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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28ARCHIMEDIS extra humidi ſuperficiem, axem habetin perpendiculari
per _k_:
& propter ea, quæ ſuperius dicta ſunt, centrum gra-
uitatis ipſius eſt in linea n _k_, quod ſitr;
totius autem por-
tionis centrum grauitatis eſt in linea f t, inter _k_ &
f, quod
ſit x.
reliquæ ergo figuræ, eius ſcilicet, quæ eſt in humido,
centrum erit in rectalinea r x producta ad partes x;
& aſ-
16[Figure 16] ſumpta ex ea linea quadam, quæ ad x r eandem habeat pro
portionem, quam grauitas portionis, quæ eſt extra humi-
dum, ad grauitatem figuræ, quæ in humido.
Sit autem o
centrum dictæ figuræ:
& per o perpendicularis ducatur
l o.
Feretur ergo grauitas portionis quidem, quæ eſt ex-
tra humidum, per rectam r l deorſum;
figuræ autem, quæ
in humido, per rectam o l ſurſum.
non manet igitur flgu-
ra;
ſed partes eius, quæ ſuntad h, deorſum ferẽtur; & quæ
ad e ſurſum.
atque hoc ſemper erit, donec f t ſecundum
perpendicularem fiat.
COMMENTARIVS.
ITAQVE figura, quæ extra humidi ſuperficiem,
11A axem habet in perpendiculari per _k_.
]
D_vcatvr_ enim b c, quæ ſecet lineam n k in m: ipſa uero
n k circunferentiam a b c d ſecet in g.
eodem modo, quo ſupra,

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