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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14115DE CENTRO GRAVIT. SOLID. bere proportionem, quam ſpacium g h ad dictã
figuram, hoc modo demonſtrabimus.
Intelligatur circulus, uel ellipſis x æqualis figuræ rectili-
neæ in g h ſpacio deſcriptæ:
& ab x conſtituatur conus, uel
95[Figure 95] coni portio, altitudinẽ habens eandẽ, quã cylindrus uel cy
lindri portio c e.
Sit deinde rectilinea figura, in quay eade,
quæ in ſpacio g h deſcripta eſt:
& ab hac pyramis æquealta
conſtituatur.
Dico conũ uel coni portionẽ x pyramidiy æ-
qualẽ eſſe.
niſi enim ſit æqualis, uel maior, uel minor erit.
Sit primum maior, et exuperet ſolido z. Itaque in circu
lo, uel ellipſi x deſcribatur figura rectilinea;
& in ea pyra-
mis eandem, quam conus, uel coni portio altitudinem ha-
bens, ita ut portiones relictæ minores ſint ſolido z, quem-
admodum docetur in duodecimo libro elementorum pro
poſitione undecima.
erit pyramis x adhuc pyramide y ma
ior.
& quoniam piramides æque altæ inter ſe ſunt, ſicuti ba
116. duode-
cimi.
ſes;
pyramis x ad piramidem y eandem proportionem ha-
bet, quàm figura rectilinea x ad figuram y.
Sed ſigura

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