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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 90, page id 797435492:0142
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P E C F. ZIII.
alsimilancur. unde NK. R F:: ANI. NIF. seu permutando DIK
AHI:: KF. HYF. exaE auteM prIuS RF. NF:: GF. F A : : CK
CR. CAt igItIE NR. AN:: C.R. C. R. unde (juxta dictum TheO-
rema) constat factum.
ZIV. Ad constructionem istam adverrences anirmum, hujusmodi
Facile Consectaria deduceris:
1. Si circulus C N H refringentem contingat ad HI; iphuS AH
perpendicularis utique) refractus in R cerminabitur; _x aliorum
incidentium retracti ad unas iplius R parres (ulrra nempe vel citra
IE respedtuceneri, pro direrlirate casuum ab iplius A posicione retul-
cancium) cadent.
2. Si dictus ille circulus refringenti non occurrat omnino, Problema
constructionem respuet; nec ullus retractus punctum R permeabit.
3. Si circulus ON H refringenti coincidat (id quod facile concipi
Pocele, ec in aliquo revera calu continsit) omnes retracti in punctum
KconAuent. 1) Eixc _ alia constructionem iltam consectantur soler-
ter expanlem; quorum saltem nonnulla haud abs re fuerit exerriiis
octendi; relut hoc imprimis palmarium.
ZV. Situerit AB. CR:: BZ. CZ; dico punctum Z esse limi-
tem, ulira vel cirra quem nullus retractus axim intersecar, Peu per-
pendicularis ipsius A B retractum in Z terminari.
Nam cujusrisincidentis AN refractus axi occurrat in R, erit ideo
CK. CR:: NK. N A. ergo quum AE CR. CZ:: AB. BZ;
erit C R. CR F CR. CZ =-NR. NA + AB. BZ.
L. Est aurem (in prima figura, ubi pancta L, e K Tunt ad partes
centri, vel ubi retracti ad axem directe prOCurrenEeS COnVergunE
BRL NK, _ AB = S ABI, adeoque BR. ABE NR. N A.
ergo CK. C R . t. CR. CZBK. AB + AB. BZ. hoc est
CK. CZ = 3BK. BZ. vel inverse permutando BR. C KRC BL.
CL. diridendoque BC. CRE BC. CZ. ergo CR ACZ:
adeoque punctum P supra Z exictit, versus centrum; quod exat pro-
Polium octendere.
2. In secunda vero fguras ubi puncta Z, R ad alteras supra punctum
A PaTteS a CentrO avertaS CadunE) connectatur subtensa BN, _ du-
Catur AS ad RH parallela; haec secabit angulum B A. HI, majorem
ip(O BKNB, vel B AS; e cum angulus AB H sic obculus, erit AN
E. AS. adeOgneRN. A NT =SKN. AS:: K B. A B. erit etiam hie
isitur (ur Cupra) C H. CZ  BB. BZ. vel permurarim C. R. BR
F18. 237.
E18. 238.
18. 139.