes for analysis. The spectrum is formed in an unusual physical setting: cold gas which is excited and ionized by energetic electrons from the radioactive debris of the supernova explosion. The spectra of SN 1987A at this phase are surprisingly similar to those of the nova shells of CP Puppis and T Pyxidis decades after outburst. SN 1987A and the novae are characterized by emission from material with electron temperatures of only a few hundred degrees Kelvin, and show narrow Balmer continuum emission and strong emission lines from O$^+$. The Balmer continuum shape requires the electron temperature in the supernova ejecta to be as low as 500 K on day 1862 and 400 K on day 2210 after outburst. The OIIUV doublet is surprisingly strong and is plausibly powered by collisional ionization of neutral oxygen to excited states of O$^+$. The line intensity ratio of the OID doublet obtained from Gaussian fits of the line profiles is 1.8$pm0.2$, contrary to the optically thin limit of 3. This ratio is {it not} due to an optical depth effect, but rather is an artifact of assuming a Gaussian profile to fit the OID doublet profile. Specifying the line ratio $R, = , F([{rm OI}]6300)/F([{rm OI}]6364)$ = 3 is consistent with the data and allows a calculation of the decomposed line profile. All the observed strong lines are found to be blueshifted by a similar amount
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