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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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III
PRINCTPTA MATTIEMATICA
28)
Designer jamr V velocitarem maximam in oscillatione quavis, LIVEn
Cintque A, B, C quancitates datae, ec finsamus quod difterentia SECVNNOS.
arcuum sIE AV +BVZ + CV.. Cum relocicates maximae sinc in
Creloide uc semisses arcuum olcillando descripeorum, in Circu-
l0 vero ut semissium arcuum illorum chordae; adeoque paribus
arcubus majores sint in Creloide quam in Circulo, in ratione
lemissium arcuum ad corundem chordas; tempora aurem in Cir-
culo sint majora quam in Crcloide in velocitacis ratione reci-
proca; patet arcuum differentias (quae lune ue resictentia d qua-
dratum temporis conjunctim) casdem Fore, quamproxime, in vera-
que Curra: deberent enim difterentiae illae in Creloide augeris una
cum relistentia, in duplicata circirer ratione arcus ad chordam, ob
relocitatem in ratione illa simplici auctam; ex diminui, una cur
quadrato temporis, in eadem duplicata ratione. ltaque ut reductio
hat ad Creloidem, caedem lumendae lunt arcuum disterentia quae
Fuerunt in Circulo obserratae, velocitates vero maximae ponen-
da sunt arcubus dimidiatis vel inceoris, hoc cst, numeris 23 Y, 23
4. 8, 16 analogx. Scribamus ergo in casu secundo, quarto et lex-
to numeros 1, 4 ec 16 pro V; ec prodibit arcuum disterentia
T2F
A +. B + C in casu secundo;
25+ = 4. A + 8B F T6C in casie
quarto; e = = 16A + 64 B + 256C in casu sExIO: FF ex his X
quarionibus, per debitam collationem ex reductionem Analyticam,
FE A = 00000976, B =0,0010847, & C, = 0,0029558. FA igitur
difterentia arcuum ut 0,0000926 V +0,00r0847 V3 +0,0029558.
ec proxrerea cum (per Corollarium Propositionis XXX) relictentia
Globi in medio arcus oscillando descripti, ubi volocitas eAt V,
SE 2d ixEuS pondus uE Z AV + 23BVZ + = CV. ad longicudinem
Ponduli; sI prO A, B ec C scribantur numeri inventi, het relistentia
Crlobi ad ejus pondus, uc0,0000585V +0,0007545V2 + 0,0022169V
ad lonsitudinem Penduli inter cenerum suspensionis et Regulam
id cA, 2d 121 digitos. Unde cum V in calu secundo designet 1.
in quarto qu in sexto 16: crit relistentia ad pondus Globi in casu
secundo uc 0,0030298 2d 22Y, in quaYEO UE 0,0417+02 ad 1217 in
TCXTO Ut 0,61675 2d 125.
Arcus quem punctum in silo norarum in catu sexto descripsics
CFaE 120 - =- seu. 119,3 digitorum. EE propterea cum radius cAec:
222 dixitorum, ec lonsicudo Penduli incer punctum suspensionis
de