Now, the best method for a plane-being of familiarizing himself with
shapes in our space, would be to practise the realization of them from
their different projections in his plane. Thus, given the three
projections just mentioned, he should be able to construct the figure
from which they are derived. The projections (Fig. 19) are drawn below
the perspective pictures of the shape (Fig. 18). From the front, or
Moena view, he would conclude that the shape was Urna Mala, Moles Mala,
Bidens Mala, Tibicen Mala; or instead of these, or also in addition to
them, any of the cubes running in the Y direction from the plane. That
is, from the Moena projection he might infer the presence of all the
following cubes (the word Mala is omitted for brevity): Urna, Frenum,
Sector, Moles, Plebs, Hama, Bidens, Pallor, Cortis, Tibicen, Mora,
Merces.
Next, the Alvus view or projection might be given by the cubes (the word
Mala being again omitted): Urna, Moles, Saltus, Frenum, Plebs, Sypho,
Uncus, Pallor, Tergum, Spicula, Mora, Oliva. Lastly, looking at the
ground plan or Syce view, he would infer the possible presence of Urna,
Ostrum, Comes, Moles, Bidens, Tibicen, Plebs, Pallor, Mora.
Now, the shape in higher space, which is usually there, is that which is
common to all these three appearances. It can be determined, therefore,
by rejecting those cubes which are not present in all three lists of
cubes possible from the projections. And by this process the plane-being
could arrive at the enumeration of the cubes which belong to the shape
of which he had the projections. After a time, when he had experience of
the cubes (which, though invisible to him as wholes, he could see part
by part in turn entering his space), the projections would have more
meaning to him, and he might comprehend the shape they expressed
fragmentarily in his space. To practise the realization from
projections, we should proceed in this way. First, we should think of
the possibilities involved in the Moena view, and build them up in cubes
before us. Secondly, we should build up the cubes possible from the
Alvus view. Again, taking the shape at the beginning of the chapter, we
should find that the shape of the Alvus possibilities intersected that
of the Moena possibilities in Urna, Moles, Frenum, Plebs, Pallor, Mora;
or, in other words, these cubes are common to both. Thirdly, we should
build up the Syce possibilities, and, comparing their shape with those
of the Moena and Alvus projections, we should find Urna, Moles, Plebs,
Pallor, Mora, of the Syce view coinciding with the same cubes of the
other views, the only cube present in the intersection of the Moena and
Alvus possibilities, and not present in the Syce view, being Frenum.
Public-domain text, read in full here on John Shaqi.
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