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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)
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L E C T.
IX.
nihilominus praratim admieruntur: ist. cantummodo raprim intinua.
ca, subnectemus aliam ab illorum sustu non abtorrenrem; illara
Rempe (quando scilicet haud alia metior. ut rarias perrencans analyses,
_ hoc in alia complura Problemata transtormans existimari postum.
Facile portit excositari; quum e operx mex latis alioquin exerci.
eatx nonnunquam ridearur parcendum) quam olim Alhazenus arabs
seripris commendarie. ab horribili eamen illa prolixitare simul ac
obscuritare; neque non ab incondita sermonis barbarie nonnihil re-
pursatam. Quorlum hoc pramicrimus Lemmaticum Problemn.
VI. Trianguli D P N angulus ad P rectus sic; _ in hujus unO cru. Fi8. 9r.
re PB adlignerur punutuM F; per F recta ducenda est, gux reli-
guuni latus DP (protractam nempe) ac hypotenusam D N ita secet
ut ab illis intercepta ad scementum liyporenula lateri primo contermi-
num datam obtineat proporrionem R ad S.
Hloc ita peragatur licet. Ducatur F H ad PD parallela. _ Dia-
metro HI N deseribatur Circulus H F N (is nempe per F cransibir, ob
angulum II F. N rectum) cum connectatur D F; de hac angulus
FHAI = ang. F D NT. SiF etiam R. S:: DF. T. _ i puncto1 duca-
tur recta IL. R diametrum HI N intersecans ad L, _ circulo occurrens
in R, ita quidem VE SIE INFCTCCPFA LK = T (hoc aurem quomodo
peaectetur in superioribus ostentum) denuo per puncta R P crajiciatur
recta C F, iplam DP secans in Z. Dico Factum, vel ipse CX.
CN:: R. S. ConnectaTuE enim reCta N K. _ quoniam ang. FK V
vel FHI) = FDN, eric criangulum F D C simile triangulo Conser. (5.
LRC, ac inde FD. DC:: KL. CK. irem ob ang. F K HI = an∞.
FHIH = anG. XDC; erunt criangula XDC, NK C sibi quoque
Similia, proindéque DC. CZ:: CK. C N. quaprOPEer exit ex
aquali FD. CX:: R L. C N. vel permutando FD. CR:: CX.
CN; hoc est FD. T (vel R. S):: CX. CN; quod taciendur
erat.
Adverrendum est aurem, quod datum punctum F in recta PH
indetinite procensa varie stacui porest; vel nimirum inter puncta P,
N; vel extra illa parces ad alcerutras. item quod in iltorum caluum
linsulo quoque recta IR (condicione saudens praestirutâ) plurita-
riam duci potest; ut ancetac inculcatum; unde plures craergent solu-
tiones. at quoad omnes calus persimilis erir constructio, nec fere di-
verla demonstratio. quare cux plura ?
VII. Proponalit sald clCulus rell eclets (13 Gli pri Dculis, cljs
cen