Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[81.] THE OREMA XII. PROPOSITIO XVI.
[82.] THE OREMA XIII. PROPOSITIO XVII.
[83.] THEOREMA XIIII. PROPOSITIO XVIII.
[84.] THEOREMA XV. PROPOSITIO XIX.
[85.] THE OREMA XVI. PROPOSITIO XX.
[86.] THEOREMA XVII. PROPOSITIO XXI.
[87.] THE OREMA XVIII. PROPOSITIO XXII.
[88.] THEOREMA XIX. PROPOSITIO XXIII.
[89.] PROBLEMA V. PROPOSITIO XXIIII.
[90.] THEOREMA XX. PROPOSITIO XXV.
[91.] THEOREMA XXI. PROPOSITIO XXVI.
[92.] THEOREMA XXII. PROPOSITIO XXVII.
[93.] PROBLEMA VI. PROPOSITIO XX VIII.
[94.] THE OREMA XXIII. PROPOSITIO XXIX.
[95.] THEOREMA XXIIII. PROPOSITIO XXX.
[96.] THEOREMA XXV. PROPOSITIO XXXI.
[97.] FINIS LIBRI DE CENTRO GRAVITATIS SOLIDORVM.
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76ARCHIMEDIS
Ex quibus perſpicuum eſt lineas omnes ſic ductas ab
ipſis ſectionibus in eandem proportionem ſecari.
eſt enim
diuidendo, conuertendoque cm ad mb, &
cf ad fb, ut
ce ad ea.
LEMMA III.
Sed & illud constare potest; lineas, quæ in portioni-
bus eiuſmodi ſimilibus ita ducuntur, ut cú baſibus æqua-
les angulos contineant, ab ipſis ſimiles quoque portiones
abſcindere:
hoc eſt, ut in propoſita figura, portiones h b c,
m f c, quas lineæ c h, c m abſcindunt, etiam inter ſe
ſimiles eſſe.
D_ividantvr_ enim ch, cm bifariam in punctis p q: & per
ipſa ducantur lineæ r p s, t q u diametris æquidiſtantes.
erit portio-
nis b s c diameter p s, &
portionis m u c diameter q u. Itaque fiat
ut quadratum c r ad quadratum c p, ita linea b n ad aliam lineam,
quæ ſit s x:
& ut quadratum c t ad quadratum c q, ita fiat f o ad
u y.
iam exijs
47[Figure 47] quæ demóſtra
uimus in com-
mentarijs in
quartam pro-
poſitioné.
Ar-
chrmedis de co
noidibus, &

ſphæroidibus,
patet quadra-
tum c p æqua-
le eſſe rectan-
gulo p s x:

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