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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 283, page id 1041163592:0317
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IIIIIII
PRINOIPTA MATHEMATICA.
283
Cum Figura BRV T a in puncto medio V, haec s ad partem al. L. IDEn
cerutram BRV vel VSa excedic Figuram illam, deticiet ab cadem SEevuvVS.
ad parrem alceram, ex sic eidem aequabitur quam proxime.
PROPOSITIO ZXXI. THEOREMA XXV.
Si Corporis oscillantis resistentia in sinculis arcuum descriptorum
partibus proportionalibus aureatur vel minuatur in data ratio-
ne; differentia inter arcum descensu descriptum et arcum sub-
sequente ascensu descriptum, aurebitur vel diminuetur in eadem
ratione.
Oritur enim differentia illa ex recardatione Penduli per resi-
Aentiam Mediis adeoque est ut recardatio tora cique provortio-
nalis relictentia recardans. Un superiore Propositione rectansu-
lum sub recta = a B ec arcuum illorum CB, Ca difterentia Aa-
aequalis CTaE arCK BKT. Et arca illa, si maneae longitudo a B,
ausetur vel diminuitur in rarione ordinatim applicatarum DK
hoc et, in racione relictentia, adeoque es uc longicudo a B ee
relstentia conjunctim. Proindeque rectangulum (ub Aa _ Z aB
est uc a B ec relistentia conjunetim, et propterea Aa uc relisten-
EIa. d. F. D.
Corol. 2. Inde R resistentia sic ut relocitas, differentia arcuum
in eodem Lledio erit ut arcus totus delcripeus: ec COntra.
Corol. 2. Si relictentia sic in duplicata ratione velocitaris, difte-
rentia illa erit in duplicata ratione arcus totius: C contra.
Corol. 3. Ec universaliter, E relistentia sic in triplicata vel alia
quaris ratione relociratis, differentia erit in eadem ratione arcus
TOTIUS : dE COnETa.
Corol. 4. EF E relictentia sic parcim in ratione simplici relocita-
eis, partim in ejusdem rarione duplicata, difterentia erie parrim in
ratione arcus cocius ex partim in ejus rarione duplicata: e contra.
Eadem erit lex ex ratio resctentix pro relocitate, qua est differen-
tiae illius pro longitudine arcus.
Corol. 5. Ideoque sis pendulo insequales arcus successire descri-
bente, inveniri pocest ratio incrementi ac decrementi differentix nu-
jusprolonsicudine arcus desexipei; habebitur eriam rario incrementI
ac decrementi relictentix pro velocitare majore vel minore.
D02
Scholium
AI MIIMNIIIII
NTMLITMHMIEMMAMNEMERIAMNI
MipIIII