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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 53, page id 797435492:0089
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Lo E C F.
V. Verum extra casushos, e particulares alios (mihinon incog.
nitoS, at nunc a mectorSuS) Problema aei; Tolidum est; in summo
quipre gradu tale; quatuorque subinde Solutiones admittens; perque
lineam erolri pocest (ut alia pleraque, licuri pridem adnioricum
nobis) sibi peculiarem; illam tioc modo quim expedicistime per
puncta describendam: Per dacum punctum X procendatur indetinite
recta GF. ad datam. C B parallela; connectarurque recta XC:
d super hanc ceu diamerrum. describatur circulus XIC I. tum c
puncto C prodeant quorcun que recta circulum Z I C secantes punctis
l, rectamque CF punctis HI; ee adsumantur in rectis CH l rectae
lA xequales interceptis III. (ita scilicet ut puncta lrectas N H per- F18. 72.
Pecuo bilecent) perque puncta quoeris ejusmodi N craducta concipia-
cur linea; nimirum haec (quâ cerre nulla Sectio conica Faciliis de-
lincatux) problemaris noctri conttructioni deservir, ejusque liquido
naturam patetacir; siquidem ejusce cum dari circuli intersection.s
N (illae vero subinde quatuor erunc, interdum tres (contactum e-
nim inter sectionibus adnumero) nonnunquam Solummodo dux; pro-
UE dacus circulus magnirudine praeditus est alia ac alia; guxe strictim
adnoco tantum, animum adrerrenti manifeste consticura) possibiles
quasque Solutiones extribebune. ducacue enim ab ipso X ad ejusmodi
quamvis incersectionem N recta XN; _ per Ntranseat M P. ad B. C
parailela (vel ad C X) connexaque C N circulum X LC secer in I,
rectamque CX in H; item jungatur XI. e quoniam e descriptx
linex nacura seu constructione est PHI =INI; angulusque C IX, in.
Semicirculo, rectus est; erit XN = -ZII; vel ang. XNII = an9.
XHI. atqui ang. XH l’ alterno HINIP par est. Quapropter anouli.
ZN I, HINP pares sunc. adeoque recta N X iplius NP reAexus
exit. quod oporrebat tieri. Sic, inquari, enodari poterat id Pro-
blematis. ac quoniam (uc innuebam lupra) Ccomerrarum palato mi
nus sapinnt hujnsmodi Problemarum inusicatae solutiones; alirer id
lacis brevirer atque perspicue) dabimus effectum hoc. Paltem eo
laciens Lenimaricum Problema prxemittentes.
VI. Daro circulo (cujus politione data diameter G F) S puncto
C in ejusce circum serentia quoque dato; pex hoc recta ducatur; enjus
pars diamerro circumterentix que interjecta aequetur dutae recta L.
Id sic exequimur. Connectatur recta CF; 4 huic perpen-
dicularis ducatur recta FV5 ex accipiatur ad iplas L, CF tertia
proporrionalis P; e per C ansulo C FV inseratur recta R S pOr
ipsF (id aurem quom odo praectandum, edoenimus suprd) cum Per C.
ducatur
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