Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[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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page |< < of 213 > >|
ARCHIMEDIS
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
Figure: /permanent/library/4E7V2WGH/figures/0076-01 not scanned
[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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