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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DE CENTRO GRAVIT. SOLID.
metrum habens e d. Quoniam igitur circuli uel ellipſis
a e c b grauitatis centrum eſt in diametro b e, &
portio-
nis a e c centrum in linea e d:
reliquæ portionis, uidelicet
a b c centrum grauitatis in ipſa b d conſiſtat neceſſe eſt, ex
octaua propoſitione eiuſdem.

THEOREMA V. PROPOSITIO V.

SI priſma ſecetur plano oppoſitis planis æqui
diſtante, ſectio erit figura æqualis &
ſimilis ei,
quæ eſt oppoſitorum planorum, centrum graui
tatis in axe habens.
Sit priſma, in quo plana oppoſita ſint triangula a b c,
d e f;
axis g h: & ſecetur plano iam dictis planis æquidiſtã
te;
quod faciat ſectionem K l m; & axi in pũcto n occurrat.
Dico _k_ l m triangulum æquale eſſe, & ſimile triangulis a b c
d e f;
atque eius grauitatis centrum eſſe punctum n. Quo-
niam enim plana a b c
Figure: /permanent/library/4E7V2WGH/figures/0125-01 not scanned
[Figure 82]
K l m æquidiſtantia ſecã
16. unde-
cimi.
tur a plano a e;
rectæ li-
neæ a b, K l, quæ ſunt ip
ſorum cõmunes ſectio-
nes inter ſe ſe æquidi-
ſtant.
Sed æquidiſtant
a d, b e;
cum a e ſit para
lelogrammum, ex priſ-
matis diffinitione.
ergo
&
al parallelogrammũ
erit;
& propterea linea
34. prim@_k_l, ipſi a b æqualis.
Si-
militer demonſtrabitur
l m æquidiſtans, &
æqua
lis b c;
& m K ipſi c a.

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