Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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[21.] ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER SECVNDVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. PROPOSITIO I.
[22.] PROPOSITIO II.
[23.] COMMENTARIVS.
[24.] PROPOSITIO III.
[25.] PROPOSITIO IIII.
[26.] COMMENTARIVS.
[27.] PROPOSITIO V.
[28.] COMMENTARIVS.
[29.] PROPOSITIO VI.
[30.] COMMENTARIVS.
[31.] LEMMAI.
[32.] LEMMA II.
[33.] LEMMA III.
[34.] LEMMA IIII.
[35.] PROPOSITIO VII.
[36.] PROPOSITIO VIII.
[37.] COMMENTARIVS.
[38.] PROPOSITIO IX.
[39.] COMMENTARIVS.
[40.] PROPOSITIO X.
[41.] COMMENTARIVS.
[42.] LEMMA I.
[43.] LEMMA II.
[44.] LEMMA III.
[45.] LEMMA IIII.
[46.] LEMMA V.
[47.] LEMMA VI.
[48.] II.
[49.] III.
[50.] IIII.
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142FED. COMMANDINI linea x cum ſit minor circulo, uel ellipſi, eſt etiam minor fi-
gura rectilinea y.
ergo pyramis x pyramide y minor erit.
Sed & maior; quod fieri nõ poteſt. At ſi conus, uel coni por
tio x ponatur minor pyramide y:
ſit alter conus æque al-
tus, uel altera coni portio χ ipſi pyramidi y æqualis.
erit
eius baſis circulus, uel ellipſis maior circulo, uel ellipſi x,
quorum exceſſus ſit ſpacium ω.
Siigitur in circulo, uel elli-
pſi χ figura rectilinea deſcribatur, ita ut portiones relictæ
ſint ω ſpacio minores, eiuſinodi figura adhuc maior erit cir
culo, uel ellipſi x, hoc eſt figura rectilinea _y_.
& p_y_ramis in
ea conſtituta minor cono, uel coni portione χ, hoc eſt mi-
nor p_y_ramide_y_.
eſt ergo ut χ figura rectilinea ad figuram
rectilineam _y_, ita pyramis χ ad pyramidem _y_.
quare cum
figura rectilinea χ ſit maior figura_y_:
erit & p_y_ramis χ p_y_-
ramide_y_ maior.
ſed erat minor; quod rurſus fieri non po-
teſt.
non eſt igitur conus, uel coni portio x neque maior,
neque minor p_y_ramide_y_.
ergo ipſi neceſſario eſt æqualis.