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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 34, page id 797435492:0242
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E. F C T. IV
Nam sumpio quovis in recta YS puncto R, _ ducta RC ad
AZ parattela; quoniam vertus partes AY relocitas ascendentis
puncti, curram efficientis, semper decrescit ab MI ad O, illi vero
ex hypochesi par relocitas puncti rectam M T signenris haud de-
creseir ab M ad R, CIrque rempuS MC commune, erit spacium
COminus quam CR; unde punctum R erit extra curram. Item,
quia versus alceras parres, velocitas descenlentis, quo curra fic, in
crescir semper ab M versus O; agnalis autem ei relocitas, qua recta
M S. FE, hand crescit ab. M ad K; idemque Ec rursus cempus MC,
liquet rectam CO excedere rectam OK; _ idcirco punctum R supra
curram existere. Ouare manitectum est omnia dictae rectae puncta
extra curram exictere; e cam proinde curram contingere:
L. F. D.
ZIII. Ex hisce Rarim consectatur, hujusmodi curvas ad unum
punctum ab una tantum recta contingi.
Nam. FanSerE BONatuE rCAa MI L curram A MO ad M; _ (
fieri porest altera MZ eriam tangat. Erso eodem tempore, eadem
velocirate (illi scilicet, quae puncti curram describentis ad contactum
M acquisiex relocitari Xquatur) deseribetur utraque recta XP, TM;
guare Z P, T P aequales ernnE, FOtuM _ parS: G. P. A. ErgO
nOn taNSeF aIECTA PEXTEE POSITaM MIT. I) Hlanc speciatim de circule
demonstravit Enclides; de Sectionibus Conicis Apollonins, de lineis
aliis alii. Exhinc Luerum emeroit hand aspernandum, quod eadem
Oper a propositiones de tangentibus inversa demoxstrantur. Nempe (I
dererminetur angulus. PM T (vel alter quispium quem recta po-
sirione data cum cansente Facit ad punctum currae delignacum) aut (X
determinetur quantitas rectae PY (vel similis cujulpiam alterius à
puncto in data positione recta designato Per tangentem inteFCCPEX
eo tansens determinabitur. Et permuratim, I tansens litu deter-
minetur, angulorum arque linearum ejusmodi quantiras inde digno-
SCetur. Adeoque parcetur opera, qualem insurapserune plerique
cales propoliriones inversas demonstrandi. Ouod ex eo magis ob-
Terratu dienum est, quia Caepe talium inverlarum proxositionum
una quam altera lonse promprius invenitur, atque tacilius demon-
Aratur. Cujus obserrationis, nisi lonsius cragari nollem, in prompru
Forent Specimina.
2I.V. L acus iertur puncts delcendentis relociates in duobus
quibusris desienacis currae punctis ad se proportionem habere reciproce
COM.
FuCB. IIL. 16.
32333
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