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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13311DE CENTRO GRA VIT. SOLID.& per o ducatur o p ad k m ipſi h g æquidiſtans. Itaque li
nea h m bifariã uſque eò diuidatur, quoad reliqua ſit pars
quædam q m, minor o p.
deinde h m, m g diuidantur in
partes æ quales ipſi m q:
& per diuiſiones lineæ ipſi m K
æ quidiſtantes ducantur.
puncta uero, in quibus hæ trian-
gulorum latera ſecant, coniungantur ductis lineis r s, t u,
89[Figure 89] x y;
quæ baſi g h æquidiſtabunt. Quoniam enim lineæ g z,
h α ſunt æ quales:
itemq; æquales g m, m h: ut m g ad g z,
ita erit m h, ad h α:
& diuidendo, ut m z ad z g, ita m α ad
α h.
Sed ut m z ad z g, ita k r ad r g: & ut m α ad α h, ita k s
112. ſexti. ad s h.
quare ut κ r ad r g, ita k s ad s h. æ quidiſtant igitur
22I1. quinti inter ſe ſe r s, g h.
eadem quoque ratione demonſtrabimus
332. ſexti.

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