Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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[61.] ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.
Page: 107
[62.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.
Page: 113 (1)
[63.] PETITIONES.
Page: 114
[64.] THEOREMA I. PROPOSITIO I.
Page: 114
[65.] THEOREMA II. PROPOSITIO II.
Page: 118
[66.] THE OREMA III. PROPOSITIO III.
Page: 121 (5)
[67.] THE OREMA IIII. PROPOSITIO IIII.
Page: 122
[68.] ALITER.
Page: 123 (6)
[69.] THEOREMA V. PROPOSITIO V.
Page: 125 (7)
[70.] COROLLARIVM.
Page: 127 (8)
[71.] THEOREMA VI. PROPOSITIO VI.
Page: 127 (8)
[72.] THE OREMA VII. PROPOSITIO VII.
Page: 129 (9)
[73.] THE OREMA VIII. PROPOSITIO VIII.
Page: 131 (10)
[74.] THE OREMA IX. PROPOSITIO IX.
Page: 143 (15)
[75.] PROBLEMA I. PROPOSITIO X.
Page: 145 (17)
[76.] PROBLEMA II. PROPOSITIO XI.
Page: 146
[77.] PROBLEMA III. PROPOSITIO XII.
Page: 147 (18)
[78.] PROBLEMA IIII. PROPOSITIO XIII.
Page: 148
[79.] THEOREMA X. PROPOSITIO XIIII.
Page: 149 (19)
[80.] THE OREMA XI. PROPOSITIO XV.
Page: 153 (21)
[81.] THE OREMA XII. PROPOSITIO XVI.
Page: 154
[82.] THE OREMA XIII. PROPOSITIO XVII.
Page: 155 (22)
[83.] THEOREMA XIIII. PROPOSITIO XVIII.
Page: 156
[84.] THEOREMA XV. PROPOSITIO XIX.
Page: 157 (23)
[85.] THE OREMA XVI. PROPOSITIO XX.
Page: 160
[86.] THEOREMA XVII. PROPOSITIO XXI.
Page: 164
[87.] THE OREMA XVIII. PROPOSITIO XXII.
Page: 166
[88.] THEOREMA XIX. PROPOSITIO XXIII.
Page: 171 (30)
[89.] PROBLEMA V. PROPOSITIO XXIIII.
Page: 172
[90.] THEOREMA XX. PROPOSITIO XXV.
Page: 174
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32ARCHIMEDIS 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
11Suppleta
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
22B tionis in humido demerſæ. ſumantur deinde centra graui
tatum: ſitq; ſolidæ magnitudinis a p o l grauitatis centrũ
33C r; ipſius uero i p o s centrum ſit b: & iuncta b r produca-
44D tur 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
55E r o minor, quàm quæ uſque ad axem. Quare angulus r p ω
66F acutus 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
19[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-
77G ſum feretur ſecundum perpendicularem, quæ per b ducta
eſt, ipſi r t æquidiſtans: quod uero eſt extra humi dum

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