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
Dico eas proportion ales eſſe in proportione, quæ eſt la-
teris a b adlatus d e, itaut earum maior ſit a b c e, me-
dia a d c e, &
minor d e f c. Quoniam enim lineæ d e,
a b æquidiſtant;
& interipſas ſunt triangula a b e, a d e;
erit triangulum a b e
Figure: /permanent/library/4E7V2WGH/figures/0172-01 not scanned
[Figure 126]
1. ſextí.ad triangulum a d e,
ut linea a b ad lineam
d e.
ut autem triangu
lum a b e ad triangu-
lum a d e, ita pyramis
5. duodeci
mi.
a b e c ad pyramidem
a d e c:
habent enim
altitudinem eandem,
quæ eſt à puncto c ad
planum, in quo qua-
drilaterum a b e d.
er-
11. quinti.go ut a b ad d e, ita pyramis a b e c ad pyramidem a d e c.
Rurſus quoniam æquidiſtantes ſunt a c, d f; erit eadem
ratione pyramis a d c e ad pyramidem c d f e, ut a c ad
4 ſexti.d f.
Sed ut a c a l d f, ita a b ad d e, quoniam triangula
a b c, d e f ſimilia ſunt, ex nona huius.
quare ut pyramis
a b c e ad pyramidem a d c e, ita pyramis a d c e ad ipſam
d e f c.
fruſtum igitur a b c d e f diuiditur in tres pyramides
proportionales in ea proportione, quæ eſt lateris a b ad d e
latus, &
earum maior eſt c a b e, media a d c e, & minor
d e f c.
quod demonſtrare oportebat.

PROBLEMA V. PROPOSITIO XXIIII.

Qvodlibet fruſtum pyramidis, uel coni,
uel coni portionis, plano baſi æquidiſtanti ita ſe-
care, ut ſectio ſit proportionalis inter maiorem,
&
minorem baſim.

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