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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 43, page id 797435492:0075
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L B C F.
jam aliquories insinuara; Scilicet uF SE AB. FB: : V I9 =Rg. l;
ee delignetur quilibet refraCruS R H, Tum continuerur ratio YB ad
BN, uc sir ad has proportione quarra BP,  per punctura P du. 418. 57. 38.
eatur recta PZ ad A B parallela; retracto R N occurrensin L; dico
nullum alium retraecum per Z transire. Nam Si Reri porek transeat
alius LR; _ per PtraduCantuY reCIX NYC, RYS; e pramon-
Ctratis apparet quod sit RS F = NC. item e praedieris manitestum ett r 12. L oct. 4.
quodRS+E NC, QuX RepUBNANE.
XVI. Non dispari rarione, quoad casum secundum, designetur quilibet
retractus RH; _ Aat RB. GB:: N RG - Ig. R; tum adnexa
GH, ad iplas NC, C B sumatur tertia proportionalis V; e hat
NO. V:: BN. NP; _C pex pUNCT P duCREUE P Y ad B A Pa-
rallela retractum N K decussans in Z, dico nullum alium refractum
per iptum Z meare. Ilam, si neges, transeat alius Z R; _ per
Y trajiciatuE RZS; _ quoniam Z P. XP :: RB. GB:: N R9
=Ig. R. ex antedicris apparet Fore RS =NC. quinetiam ob + 1g. Lett. 4i
NOg. GB9:: NC. V:: BN. NP. erit diridendo NB9.
GB9:: B P. NP. hoc est NPg. P ZG:: BP. NP; inde Facile
deducitur esse B P quartam proportionalem in ratione Y P ad PN.
consequenterque fore R S minima N C majorem. Quod adver-
Pacur octensis. itaque porius per Z nullus alius transi retractus:
Q.F. D.
XVI. Prxrerea, Si retractum NK Z intersecet alius quilibet M I,
ad rectiorem perrinens incidentem (hoc est ur incidentix punCtu M
inter B,  NI jaceat) intersectio Z Tolicario puncto Z cirerior erit
(seu perpendiculari R B propinquior). Nam ab X demittatur per- F18. 59, 60
pendicularis X O. ipsam NC secans in V; e (in primo catu) per
M, PETAdUICATUT RCCEA MYHI. CrEOMH --NV. quare minima earum
quae per X angulo X QP interseri poltuncinter puncta M, N cadet
uri nuper admonitum, e adstruCEU). Puta ad p. ergo quum sIc
B L quarta proportionalis in rarione YB ad B NY; e B O quarra
proporrionalis in ratione YB ad BP, erit PBC OB; adeoque
reCtA X G reCtSZ P, R B interjaCeE: C. F. D.
In secundo calu, per y trajiciatur recta M v HI. ergo cum sIF
DX. QV:: PZ. P Y:: V R9 - Ig. R. eriE HIM =- ON. ergo
minima per 2 ducibilium angulo A B F incercipienda punctis M, N
intercidet; puta ad p. quare  B quarta proportionalis erit in ratione
adP; et cAr . OPC. (rQ. N.):: YP. PN. e
CIm.
3 haejus Let.