Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[11.] PROPOSITIO IIII.
[12.] PROPOSITIO V.
[13.] PROPOSITIO VI.
[14.] PROPOSITIO VII.
[15.] POSITIO II.
[16.] COMMENTARIVS.
[17.] PROPOSITIO VIII.
[18.] COMMENTARIVS.
[19.] PROPOSITIO IX.
[20.] COMMENTARIVS.
[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.
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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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