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
ceatinclinata. Demonſtrandum eſt non manere ipſam; ſed
rectam reſtitui.
Itaque ſecta ipſa plano per axem, recto ad
planum, quod eſt in ſuperficie humidi, portionis ſectio ſit
a p o l rectanguli coni ſectio:
axis portionis, & ſectionis
diameter n o:
ſuperficiei autem humidi ſectio ſit i s. Si
igitur portio non eſt recta;
non utique erit a l ipſi i s æ-
quidiſtans.
quare n o cum i s non faciet angulos rectos.
ducatur crgo k ω contingens ſectionem coni in p [quæ
Suppleta
a. Federi-
co Cõm.
ipſi i s æquidiſtet:
& à puncto p ad i s ducatur p f æquidi
ſtans ipſi o n, quæ erit ſectionis i p o s diameter, &
axis por
Btionis in humido demerſæ.
ſumantur deinde centra graui
tatum:
ſitq; ſolidæ magnitudinis a p o l grauitatis centrũ
Cr;
ipſius uero i p o s centrum ſit b: & iuncta b r produca-
Dtur ad g, quod ſit centrum grauitatis reliquæ figuræ i s l a.
Quoniam igitur n o ipſius quidem r o ſeſquialtera eſt;
eius autẽ, quæ uſque ad axẽ minor, quam ſeſquialtera;
erit
Er o minor, quàm quæ uſque ad axem.
Quare angulus r p ω
Facutus erit:
cum enim linea, quæ uſque ad axem maior ſit
ipſa r o;
quæ à puncto r ad k ω perpendicularis ducitur,
uidelicet r t, cũ
Figure: /permanent/library/4E7V2WGH/figures/0032-01 not scanned
[Figure 19]
linea f p extra
ſectionem con
ueniet:
& pro-
pterea inter p
&
ω puncta ca-
datneceſſe eſt.
Itaq; ſi per b g
ducantur lineæ
ipſi r t æquidi-
ſtantes;
angu-
los rectos cum
ſuperficie humidi continebunt:
& quod in humido eſt ſur-
Gſum feretur ſecundum perpendicularem, quæ per b ducta
eſt, ipſi r t æquidiſtans:
quod uero eſt extra humi dum ſe-

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