Ua hoʻohana ʻia nā hōʻailona Geometrical i ka ʻike kuʻuna ma loko o nā lāhui āpau e lawe i ka manaʻo intrinsic a me ka hiki i ko mākou ʻike. Ma loko o kēia pūnaewele ua paʻi mākou i kekahi o nā hōʻailona geometrical a Mr. Percival i hōʻike ai, a wehewehe i ke ʻano o, i Manaʻo a Hoʻopau. Ua ʻōlelo ʻo ia ua paʻa ka waiwai o kēia mau hōʻailona no ke kanaka inā manaʻo ʻo ia i loko o ia mau mea e hōʻea i ka ʻoiaʻiʻo, i loaʻa i nā hōʻailona. Ma muli o kēia mau hōʻailona wale nō nā laina a me nā ʻūlū i kūkulu ʻole ʻia i loko o kahi mea i ʻike ʻia o ka mokulele kino, e like me kahi kumulāʻau a i ʻole he kiʻi kanaka, hiki iā lākou ke hoʻoulu i ka noʻonoʻo ma nā mea abstract, non-corporeal a i ʻole nā ​​mea. E like me ia, hiki iā lākou ke kōkua i ka hoʻomaopopo ʻana i nā ʻāina non-physical ma mua o ko mākou mau manaʻo, no laila ke hāʻawi nei i ka ʻike i nā kānāwai nui aʻe o ke ao i kau ʻia i loko. Manaʻo a Hoʻopau.

"ʻO nā hōʻailona Geometrical nā hiʻohiʻona o ka hiki ʻana mai o nā ʻāpana o ke kūlohelohe i ke ʻano a me ka paʻa a me ka holomua o ka mea e hana ana, ma o ka waiwai i ka ʻike ponoʻī, a me ka ʻike i loko a ma waho o ka manawa a me kahi." –HWP

ʻO kēia ʻōlelo a Percival he mea hiki loa. Ke ʻōlelo nei ʻo ia ma o kā mākou makemake e ʻike i ke ʻano a me ke ʻano nui o kēia mau hōʻailona, ​​hiki iā mākou ke ʻike i ka mea i ʻike pinepine ʻole ʻia iā mākou - ʻo wai a he aha mākou, pehea a no ke aha mākou i hōʻea ai i aneʻi, ke kumu a me ka hoʻolālā o ke ao holoʻokoʻa. . . a ma ʻō aku hoʻi.