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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 78, page id 797435492:0126
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L E C Y. ZI.
cescir exeo, quod earum omnium au se proporriones in eodem ubique
modo fundantur in una ratione I ad R. verbis, e Schemaris effin-
sendis parco. Pro lequentibus haec adjungo Lemmatia.
ZI. F. SInE Eria quanta A, B, C (quorum maximuM A) se dein-
ceps aequaliter excedentia; sine eriam altera roridem M, N, O; _
SIEA. B:: M. N; ac B, C:: N, O; dico Fore quoque tria M, H
Oin ratione continua arithmesica. Itam ob A. B:: M. N. Crit
dirisim A = B. B:: M =N. N. item obB. C:: N. O. exit per
rationis conversionem B. B - C:: N. H- O. ergo erit ex aquo
A = B. B - - C:: M -- H. N -O. itaque cum liE ex HTyporties
A - B = B -C; exit etiam M -- N =- N - O: 9. F, D.
XII. 2. In circuli quadrante Z. O erium arcuum ZG, Z FI, ZI
Sinus recti Fa, F6, F V aqualiter crescant (ue nempe (I a6 =6v
dicotore Ca -HC 1116- 1y.
Nam ducatur subrensa C L ixsam HIC secanS, in X; _ SINE XR
IS ad F  parallelae; patet ipsas GR, X S xequari hoc est Fore
Ca - X6 = X6 -ly; unde liquidum est esse C a - HIC- - 116
=Iv: . F. D.
XIII. 3. Sunto concentrici bini circulorum quadrantes F Z Z
FES; _ ad F Z parallela ducatur recta quaevis L Oy; circulos inter-
secars punctis C, ; dicoFore FZ = L. OC FZ -Lg.
Nam connexa FC circulum E V E producta secer in T. connectan-
curque subtensa Z C, ET (haec iplam L v secans in S) Paterque jam
rectasZ G, CT parallelas esse; adeo que quadrangulum Z CSE Fore
parallelogrammum; unde 65 =26: adeoque FC -- L S = FY
LO. ersoFC = L y =SFZ =L C: O. F. D.
XIV. Sint jam tres radii parabteli MIN, O R, V X, a se distantes
requalirer (hoc est ut ductis NV, R s, X E ad azem A C perpendicu-
laribus (IE XE =RS = Rs NV) e ipsorum retracti cum axe
conveniune punctis R, L, O; erit obliguiorum concurtibus interjectum
spatium OL. majus spatio L. R, quod a rectiorum occursibus conri-
netUI.
Nam dUCaNEUE N C, RC, XC circulo retractario OCCUrrenteS
punctis C, II, I; ex ad has a retractarii centro F ducantur perpendi-
culares F =, FC, Fγ: _ quoniam trianoula C X3, C F ~ limilia
sune; exit X5. CX:: F V. C F. irem simili de caula, est C R (C X)
18. 125
I8. IY
E18. 227
pel