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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ARCHIMEDIS
quia o g ipſius g x eſt dupla. Sit p h dupla h t: & iun-
cta h κ ad ω producatur.
erit totius quidem portionis cen
trum grauitatis k;
partis eius, quæ intra humidum h; eius
uero, quæ extra humidum in linea κ ω, quod ſit ω.
Itaque
demonſtrabitur
Figure: /permanent/library/4E7V2WGH/figures/0092-01 not scanned
[Figure 56]
ſimiliter &
k z ad
humidi ſuperſi-
ciem perpẽdicu-
laris, &
quæ per
puncta h ω æqui-
diſtantes ipſi κ z
ducuntur.
quare
nõ manebit por
tio, ſed inclinabi
tur, donec baſis
ipſius in uno pũ
cto contingat ſu
perficiem humi-
di:
atque ita con
ſiſtet.
nam in por
tionibus æquali-
bus a o q l, a p m l, ductæ erunt ab extremitatibus baſium
a q, a m, quæ æquales portiones abſcindunt:
etenim a o q
ipſi a p m, utin ſuperioribus æqualis demonſtrabitur.
ergo
Eæquales faciunt acutos angulos a q, a m cum diametris ba
ſium:
quòd anguli ad χ & n æquales ſint. quare ſi ducta
h k ad ω producatur, erit totius portionis grauitatis cen-
trum k;
partis eius, quæ in humido h; at eius, quæ extra
humidum in linea h κ;
quod ſit ω: & h k ad humidi ſuper-
ficiem perpendicularis.
per eaſdem igitur rectas lineas,
quod quidem in humido eſt, ſurſum, &
quod extra humi-
dum deorſum feretur.
quare manebit portio, cuius baſis
humidi ſuperficiem in uno puncto continget:
& axis cum
ipſa angulum faciet æqualem angulo χ.
Similiter demon-
F

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