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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 33, page id 797435492:0057
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E B C Y. IV.
iplius perpendicularis AB (quasi, retractus in ipsum punctum Z. ter-
inatur. POrTO:
VTII. Lomma: TIE AB ad E F normalis, _ a duobus in AB
sumpris urcunque punctis A, I (quorum A proprius ip(I B) ad duo
puncta quae ris M, N in ipsa P. P acceptis (quorum vero M lic ipli B
vicinius) connectantur rectae AN, AN; EIM, IN; dico FOrC AN.
AME IN. TM.
Nam centro H per A describatur circulus P AOR (rectas LM,
IN intertecans punctis O, R2) _ Per R duCAtuF R T ad. F. F parallela,
secans IM in S. Ft ob angulum N R T obcusum, patet rectam R I
extra circulum cotam excidere; unde SM C= (OMC) AM.
aceoque AB. AME AB: SM:: R N. SM:: IN. IM. li-
quet igItE eNsE A N. AMC IN. IM: OuodE. D. Hinc
Si duorum radiorum AM, A N (quorum hic obliguior) retracti
Ma, N a cum axe A Bconveniant punctis I, R, eric in primo calu lB
RB: in secundo IBC RB. Ftenim connexa IN; est in primo
catu, NR. MI: : N A. MAC NP. MI. adeoque NR L Y.
unde BRC BI. ast in sCCUNdO, N R. MI:: N A. MA -~NI.
MI quare NR = = NI; _ inde BR ~ BI.
IX. Coroll. Retractorum in primo casu concursus extra angulum
A BNverlantur; in secundo, intra eundem. Sed haec eadem in decur-
su liquidius, ac multitariam constabunt.
X. Porro, bina quoad hoscasus Theoremata subjiciemus, ulus traud
contemnendi.
r. Sitiat (in primo ca(u) ZB. AB:: I. V I9- Rg. SE autem CU- F18. 39
jutrisincidentis AN retractus RN a; _ connectatur YNV: erit R B.
XH: :V I9- RG. R.
Nam ob Y Bg. ABg:: (a) Ig. I9 = Rg. erit per converti-
(a) FypoIh.
onemrationis YBg. TBg - AB9:: I9. R9:: (b) KNg. AN9. (3) a Mojus
_c permutando ZBg. R HI g:: Y Bg - ABg. AW g. componen-
doque YBg + RNg. RN9:: YBg + BNg. A N g. (RemDC
YBg - AB9. + ANg -- TB9 + BNg; quoniam AN 9.
AB9 =BN 9) Ouare rurtus permucando cst YB9. = R B 9.
YB9. + BNg:: R Ng. ANg. diridendoque RN q - BN 9.
YBq F BNg:: R Ng AN9. AH9; hoc est RBg. YNa
:: l9 = Rg. Rg: O. F. D.
S L. C61813
Eie