Archimedes - Archimedis De iis qvae vehvntvr in aqva libri dvo

Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

[31.] LEMMAI.

[32.] LEMMA II.

[33.] LEMMA III.

[34.] LEMMA IIII.

[35.] PROPOSITIO VII.

[36.] PROPOSITIO VIII.

[37.] COMMENTARIVS.

[38.] PROPOSITIO IX.

[39.] COMMENTARIVS.

[40.] PROPOSITIO X.

[41.] COMMENTARIVS.

[42.] LEMMA I.

[43.] LEMMA II.

[44.] LEMMA III.

[45.] LEMMA IIII.

[46.] LEMMA V.

[47.] LEMMA VI.

[48.] II.

[49.] III.

[50.] IIII.

[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.

14718DE CENTRO GRAVIT. SOLID. tione quarta Apollonius demonſtrauit. Si igitur à ſingu-
lis horum circulorum, duo cylindri fiant; unus quidem ad
baſis partes; alter ad partes uerticis: inſcripta erit in co-
no ſolida quædam figura, & altera circumſcripta ex cylin-
dris æqualem altitudinem habentibus conſtans; quorum
unuſquiſque, qui in

100[Figure 100] figura inſcripta con-
tinetur æqualis eſt ei,
qui ab eodem fit cir-
culo in figura circũ-
ſcripta. Itaque cylin
drus o p æqualis eſt
cylindro o n; cylin-
drus r s cylĩdro r q;
cylindrus u x cylin-
dro u t cſt æqualis;
& alii aliis ſimiliter.
quare conſtat circũ-
ſcriptam figuram ſu-
perare inſcriptam cy
lindro, cuius baſis eſt
circulus circa diametrum a c, & axis d e. atque hic eſtmi-
nor ſolida magnitudine propoſita.

PROBLEMA III. PROPOSITIO XII.

Data coni portione, poteſt ſolida quædam
figura inſcribi, & altera circumſcribi ex cylindri
portionibus æqualem altitudinem habentibus;
ita ut circumſcripta inſcriptam exuperet, magni
tudine, quæ minor ſit ſolida magnitudine pro-
poſita.

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