Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIMEDIS
@e centro grauitatis ſolidorum demonstrauimus: erit magnitudi-
nis ex utriſque portionibus b n c, b g c conſtantis;
hoc eſt portionis
in humido demerſa grauitatis centrum in linea n g, quæ ipſarum
ſphæræ portionum centra graui-
Figure: /permanent/library/4E7V2WGH/figures/0026-01 not scanned
[Figure 14]
tatis coniungit.
ſi enim fieri po-
teſt, ſit extra lineam n g, ut in
q:
sîtq; portionis b n c centrum
grauitatis u;
& ducatur u q.
Quoniam igitur à portione in bu-
mido demerſa aufertur ſphæræ
portio b n c, non habens idem cen
trum grauitatis:
erit ex octaua
primi libri Archimcdis de centro
grauitatis planorum, reliquæ por
tionis b g c centrum in linea u q
producta.
quod fieri non potest; eſt enim in axe ipſius mg. sequi-
tur ergo ut portionis in humido demerſæ centrum grauitatis ſit in li
nean k.
quod oſtendendum propoſuimus.
_Sed totius portionis grauitatis centrum eſt in linea ft, in-_
D_ter_ k, _&
f, quod ſit x. ]_ Compleatur ſphæra, ut ſit portionis additæ
axis t y;
& centrú grauitatis z. Itaque quoniá à tota ſphæra, cuius
grauitatis cétrum eſt k, ut etiam in eodem libro demóſtrauimus, au
8. primi
Archime
dis.
fertur portio e y h centrú grauitatis habens z:
erit reliquæ portionis
e f h cétrú in linea z k producta.
quare inter k. & f neceſſario cadet.
Reliquæ ergo figuræ, quæ eſt extra humidum, centrum erit
Ein linea r x producta.
] _Ex eadem octaua primi libri Archime-_
_dis de centro grauitatis planorum._
_Feretur ergo grauitas, figuræ quidem quæ extra humi_-
F_dum per rectam s l deorſum;
portionis autem, quæ in_
_humido ſurſum per rectam r l.
]_ Ex antecedenti poſitio-
ne.
magnitudo @enim, quæ in humido demerſa est, tanta ui per li-
neam r l ſurſum@fertur, quanta quæ extra humidum per li-
neam s l, deorſum:
id quod ex propoſitione ſexta huius li-
briconſtare poteſt.
& quoniam feruntur per alias, atque alias li-

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