Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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[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.
[51.] V.
[52.] DEMONSTRATIO SECVNDAE PARTIS.
[53.] COMMENTARIVS.
[54.] DEMONSTRATIO TERTIAE PARTIS.
[55.] COMMENTARIVS.
[56.] DEMONSTRATIO QVARTAE PARTIS.
[57.] DEMONSTRATIO QVINT AE PARTIS.
[58.] FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.
[59.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.
[60.] CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.
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14919DE CENTRO GRAVIT. SOLID. 102[Figure 102]
THEOREMA X. PROPOSITIO XIIII.
Cuiuslibet pyramidis, & cuiuslibet coni, uel
coni portionis, centrum grauitatis in axe cõſiſtit.
SIT pyramis, cuius baſis triangulum a b c: & axis d e.
Dico in linea d e ipſius grauitatis centrum ineſſe. Si enim
fieri poteſt, ſit centrum f:
& ab f ducatur ad baſim pyrami
dis linea f g, axi æquidiſtans:
iunctaq; e g ad latera trian-
guli a b c producatur in h.
quam uero proportionem ha-
bet linea h e ad e g, habeat pyramis ad aliud ſolidum, in
quo K:
inſcribaturq; in pyramide ſolida figura, & altera cir
cumſcribatur ex priſmatibus æqualem habentibus altitu-
dinem, ita ut circumſcripta inſcriptam exuperet magnitu-
dine, quæ ſolido _k_ ſit minor.
Et quoniam in pyramide pla
num baſi æquidiſtans ductum ſectionem facit figuram ſi-
milem ei, quæ eſt baſis;
centrumq; grauitatis in axe haben
tem:
erit priſmatis s t grauitatis centrũ in linear q; priſ-
matis u x centrum in linea q p;
priſmatis y z in linea p o;
priſmatis η θ in l_i_nea o n;
priſmatis λ μ in linea n m; priſ-
matis ν π in m l;
& denique priſmatis ρ σ in l e. quare

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