De quibusdam effatis Geometricis

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Gonzalo
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De quibusdam effatis Geometricis

Post by Gonzalo »

I,4. Tria puncta A, B, C, non manentia in ipsa linea recta quoddam planum significatur. Dicimus ac scribimus ABC = α.
I,5.Omnia tria puncta A, B, C, alphae plani, quae non in ipsa linea recta manerent, aliud planum alpha macte significatur.



[Anglice (ex editione La Sallensis, impressa anno MCML):
I,4. Three points A, B, C, not situated in the same straight line always completely determine a plane α (alpha). We write ABC=α.
I,5. Any three points A, B, C of a plane α, which do not lie in the same straight line, completely determine that plane.
]

Gundisalvus omnibus colentibus Scientiae Geometriae plurimam salutem dicit,
Parvum dubium retineo de effatis quarto atque quinto in Institutionibus Geometriae ab Davido Hilberte. Non mea mens diligenter dissimilitudinem accipit inter has duas postulationes super origine geometrici plani. Possum intellegere quartum & quintum effata sicut illud postremum primi amplificationem constituisset.

Quid putatis, sodales?
Last edited by Gonzalo on Mon Oct 01, 2007 7:43 pm, edited 7 times in total.

Tertius Robertus
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Post by Tertius Robertus »

gundisalvo robertus salutem

in i.4 dictum est "quaelibet in spatio tria puncta non in eadem linea manentia quoddam planum significare", unicum, si mihi licet addere. in i.5 autem dicitur de punctis, quae quidem in plano jam definito sint, quae quolibet modo ex ipso plano selecta illud ipsum planum tote, cuncte, sine dubio, sine ambiguitate definiunt. exempli gratia, in spatio r³ puncta (0,0,0) (1,0,0) (0,1,0), quoniam non in eadem linea manent, ut didicimus in i.4, planum α definiunt. ex quo elligere possumus alia tria puncta, ut nobis liceat 8), quae idem planum definiunt, e.g., (0,0,0) (2,0,0) (0,2,0). talis est differentia inter eas. :)

aliud, quintus, a, um, et quartus, a, um, declinanda sunt; alios errores, quos fecisti, atque videre potui, corrigatos invenire potes ubicumque verba sublineata scripsi

vale!

Gonzalo
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Post by Gonzalo »

Gratias ago ob tuam sapientem rationem ad effata bene intellegendam. Magnam partem Euclidis & Archimedis opera erudii, nunc etiam Hodiernam seu Recentem (ss.XVI/XVII-hodie) Geometriam studeo (incepi Newtoni Geometriae labores, sed anteposui ad eas erudiandas Hilbertis Institutiones).
Esne tu Mathematicus, Tertie?
Last edited by Gonzalo on Tue Oct 02, 2007 4:07 pm, edited 2 times in total.

Tertius Robertus
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Post by Tertius Robertus »

in universitate scientiis mathematicis quas anglici "pure mathematics" appellant studui. non sine pudore hoc fateor... :oops:

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