= Solution
Astronomical instruments do more than make an existing observation more accurate. They select measurable quantities, embody mathematical assumptions and create new classes of evidence. The <astrolabe> and the <telescope> illustrate two different relationships between a <mathematical model> and observation.
A planispheric <astrolabe> represents the <celestial sphere> on a flat plate by <stereographic projection>. A rotating <star> map is fitted over a plate appropriate to the observer's <latitude>; the back carries a sighting rule, or <alidade>, and an angular scale. A measured stellar <altitude> can be matched to the engraved geometry to infer the celestial configuration and hence the time. The instrument combines an observation with a physical analogue calculation. Its geometry is indispensable to the inference: the sighting alone does not tell the time.<Astrolabe by Silke Ackermann>[Epact instrument description: rete, latitude plates, alidade and time-telling procedure]{ref}
This also explains why manufacture, calibration and users' knowledge mattered. An unsuitable <latitude> plate or an inaccurate sighting produces a systematic error rather than a philosophical refutation of celestial geometry. Conversely, engraved scales and repeatable settings allow predictions and observations to be compared in an organized way. The <astrolabe> belongs to a history of practical calculation as well as cosmological ideas. Its use to represent apparent sky rotation does not establish that its user had independently proved every physical claim of a geocentric cosmology.
The early <telescope> changed what could be included in an astronomical description. In <Sidereus Nuncius by Galileo Galilei>, the <Moon>'s changing <light> and shadow supports an interpretation of surface relief, the <Milky Way> resolves into many <stars>, and repeated observations distinguish small bodies accompanying <Jupiter> from ordinary fixed <stars>. Temporal sequences were crucial: a few points in one image are ambiguous, whereas their changing configurations around the same bright body support an orbital interpretation.<Sidereus Nuncius by Galileo Galilei>[1610 account: lunar surface, the Milky Way and the sequence of observations near Jupiter]{ref}
There were physical reasons not to accept every magnified appearance immediately. <Lens> defects, limited resolution, stray <light> and imperfect alignment can create or distort features. Consistency under repeated observations, comparison with familiar terrestrial objects and a successful account of how the instrument forms images help distinguish an optical artefact from a celestial object. An instrument extends sight only through a chain of physical inferences; it does not remove that chain.
The discoveries also had discriminating, rather than unlimited, theoretical <force>. A visibly irregular <Moon> challenged the doctrine of perfectly smooth celestial bodies. Moons accompanying <Jupiter> showed that not every visible revolution had the <Earth> as its immediate centre. Neither observation alone proved that the <Earth> moves around the <Sun>: a different system could allow <Jupiter>'s moons while retaining a stationary <Earth>. Later observations such as the phases of <Venus> must also be distinguished chronologically from the observations published in the March 1610 book.
The two instruments thus shaped <astronomy> in complementary ways. The <astrolabe> made a mathematical sky model operational, whereas the <telescope> exposed phenomena that demanded changes to parts of the accepted model. In both cases, reliable knowledge depended on geometry, material workmanship, repeated observations and explicit limits on what the observations entailed.
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