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.
o n ipſi a c. Quoniam enim triangulorum a b k, a d k, latus
b k eſt æquale lateri k d, &
a k utrique commune; anguliq́;
ad k recti baſis a b baſi a d; & reliqui anguli reliquis an-
8. primigulis æquales erunt.
eadem quoqueratione oſtendetur b c
æqualis c d;
& a b ipſi
Figure: /permanent/library/4E7V2WGH/figures/0119-01 not scanned
[Figure 75]
b c.
quare omnes a b,
b c, c d, d a ſunt æqua-
les.
& quoniam anguli
ad a æquales ſunt angu
lis ad c;
erunt anguli b
a c, a c d coalterni inter
ſe æquales;
itemq́; d a c,
a c b.
ergo c d ipſi b a;
& a d ipſi b c æquidi-
ſtat.
Atuero cum lineæ
a b, c d inter ſe æquidi-
ſtantes bifariam ſecen-
tur in punctis e g;
erit li
nea l e k g n diameter ſe
ctionis, &
linea una, ex
demonſtratis in uigeſi-
ma octaua ſecundi coni
corum.
Et eadem ratione linea una m f k h o. Sunt autẽ a d,
b c inter ſe ſe æquales, &
æquidiſtantes. quare & earum di-
midiæ a h, b f;
itemq́; h d, f e; & quæ ipſas coniunguntrectæ
33. primitlineæ æquales, &
æquidiſtantes erunt. æquidiſtãt igitur b a,
c d diametro m o:
& pariter a d, b c ipſi l n æquidiſtare o-
ſtendemus.
Si igitur manẽte diametro a c intelligatur a b c
portio ellipſis ad portionem a d c moueri, cum primum b
applicuerit ad d, cõgruet tota portio toti portioni, lineaq́;
b a lineæ a d; & b c ipſi c d congruet: punctum uero e ca-
det in h;
f in g: & linea k e in lineam k h: & k f in k g. qua
re &
el in h o, et fm in g n. Atipſa lz in z o; et m φ in φ n
cadet.
congruet igitur triangulum l k z triangulo o k z: et

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