Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
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page |< < (40) of 213 > >|
DE IIS QVAE VEH. IN AQVA.
ipſi i m æquidiſtãs, & contingens ſectionem in p; pt uero
æquidiſtans b d, &
p s ad ipſam b d perpendicularis. Demõ
ſtrandũ eſt, portionẽ non cõſiſtereita, ſed inclinari, donec
baſis in uno puncto ſuperficiem humidi cõtingat.
Maneãt
enim eadem, quæ in ſuperiori figura:
ducaturq; o c ad b d
perpendicularis:
& iuncta a x ad q producatur. erit a x
æqualis ipſi x q.
deĩde ducatur o χ ipſi a q æquidiſtãs. Quo
niã igitur portio ad humidũ eã in grauitate proportione
habere ponitur, quam quadratum x o ad quadratum b d:
& eandem proportionem habet pars ipſius demerſa ad to
tam;
hoc eſt quadratum t p ad quadratum b d: æqualis uti
que erit t p ipſi x o:
cumq; portionum i p m, a o q diame-
tri ſint æquales, &
portiones ipſæ æquales erunt. Rurſus
Bquoniam in por
C
Figure: /permanent/library/4E7V2WGH/figures/0091-01 not scanned
[Figure 56]
tionibus æquali
bus, &
ſimilibus
a o q l, a p m l,
ductæ ſunt lineæ
a q, i m, quæ æ-
quales portio-
nes auferunt;
il-
la quidem ab ex
tremitate baſis,
hæc autem non
ab extremitate:
cõſtat eam, quæ
ab extremitate
baſis ducta eſt,
minorem facere
angulum acutũ
cum diametro totius portionis.
& quoniam angulus, qui
Dad χ minor eſt angulo, qui ad n;
maior erit b c, quàm b s:
cr autem, quàm ſr minor. quare & o g minor, quàm p z:
&
g x maior, quàm z t. ergo p z maior eſt, quàm dupla z t;

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