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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 145, page id 797435492:0399
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1
i
t
L E C Y. XIII.
In pramissas explicationes animadvertarur generatim.
2. Propolicam quamris xquationem explicans curva designatur
hoc modo: Proxonatur, exempli causa, aegnatio a. )- bat.) - c6a3
d3aa fa =n; In recta indetinite procensa HII designetur pun. F1B. 219.
ctum A, proradicum termino, vel origine; tum arbitrarie sumpea
AC pro indeterminata radice a; hac C K aequalis primo lcrici pro-
Politam xquarionem continentis sradu; nempe su hic GR == a. I b
aa Curique rationem a adc semel concinuando AE
 rationem a ad d bis continuando AF
a
 aC Ita POrrO) tum inter
AG, CRtor mediarum proportionalium, quot aequationis proposiex
pradus exisit (is aurem a pura quae sita radicis poreltare indicatur) in
hoc nempe casu quatuor mediarum proporrionalium prima (C CO;
per ejulmodi puncta C) traducta curra AOO propolito deserriet.
2. Deradicibus FalsIS, Pen nesativis nihil actisimus supra; cxre-
rum ex reperiuntur hoc modo. Equarioni propolux Tubrogerur
altera, cujus in locis paribus (eriam vacuos locos adnumerancio)
liona sunt illis contraria, quae habet aequario propolica; crunt hu-
jusce subditiciae aequationis radices verx, seu policira iplius propolite
aequarionis radices Fallae, Peu nesativx. ExemploIE aeqatio a 3.  baa
=n3; vel a3- F ba a  - n3 = = O. ScibrOSeTUE a3- ba at.  - n3- = 0; _
hujus, t uti supra edoctum, rerx radices desigrentur, hae proposita + En Serie 3.
agnarionis FalIX erunE. RurIUS (IE A13 - bAa = - n3, vel a3- baa n3
0; substituatur xequario a3-] baa.  n3 =0; haec nullam veram
radicem obtiner; ergo nec aegnario proposica Falsam admirrie.
3. Duinimo data vera radice quapiam, deprestiocis pradus requa-
tio quaedam (alsIs reveriendis inserrier, qualis ita determinatur. Pro-
Donacur xquario quaeris, puta a3 t baa =- n3; Cujus nora lic radix una,
quae rocerur f. Construatur xequario plane similis propolix, ca(
demque coefficientes habens, tarirum pro a substicuendo f; nempe
3 - - bff = n3. ergo a3. I. ba a - = n3 - f3 + bFf; adeoque
ad t baa - f3 - bff =- 0. dividatur haec x quario (id quod sein-
per tieri porest) per a f; proveniet aa
I ba I bf
LFa-) ff =O; Cujus X
quaciones exdem erunt cum reliquis aequationis proxolicae radicibus s
qux proinde duas collisicur radices Falsas habere; itaque mutacis loco-
rum parium sienis, ut ila tiat aa
-ba. - bf
fa) ff=0; hujus aequarionis
verE