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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRINCIPIA MATHEMATICA.
3
Rtenim Bantibus quae in Lemmate ex Theoremace novissimo
constructa sune, concipe axem Sphaerae AB diridi in particulas
innumeras aequales D d, ec Sphaeram totam dividi in coridem
laminas Spharicas concaro. conrexas P Ffé; ec crigatur perpen-
diculum an. Per Theorema superius, vis qua lamina L l fe
trahic corpusculum P es uE D F 9X FF ec vis particulae unius ad
distantiam F F. vel F F exercita conjunctim. FK autem per Lem
ma novissimum, D d ad Ff uE F F. ad FS, e inde Ff aequalis
PSX T
PF; _C D F gX Ff aequale D d in D F. qZFS
DF d proPter.
ea vis laminae F. Ffe CA ut D d in D E. qX Pd
EPF
ex ris particulae ac
distantiam P F exercita conjunctims hoc cA (ex FIy pOtheM) ut
DNX D d Ccu area eranescens D Nn d. Sune igitur laminarum
omnium vires in corpus F exerCIta, UC arCK OmneS D NVnd, hOC
es Sphaerae vis FOLD uE arca toca AB N A. 9. F. D.
Corol. T. Flinc s vis centripeta ad particulas lingulas cendens,
eadem semper maneat in omnibus dictanciis, e Aat D N uE
DF 9XES
F: erit vis tora qua corpusculum a Sphaera attrahitur,
uc arca AB N A.
Corol. 2. Si particularum vis centripeta sit reciproce ut distantia
corpusculi a se actracti, et Aat D N uE  F.gXPS
FF
: Crit vis qua
corpusculum P a Sphaera eora actrahitur ut arca ABNA.
Corob. 3. Si particularum ris centripeta sic reciproce ut cubus di-
Tantiae corpusculi a se aEFractis _E HAE D NV UF D F. gX PS.
F Lg.
crit
vis qua corpusculum a cota Sphaera accrahitur ut area IB NV A.
Corol. 4. EF universaliter si vis centripeta ad singulas Sphaerae
Particulas tendens ponatur esse reciproce ut quantitas V, Hac au-
tem D N UE D E gXPS
PF. YV; erit ris qua corpulculum a Sphaera tota
accrahitur ut area AB LIA.
lo TH K_
PRLMD 
CROFC