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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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MIIIIIII
PRINCTDTA MATETEMATTCA.
Globus vel Cylindrus incidie, ri reRexionis quam maxima reslIAnE. LIBEE
FF cum relistentia Cilobi (per Propolitionem novissimam) sic duplO SECVNDOS.
minor quam resistentia Cylinctris se Globus sic ad Cylindrum uE
duo ad eria, ec Cylindrus incidendo perpendicularicer in particulas
iplasque quam maxime refectendo, duplam sui ipsius velocitarem
ipsis communicet: Cylindrus quo tempore dimidiam lonsitudinem
axis lui describie communicabie morum particulis qui siE ad cocum
Cplindri morum uc densitas Medii ad denstatem Cylindri; e C710-
bus quo tempore totam longitudinem diamerri sux describit, com-
municabie motum cundem particulis; ec quo tempore duas tertias
Partes diametri sux describit communicabit motum particulis qui
sE ad eorum Globi motum uc densicas. Medii ad densitatem Cl0bi.
Et propcerca Globus relictentiam paritur quae sic ad vim qua FOtUS
ejus motus vel auterri pole vel generari quo tempore duas tertias
partes diametri sux describit, uc densitas Medii ad densitatem.
Clobi.
Cas. 2. Fonamus quod parciculae Ntedii in Globum vel Crlin-
drum incidentes non refectantur; et Cylindrus incidendo perpen.
diculariter in particulas simplicem Cuam velocicatem ipsis commu:
nicabie, ideoque resistentiam paritur duplo minorem quam in pri-
ore calu, e resistentia Clobi erit etiam duplo minor quam prius.
Cas. 3. Ponamus quod particulx Medii vi reflexionis neque ma-
xima neque nulla, sed medioeri aliqua resiliant a C1lob0; et resi:
Sentia Gilobi crit in eadem rarione medioeri incer resistentiam in
primo casu de relictenciam in secundo. Q. L.. L.
Corol. T. Fline EGlobus ex particulx sinc infnice dura, ex vi om-
ni elastica ex propterca criam vi omni reRexionis destituta: re
liltencia Clobi crit. ad rim qua cocus ejus motus vel auterri posie
vel gencrari, quo tempore Cilobus quatuor certias partes diametri:
sux describie, ut densicas Mesii ad densitarem Globi.
Corol. 2. Relctencia Globi caeteris paribus, cs in duplicata ra-
rione velocicatis.
Corol. 3. Relctencia Colobi exreris paribus, est in duplicata r2-.
eione diametei.
Corol. 4. Relistentia Clobi, caeteris paribus, est uc densitas Medii.
Corol. 5. Relistentia Clobi est in ratione quae componitur ex du
plicata ratione relocitaris et duplicata ratione diamerri de ratione
densitatis. Medii.
11
11
Corol
MILHIHIIHHENBHIEHLHHHIIIHNRAIANTENMHMHNHIENGIMMMIEMEMEHGIIMMIIIII