Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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[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.
[61.] ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.
[62.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.
[63.] PETITIONES.
[64.] THEOREMA I. PROPOSITIO I.
[65.] THEOREMA II. PROPOSITIO II.
[66.] THE OREMA III. PROPOSITIO III.
[67.] THE OREMA IIII. PROPOSITIO IIII.
[68.] ALITER.
[69.] THEOREMA V. PROPOSITIO V.
[70.] COROLLARIVM.
[71.] THEOREMA VI. PROPOSITIO VI.
[72.] THE OREMA VII. PROPOSITIO VII.
[73.] THE OREMA VIII. PROPOSITIO VIII.
[74.] THE OREMA IX. PROPOSITIO IX.
[75.] PROBLEMA I. PROPOSITIO X.
[76.] PROBLEMA II. PROPOSITIO XI.
[77.] PROBLEMA III. PROPOSITIO XII.
[78.] PROBLEMA IIII. PROPOSITIO XIII.
[79.] THEOREMA X. PROPOSITIO XIIII.
[80.] THE OREMA XI. PROPOSITIO XV.
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1194DE CENTRO GRAVIT. SOLID. o n ipſi a c. Quoniam enim triangulorum a b k, a d k, latus
b k eſt æquale lateri k d, &
a k utrique commune; anguliq́;
ad k recti baſis a b baſi a d; & reliqui anguli reliquis an-
118. primi gulis æquales erunt.
eadem quoqueratione oſtendetur b c
æqualis c d;
& a b ipſi
75[Figure 75] b c.
quare omnes a b,
b c, c d, d a ſunt æqua-
les.
& quoniam anguli
ad a æquales ſunt angu
lis ad c;
erunt anguli b
a c, a c d coalterni inter
ſe æquales;
itemq́; d a c,
a c b.
ergo c d ipſi b a;
& a d ipſi b c æquidi-
ſtat.
Atuero cum lineæ
a b, c d inter ſe æquidi-
ſtantes bifariam ſecen-
tur in punctis e g;
erit li
nea l e k g n diameter ſe
ctionis, &
linea una, ex
demonſtratis in uigeſi-
ma octaua ſecundi coni
corum.
Et eadem ratione linea una m f k h o. Sunt autẽ a d,
b c inter ſe ſe æquales, &
æquidiſtantes. quare & earum di-
midiæ a h, b f;
itemq́; h d, f e; & quæ ipſas coniunguntrectæ
2233. primit lineæ æquales, &
æquidiſtantes erunt. æquidiſtãt igitur b a,
c d diametro m o:
& pariter a d, b c ipſi l n æquidiſtare o-
ſtendemus.
Si igitur manẽte diametro a c intelligatur a b c
portio ellipſis ad portionem a d c moueri, cum primum b
applicuerit ad d, cõgruet tota portio toti portioni, lineaq́;
b a lineæ a d; & b c ipſi c d congruet: punctum uero e ca-
det in h;
f in g: & linea k e in lineam k h: & k f in k g. qua
re &
el in h o, et fm in g n. Atipſa lz in z o; et m φ in φ n
cadet.
congruet igitur triangulum l k z triangulo o k z:

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