Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.
[91.] THEOREMA XXI. PROPOSITIO XXVI.
[92.] THEOREMA XXII. PROPOSITIO XXVII.
[93.] PROBLEMA VI. PROPOSITIO XX VIII.
[94.] THE OREMA XXIII. PROPOSITIO XXIX.
[95.] THEOREMA XXIIII. PROPOSITIO XXX.
[96.] THEOREMA XXV. PROPOSITIO XXXI.
[97.] FINIS LIBRI DE CENTRO GRAVITATIS SOLIDORVM.
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14919DE CENTRO GRAVIT. SOLID. 102[Figure 102]
THEOREMA X. PROPOSITIO XIIII.
Cuiuslibet pyramidis, & cuiuslibet coni, uel
coni portionis, centrum grauitatis in axe cõſiſtit.
SIT pyramis, cuius baſis triangulum a b c: & axis d e.
Dico in linea d e ipſius grauitatis centrum ineſſe. Si enim
fieri poteſt, ſit centrum f:
& ab f ducatur ad baſim pyrami
dis linea f g, axi æquidiſtans:
iunctaq; e g ad latera trian-
guli a b c producatur in h.
quam uero proportionem ha-
bet linea h e ad e g, habeat pyramis ad aliud ſolidum, in
quo K:
inſcribaturq; in pyramide ſolida figura, & altera cir
cumſcribatur ex priſmatibus æqualem habentibus altitu-
dinem, ita ut circumſcripta inſcriptam exuperet magnitu-
dine, quæ ſolido _k_ ſit minor.
Et quoniam in pyramide pla
num baſi æquidiſtans ductum ſectionem facit figuram ſi-
milem ei, quæ eſt baſis;
centrumq; grauitatis in axe haben
tem:
erit priſmatis s t grauitatis centrũ in linear q; priſ-
matis u x centrum in linea q p;
priſmatis y z in linea p o;
priſmatis η θ in l_i_nea o n;
priſmatis λ μ in linea n m; priſ-
matis ν π in m l;
& denique priſmatis ρ σ in l e. quare

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