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 IIS QVAE VEH. IN AQVA.
ipſi i m æquidiſtãs, & contingens ſectionem in p; pt uero
æquidiſtans b d, &
p s ad ipſam b d perpendicularis. Demõ
ſtrandũ eſt, portionẽ non cõſiſtereita, ſed inclinari, donec
baſis in uno puncto ſuperficiem humidi cõtingat.
Maneãt
enim eadem, quæ in ſuperiori figura:
ducaturq; o c ad b d
perpendicularis:
& iuncta a x ad q producatur. erit a x
æqualis ipſi x q.
deĩde ducatur o χ ipſi a q æquidiſtãs. Quo
niã igitur portio ad humidũ eã in grauitate proportione
habere ponitur, quam quadratum x o ad quadratum b d:
& eandem proportionem habet pars ipſius demerſa ad to
tam;
hoc eſt quadratum t p ad quadratum b d: æqualis uti
que erit t p ipſi x o:
cumq; portionum i p m, a o q diame-
tri ſint æquales, &
portiones ipſæ æquales erunt. Rurſus
Bquoniam in por
C
Figure: /permanent/library/4E7V2WGH/figures/0091-01 not scanned
[Figure 56]
tionibus æquali
bus, &
ſimilibus
a o q l, a p m l,
ductæ ſunt lineæ
a q, i m, quæ æ-
quales portio-
nes auferunt;
il-
la quidem ab ex
tremitate baſis,
hæc autem non
ab extremitate:
cõſtat eam, quæ
ab extremitate
baſis ducta eſt,
minorem facere
angulum acutũ
cum diametro totius portionis.
& quoniam angulus, qui
Dad χ minor eſt angulo, qui ad n;
maior erit b c, quàm b s:
cr autem, quàm ſr minor. quare & o g minor, quàm p z:
&
g x maior, quàm z t. ergo p z maior eſt, quàm dupla z t;

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