Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

< >
[1. None]
[2. ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBRI DVO. A FEDERICO COMMANDINO VRBINATE IN PRISTINVM NITOREM RESTITVTI, ET COMMENTARIIS ILLVSTRATI.]
[3. CVM PRIVILEGIO IN ANNOS X. BONONIAE,]
[4. M D LXV.]
[5. RANVTIO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.]
[6. Federicus Commandinus.]
[7. ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER PRIMVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. POSITIO.]
[8. PROPOSITIO I.]
[9. PROPOSITIO II.]
[10. PROPOSITIO III.]
[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.]
< >
page |< < (4) of 213 > >|
DE 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-
8. primigulis æquales erunt.
eadem quoqueratione oſtendetur b c
æqualis c d;
& a b ipſi
Figure: /permanent/library/4E7V2WGH/figures/0119-01 not scanned
[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
33. primitlineæ 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: et

Text layer

  • Dictionary

Text normalization

  • Original

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index