Dickinson builds the entire poem on comparative anatomy, the 19th-century science that let paleontologists reconstruct extinct animals from bone fragments. Georges Cuvier famously claimed he could rebuild an entire creature from a single tooth. This wasn't metaphor—it was cutting-edge science that fascinated educated Americans in the 1860s.
The poem's logic: if scientists can see a whole vanished animal in one bone, then a trained eye can see all of summer in one winter flower. The "meekest flower of the mead"—probably a dandelion, gold and persistent—becomes a fossil of warmer seasons. Notice "else perished in the stone": without that bone, the ancient creature would be completely lost. Without that winter flower, summer would have no witness.
"So to the eye prospective led" is the pivot. A "prospective" eye sees forward, sees potential, sees what's coming. Dickinson suggests observation is a trained skill, like Cuvier's anatomical expertise. The ordinary person sees a weed; the educated eye sees "rose and lily, marigold / And countless butterfly"—an entire ecosystem compressed into one specimen.
The poem appears twice in your text, but Dickinson wrote it once. This repetition might be a transcription artifact. The structure is two stanzas: first explaining the science, second applying it to the flower. The parallel is exact—"A science—so the savants say" opens both, hammering home that this isn't poetic fancy but scientific method applied to nature.