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# Title: Leibniz-Handschriften zur Technica LH 38
# Folio 120r, page id 00068537:0239
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 121v); this page is its right half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 67 lines, status machine
# Lines: 67 recognised, mean confidence 0.93
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Vellem systema planetarium per
Machinami exhiberi, men ita tantum ut
calculi ficiri possit compendium seduitacut quantum,
qet helum
nec veriodi tantum cujusque planetae, sed
artificiale vero assimiletur et sibus astrorum inter sc ast
interse exgsoatmuchi
Nssumo autem quod sieatis s
Replerus invenit, et sic satis observationibus consentire
deprehensum est planetas in Ellipsibus ferri, et quidem
ita ut, sole posito in Focorum altero sint areae per rectas
ex  ad orbitam abscisae temporibus proportionales.
sit s illipsis APH cujus avis major AN, Frci Sit F
in quo Foci F et S. et quidem sol in S. erit A Aphelium
D Perihelium,  planeta in orbita P P, cujus
loca 1P, 2p, etc. et Eru temporaquibus planeta
percurrit arcus HIP, IX2 P,  dreas seu trilinels, SIP, HS2P,
AS. P, A3
reperi
Hoc autem demonstravi per circulationem
Harmonicam praestari; nempe si mobile feratur
in orbita quacunque plana ut XTPA, et quidem duobus
motibus compositis uno circulationis Darmenicae quam
mox explicabo, altero Y ad lica orbitam praestandam
appropriato, areae TsP erunt ut tempora arcuum in
orbita percursorum, P Circulationem vero
clpio sireutationem Harmonicam voco, quae
ita temperata est, ut distantiis SP a centro circulationis s procedentibus
crescentitus in progressione Arithmetica,  velocitates circulationum
circulandi  procedant in progressione Harmonica; Exempligratia
Ex  SA, SiB, S2P, Syp, ete sint ut 10, _, 12, 13
1079, 6, 7, oai circula velocitates
circa S, in punctis A, 1P, 2P, 3P, etc. erunt utio
coha
e
crescentibus distantiis decrescent vel contra.
Pouro circulatio parmonica Mechandde sic
praestattur. Super plano striis aspero volvatur pota
dentata tis R, ita ut dentes striis aptentur, et
striae omnes tendant ad unum centrum S. in quo explano
eriu erectus sit normaliter axis immobisis, tabo mobili
circumdatus fubo mabili cui ex quo prodeat regula
SR rotamRcir cumferens. Quodsi ergo intus in R
sit quod rotam agat circa
suum axem) eadem opera ob strias plani super quo
incedit rotus, necesse erit regulam nC volvi circa S
quodsi jan
Quod autem hec moclo tempora sint ut areae
sic demonstratur. Ex punctis ep pe
maeserantes
velocitatem circulation Mobilis circa, s, dum  replaesentabunt ejusdem Mobilis
noalis in rectam sep, normales p3C YP E
ejus ruo recessum ab S d ponatur  transire a P ad  ab 1P ad 2p vel a 2 ad sp, et tem
vei accessum ad s, n movetur moli ab 1P ad 2p Edejam
santo jam tempora transitionum  aequalia inter se quod si jam
circulatio sit harmonica, erunt reciproca circulatio velocitates reciprocae
ut distantiae a centro S, ergo erit s2p ad 53P, ut 2P2E ad 1p, E
ergo rectang s2p in 1BE erit aequale rectangulo 53P in 2 p2E, ac proinde etiam horum rectangulorum
dia, nempe triangula  P52R, 2653p, erunt aequalia inter se; atque adeo aequalibus sumtis elementis
maspius nabilibus conplate intellgi possu
motibus compositas, uno accessas t adsolem vel
ansole ad orbitam praestandam accmmodati
appropriati, altero circulationis harmonicae circa solem
= ad punctum B fixum s
relatae
interse
Ve CHiNA dcLEstis