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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1257DE CENTRO GRAVIT. SOLID. metrum habens e d. Quoniam igitur circuli uel ellipſis
a e c b grauitatis centrum eſt in diametro b e, &
portio-
nis a e c centrum in linea e d:
reliquæ portionis, uidelicet
a b c centrum grauitatis in ipſa b d conſiſtat neceſſe eſt, ex
octaua propoſitione eiuſdem.
THEOREMA V. PROPOSITIO V.
SI priſma ſecetur plano oppoſitis planis æqui
diſtante, ſectio erit figura æqualis &
ſimilis ei,
quæ eſt oppoſitorum planorum, centrum graui
tatis in axe habens.
Sit priſma, in quo plana oppoſita ſint triangula a b c,
d e f;
axis g h: & ſecetur plano iam dictis planis æquidiſtã
te;
quod faciat ſectionem K l m; & axi in pũcto n occurrat.
Dico _k_ l m triangulum æquale eſſe, & ſimile triangulis a b c
d e f;
atque eius grauitatis centrum eſſe punctum n. Quo-
niam enim plana a b c
82[Figure 82] K l m æquidiſtantia ſecã
1116. unde-
cimi.
tur a plano a e;
rectæ li-
neæ a b, K l, quæ ſunt ip
ſorum cõmunes ſectio-
nes inter ſe ſe æquidi-
ſtant.
Sed æquidiſtant
a d, b e;
cum a e ſit para
lelogrammum, ex priſ-
matis diffinitione.
ergo
&
al parallelogrammũ
erit;
& propterea linea
2234. prim@ _k_l, ipſi a b æqualis.
Si-
militer demonſtrabitur
l m æquidiſtans, &
æqua
lis b c;
& m K ipſi c a.

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