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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 28, page id 797435492:0236
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Si Y
E. _ C F. YI
diverliratem alterius direxlitas rire consequatur accommodéturque.
L.C c. 8. I recta Z A semper per rectam A Y sibi parallela feratur.
motu quolibet unitormi, vel difformi (crescente, vel decrescente
vel alcernante secundum velocirarem, juxta rationem quamris ima-
ginabilem) et in ea punctum aliquod M. deteracur, ica FaMeN VE
puncti motus linex rectx motibus per lingulas quasque cemporis
partes caldem proportionentur, producetur urique linea recta. Nem-
De lituerie semper AB. A C:: BM. C H. Vel AB, M X:: AM,
E I (Dolica Scilicet M X ad A C parallela) liquer puancta A, M
 in una recta verlari. Fs enim rectae linex proprietas in Fle-
mento VI. demonstrata, quod ad eam parallelos applicata recta
linex suis ad desionatum in ea punctum distantiis proportionales in
rectam lineam cerminantur. Quod. si motus hi sic inter se contem-
Perentur, uc allumpta quadam linea D. habear rectangulum ex diffe-
rencia linex D, e iplius BM (a. puncto mobili decurlae in recta
AZ) e ipta BM ad. quadracum ex AB (codem rempore decurla
a linea AZ) rationem semper eandem proxignetur ellipsis ant cir-
culus; circulus quidem si rario propolira fuerir aequalitas, _ an-
sulus Z A.P rectus, ellipsis si secus; ex in his erie D una diame-
trorum, licum habens in linea A. Z primo polica, a vertice A pOr-
recta vertus partes Z. Sin ica se habeane, ut rectangulum ex. suma
linearum D, e BM _ ipsa. B M semper eandem cum quadrato
ex AB proportionem serret, eo compolito motu procreabitur hy-
perbole; quadraca quidem illa (vel aequilatera rectansula) si racio
delionata fuerit aequalitatis, _ angulus Z A Y rectus; lin aliter.
alterius, prorationis altionata quantitare, speciei; cujus transversa
diameter aequabitur ipsi V, Cicum habens in Z A primo polita a
verrice A prorensa vertus. partes aversas ab 2; eE PaTAIeTEK Cx
ratione data determinatur. Ouod si perpetuo rectangulum ex ipsa
O, e decursa B M ad quadratum ex AB candem PerPeTUd Fa-
rionem obtinet, constabir effici lineam parabolisam, cujus para-
meter ex rectae D, datxque rarionis propolie quantirare facile
dEFMICTUE. EF in horum primo quidem casu si mOruS tranIVeRTS
per A Y ponatur unitormis, etiam motus descendens per A Z unitor.
mis erit; in secundo ee tertio (I motus per A Y sic unitormis, erit motus
descendens perpetuo crescens; eodem que polito quoad ultimum casum.
in quo parabola fic. punctum M continuo relocitate crescet aequalirer
Nec abilimili modo quaevis alia linea tali morus compolicione produsta
concipi potest. Sed ut eo quo cendimus aliquando perveniamus:
asedum videnmus ecquid in rem Machemasioam ucilicaris ex hujus-
modi
e
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