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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 259v, page id 00068200:0520
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minima seu
perpendicularis ad paraio um perpendicuraris
RH producatuo dum ipsi D) tangenti verlicis parabolae occurrat in β, et ipsi KS tangentt verticis
Hyperbolae in S. intervallum SC erit ipsi minima RH aequale nam ob angulum DBR aequalem
ticamu
asas
EX
ot aquales, ergo et rB et 2R2H.
endam
proim
si a me demonstratum hoc est: si recta SB perpendicularis cuurvae H in puncto
ioe
applicetur iln transferatur in Vd seu normaliter applicetur alterutri rectarum ut CB in Y, sic
ex
am Pheorema geneceft
ex
idem est en
occurrat duabus rectis parat
ut si opus producta frajiciatur per punctum curvae H. tunc nova curva, per omnia punccta
D hoc modo transiens, habebit figuras curo arcubus curvae prioris proportionales, sti
3
figura id id iVY 83 KD. V. d K erit aequalis rectargulo sub arcullia rectam
extenso D et intervallo duarum rectarum parallerarum DB. KS. Data igitur
extensione cuvae curvae paraholicae in rectam dabitur quadratura Hyperbolae, ac
proinde inventio logarithmorum. Est autem facilius curram extendere organde
Curvam extendere in rectam, quam figuram cuivilineam transformane
D387
sit initur recta  quam in eodem plano constituta semiparabola tangat vertice D inde provoluta
c
quad rectilineam
et in situm (D) EBBH) translatu tangat puncto 2, et denique in situm (DD(BB) CBHB (HAD
transeata tangat puncto 3H. erit recta rectae D pars provolutione percursa D (2H)
aequalis carvae crcu curvae parabolicae arcui D2H, et pars rectae D(3H)) aequalis arcui
Et  durante provolutione
Locus omnium punctorum, trochscilicet trochoidem parabolicam
punctum fixum D describere intelligatur novam lineam in quam cadant omnia
parabolico DBHY.
loca puncti D. nempe D(D)(DD. sumnm inter caetera provolutionis puncta
assumamus unum (2H) cui respondet situs parabolae provolutae. (D) (3B (3H) (H) ()
Hujus puncti D ZH in situ primo tangens 2H2F axi DB occurrens in 2T quod punctum
2F et in hunc tangentem perpendicularis ex D, DZ. nunc transtata puncta 2T in (27) et
A in (A) et erit (D() ordinata ex curva trochoide D (D)(D) in axem D(2H) (B3 H)
Et sodtem Rordu  D2H translata in (D) (2H) est perpendiculoris ad trochoidem in (D)
descripta igitur hac trodioide
(34))
(27
2B
p. 18
qui erunts sectores, VC. MV, VC3 MV
Descripta igitur hac curva Trochoide, si datinnderi
logarilhmum invenire libeat, ita procedere lcebit
sint duo numeri 2L2M et 3L 3M, quorum
quaeruntur Logarithmio. Dutis M2 Y vel 3M3Y
sive in altera figura 2725, 373d. constat patet
equari seu _KD2Y2dK aequari arcui, D2H, ducto in rectam  CY seu DK. seupsi
sectorem, VCMaquari spatio VC+YM adaboticom
D sit aequ. DX s et nommiliter duci intelligatur in rectam D(2H) (2H),  aequabiturK E
rect puni parabolido in rectam extenso TH) ducto in rectam Dao. seu rectangulo ∞
quod punctum (2H) sic invenietur. Sumatur DB) aequalis ipsi D 2A vel ipsi. (d (2 A) et ex (B
educta perpendicularis occurrat Trochoidi in puncto (D). inde sumta (D) (EH) aequ D EH.
habelitur punctum H ideoque et rectangulum DH. A quo ut detrndatur Triangulum
C2Y2M. Quaeratur rectangulum sub rectu CV et recta nova 2. quod sit aequale imidio
rectangulo Cx1 C2Y2M erit CV. S2 aequ C3Y. 2Y2M. Ergo CY ad C. Y ut 2Y2M, seu 2Y
est ad  s= seu ad 2Y 2. quod verum est, si 2 sit punctum in quo educta 2Y
angulo V. Y A recto occunit ipsi sc pproductae) in 2. Est enim YC ad C2Y ut V. Tad
relim
cum ips
Amus . 2Y S dimidium B a- transtatum in 7 HZ jeu aequale secori h
eodem modo
clinquet D2Y et erit rectangulum co D2E, ut loganthimus quositus
si quaeras punctum 38. habebis D3E aequale loga et Reclangula - 1d D2
equale soparitEmo seu sectori VC3MNC
(3B)