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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 35, page id 797435492:0243
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
# Lines: 41 recognised, mean confidence 0.94
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Y E C F. IY
compositam e rationibus applicatarum ab ictis punctis ad rectam AZ
(ipsiscilicet AY parallelarum) ec inxerceprarum a ransentibus ad ilta
puncta ac dictis applicatis (vel, rationem relocitarum xquari rarioni
applicacarum ex interceptarum ratione subducta.)
Nempe h duae rectxe MT, NZ curram rangene ad puncta M, N,
prorractae Z A Occurrentes in T, Z; _ applicentur II P, NO ad
TA Parallelae, velocitarum ad puncta, M, N proportio componetur
e proportione iplius TP ad PM, ex iplius  A ad 27. Nam Pig. 21
relocitas in M ad velocirarem unitormem per A Y sC habet ut TP ad
PM; ex relocitas ilta uniformis se haber ad velociratem in H, ut
ON ad OX. Ergo velocitas in M ad velociratem in HI ex his
duabus rationibus P P ad PMI, _ OH ad Q Z componetur NOretUT a
concursu tangentium ductâ PF ad A Z Parallela; FOrE TF, X B
=TP. PM - 1. O N. 9X.
ZV. Obiter interjicio generalem hinc se bene Facilem consequi
Problematis istius solutionem, quam rancifecit, ex cui tantum laborem
impendit Galilans, quamque Torricellius pronunciat cum quam optime
de ingenioliltime reperisse. Rem ita proponit Torricellim (nam ipse
Calilans ad manum non est) propolicâ quavis parabola, cujus
vertex A oportet punctum aliquod lublime reverire; e quo li grare
cadat usque ad A, _ ex puncto cum impetu jam concepto horiz Onta- F18. 22.
liter ConVertaLUE, ipla propositam parabolam delcribat (notetur, quod
motus descensirus parabolam describens non e puncto sublimi, sed ab
ipso puncto a censeturinchoare.) Huc recidit Problema, Galilai sup
policis insastendo, ut determinentur particulares relocitates motuum,
unitormis horizoncalis, seu trantrersi, e aequalirer crelcentis descen-
sivi quorum e compolitione descripra concipitur exhibira parabola.
Nosillud, qua cunque sic crelcentis descensiri motus rario, quicunque
modus, seneraliter exequemur; specialem illum de parobola casum in
exemplum subjuncturi. () Reperiatur in recta AZ (quae lane currX
diameter est) punctum aliquod, ut P, a quo si ordinatim applicerur
PM, e ducatur tansens MT, rectae AZ occurrens in T, Sic in-
tercexca TP aequalis ip(I PM; tum sumatur in Z a prorracta recta
AS = AP. Dico Factum.
Dam quoniam S A = AP, concipiet mobile descendens ab S in
Rtantum impetum, quantum ab A ad Pcurram describendo (ponitur
enim increscentis relociratis motus uerobique prortus idem) ilte rero
impetus xquatur imperui, quo mobile à T descendens unitormi moru
percurret rectum TP, eodem tempore quo recta AZ unitormiter
laca.