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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1152DE CENTRO GRAVIT. SOLID. tur, centrum grauitatis eſt idem, quod circuli cen
trum.
Sit primo triangulum æquilaterum a b c in circulo de-
ſcriptum: & diuiſa a c bifariam in d, ducatur b d. erit in li-
nea b d centrum grauitatis triãguli a b c, ex tertia decima
primi libri Archimedis de centro grauitatis planorum. Et
quoniam linea a b eſt æqualis
70[Figure 70] lineæ b c; & a d ipſi d c; eſtq́;
b d utrique communis: trian-
gulum a b d æquale erit trian
118. primi. gulo c b d: & anguli angulis æ-
quales, qui æqualibus lateri-
bus ſubtenduntur. ergo angu
2213. primi. li ad d utriq; recti ſunt. quòd
cum linea b d ſecet a c biſa-
riam, & ad angulos rectos; in
33corol. p@@
mæ tertii ipſa b d eſt centrum circuli.
quare in eadem b d linea erit
centrum grauitatis trianguli, & circuli centrum. Similiter
diuiſa a b bifariam in e, & ducta c e, oſtendetur in ipſa utrũ
que centrum contineri. ergo ea erunt in puncto, in quo li-
neæ b d, c e conueniunt. trianguli igitur a b c centrum gra
uitatis eſt idem, quod circuli centrum.
Sit quadratum a b c d in cir-
71[Figure 71] culo deſcriptum: & ducantur
a c, b d, quæ conueniant in e. er-
go punctum e eſt centrum gra
uitatis quadrati, ex decima eiuſ
dem libri Archimedis. Sed cum
omnes anguli ad a b c d recti
ſint; erit a b c femicirculus:
4451. tortil. itemq́; b c d: & propterea li-
neæ a c, b d diametri circuli:

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