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# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 7
# Folio 29v, page id 00068160:0058
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sed ut definiamus progressum conatuum centralium paracentricorum
intelligantur tangentes seu elementa curvae, 1C2C inst et 2C3C in H sitque pH ex Peducto
perpendiculanter occumens ipsi 2C3C productae in H et porro occurrens ipse
denique in 1C2CN recta sumatur A, sic ut sit H parallelqu Rve
eut _ 3CK: MH: 2C3C: LE_ CH. Rursus ob tiangula
ZCPN, et H similia erit MH: H:: CP. e ve (PH seu
+ fick 2CK
HV. CP 3 2(7C: CHSCK. PH. H. CP
Verrim ut note inveniamus WHAH et Hps
intelligatur evolvicurva _ CC, et quidem
ordine retrogrado 3C=C,C, ata ut (it er
OIV = FBC, et 2(2V = L3C2C jam
 in CEY sumatur, utsit .V W parallel. CD
erit
ussq
3CK: 1V W i 2CZCC: CV
1V B: IV2V :: CP: PH
Ergo 3CK. PH: IVEV. aP
2C3C.
Ergo ipsae 3Ckautr conatis paracentrici, sunt
go 3CK = IVEV. CP. 2BC: PH. CV. jan atunde seu ipsae ces
conatus parrcentrici 3CK, sunt in directa ratione, radiorum (ce)elementorm
curvae motus ( 2C3C), elementorum curvae molisis evolutione descripto (iv
et in neciproca ratione distam distantiarum gentu a langente (seu ipsarum
et curvae evolutae (seu CV,
vel in recipioca, ratione triangulorum CpV
ipsaesist
porro ipsae sEY sunt in composita lationeerementa curvae el evolution
descriptae sunt in composita ratione arcum evolutorum (CV) et angulorum
VC2Y seu 3C2CK ergo is cum 3Ckissint ut 1V 2V. CP. 2C3C: PHCt
et IVLV sint ut anguli  deflexuum set CV, ergo 3CK fient ut
anguli deflexn aui
deflexus et2 (3C. CP: PH. Assumaluo directrix
Faliqua vel axis AB id  nered cui ex p occunnt PR  ad anguo
ectos, et ex A educatur alia ad AQ perpendicularis, t AE, et
psis AE APi opus productae occuptie occurrat tangens CH BCH, in
dq et in f idem vero jam poterat ex superiribus derivari nec proinde opus faisset
lineae evolutione, nam invenimus 3ck  3CK. PH: H CP: 2C3C: CH. Ergo
F ipsae 3CK, sunt in directa ratione HN CP, 2C3C et recipioca PH. CH jam ipsae H
H sunt in con (ob angulum HNC recto aequivalente) sunt ut in composita
coratione ipsarum CH, et sinuum angulorum fexus N2CH, ergo quos
directa ratione elme velocitatis in curva (2C3C, singulus sinuum angulorum
a centro pH; paulo apte autem eadem invereramus, iisi quod pro simubus
deflexus prodieiant ipsi anguli deflexus, sed in angulis inassignabilibus
sinus sunt angulis proportionales. ducantur duae puraltelae AE, et RF
et velocitatum in va, e centro p, est parallita axicurrae A ARi ee A plam Cui
educatur Es occurrens ipsi ps ex pendemaliter
S. Ep L: pC. CH, ergo quia Ep constars feat Es, ut BC. CH
centra Leqdimatur ducatur si placet recta constans quaecunque positione et magnitudinet motu regulam semper gyrari circa curba, mobile ipsum
dete iminata, seducta si plac ut Ps ed pE (educta si placet
et angulo PES, aequali
(ita ut 25 seuper cadam in rplinter parallelas AE
HC
educta
P
et reciproca PH, CH, ergus erunt ipsae 3CK in directa ratione E, C p rC3C.
deflexus (3) et radiorum CP, et reciproca distantiarum dengentis
finus vocabimus Z. erit erunt ipsae 3CK, ell in directa ratione Z, CH, CP, 2C3C.
et reciproca pH seu conntus centi paracentrisi sunt ut anguli in
(quarum siplacetun eR transeat per P centrum, at Ex centro p
a perpendicularis ex curva occunt inp
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