Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[61. ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.]
[62. FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.]
[63. PETITIONES.]
[64. THEOREMA I. PROPOSITIO I.]
[65. THEOREMA II. PROPOSITIO II.]
[66. THE OREMA III. PROPOSITIO III.]
[67. THE OREMA IIII. PROPOSITIO IIII.]
[68. ALITER.]
[69. THEOREMA V. PROPOSITIO V.]
[70. COROLLARIVM.]
[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.]
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FED. COMMANDINI
teſt in portione, quæ recta linea & obtuſianguli coni ſe-
ctione, ſeu hyperbola continetur.

THE OREMA IIII. PROPOSITIO IIII.

In circulo & ellipſiidem eſt figuræ & graui-
tatis centrum.
SIT circulus, uel ellipſis, cuius centrum a. Dico a gra-
uitatis quoque centrum eſſe.
Si enim fieri poteſt, ſit b cen-
trum grauitatis:
& iuncta a b extra figuram in c produca
tur:
quam uero proportionem habetlinea c a ad a b, ha-
beat circulus a ad alium circulum, in quo d;
uel ellipſis ad
aliam ellipſim:
& in circulo, uel ellipſi ſigura rectilinea pla-
ne deſcribatur adeo, ut tandem relinquantur portiones
quædam minores circulo, uel ellipſid;
quæ figura ſit e f g
h _k_ l m n.
Illud uero in circulo fieri poſſe ex duodecimo
elementorum libro, propoſitione ſecunda manifeſte con-
ſtat;
at in ellipſi nos demonſtra-
Figure: /permanent/library/4E7V2WGH/figures/0122-01 not scanned
[Figure 78]
uinius in commentariis in quin-
tam propoſitionem Archimedis
de conoidibus, &
ſphæroidibus.
erit igitur a centrum grauitatis
ipſius figuræ, quod proxime oſtē
dimus.
Itaque quoniam circulus
a ad circulum d;
uel ellipſis a ad
ellipſim d eandem proportionē
habet, quam linea c a ad a b:

portiones uero ſunt minores cir
8. quinti.culo uel ellipſi d:
habebit circu-
lus, uel ellipſis ad portiones ma-
iorem proportionem, quàm c a
19. quinti
apud Cã
panum.
ad a b:
& diuidendo figura recti-
linea e f g h _k_ l m n ad portiones

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