Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[51.] V.
[52.] DEMONSTRATIO SECVNDAE PARTIS.
[53.] COMMENTARIVS.
[54.] DEMONSTRATIO TERTIAE PARTIS.
[55.] COMMENTARIVS.
[56.] DEMONSTRATIO QVARTAE PARTIS.
[57.] DEMONSTRATIO QVINT AE PARTIS.
[58.] FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.
[59.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.
[60.] CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.
[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.
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120FED. COMMANDINI triangulum m k φ triangulo n k φ. ergo anguli l z k, o z k,
m φ k, n φ k æquales ſunt, ac recti.
quòd cum etiam recti
ſint, qui ad k;
æquidiſtabunt lineæ l o, m n axi b d. & ita.
1128. primi. demonſtrabuntur l m, o n ipſi a c æquidiſtare. Rurſus ſi
iungantur a l, l b, b m, m c, c n, n d, d o, o a:
& bifariam di
uidantur:
à centro autem k ad diuiſiones ductæ lineæ pro-
trahantur uſque ad ſectionem in puncta p q r s t u x y:
& po
ſtremo p y, q x, r u, s t, q r, p s, y t, x u coniungantur.
Simili-
ter oſtendemus lineas
76[Figure 76] p y, q x, r u, s t axi b d æ-
quidiſtantes eſſe:
& q r,
p s, y t, x u æquidiſtan-
tesipſi a c.
Itaque dico
harum figurarum in el-
lipſi deſcriptarum cen-
trum grauitatis eſſe pũ-
ctum k, idem quod &
el
lipſis centrum.
quadri-
lateri enim a b c d cen-
trum eſt k, ex decima e-
iuſdem libri Archime-
dis, quippe cũ in eo om
nes diametri cõueniãt.
Sed in figura alb m c n
2213. Archi
medis.
d o, quoniam trianguli
alb centrum grauitatis
33Vltima. eſt in linea l e:
trapezijq́; a b m o centrum in linea e k: trape
zij o m c d in k g:
& trianguli c n d in ipſa g n: erit magnitu
dinis ex his omnibus conſtantis, uidelicet totius figuræ cen
trum grauitatis in linea l n:
& o b eandem cauſſam in linea
o m.
eſt enim trianguli a o d centrum in linea o h: trapezij
a l n d in h k:
trapezij l b c n in k f: & trianguli b m c in fm.
cum ergo figuræ a l b m c n d o centrum grauitatis ſit in li-
nea l n, &
in linea o m; erit centrum ipſius punctum k,

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