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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 114, page id 797435492:0348
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e1B. 272.
E. F C T. ZII.
ur in circumf. AM B sumpto utcunque puncto M, de per hoctrajecta
recta BMZ, ductaque rectA MEZ, gux curram AL Z secet in L,
SIEMZ = AS) in recta vero a 6 sumatur apo xequalis arcui AN, 8
ad ap applicentur rectae perpendiculares p E ae quales arcuune AM sina
bus vOrsIs AF; erie sparium crilineum M A L sparii a u E duplum.
PTamm CumatuE arous ML NI indefinice parrus, _ ei aequalis per; du
Caturque recta NV R ad A B parallela, connectaturque recta C. M. FR-
que jam AS. A B (2 CM):: (F M. FB::) AF. FM. ∞ 2 C M.
2 MA N:: C M. MHI::) FM. NR. quaprOPTeE erit ex aequO AS.
2MHI:: AF. NR; _ ideo NIR X AS = 2M HYX A F. hoc est
N RRXMZ = 2 HVX pE. unde spatium MI A Z duplo spatio a p E X-
quatur.
Hinc cum spatii a p E dimensio rulgo nOta SC, _ C supra posiris
etiam Facile deducatur; habetur spatii cissoidalis M A Z dimensio. Cai-
culum ineat qui rolet.
Icta claudet hoc Conscctariolum:
ZV. Sic circuli quadrans A C B, circulumque tansane A. II, BC;
(InEQUe CUEVa RZZ, L. F O hyperbola exdem quae (a) superius. ar-
cus vero sumprus AM in parres dirisus concipiatur indetinite multas
punctis N; per quae crajiciantur radii C H; e his occurrant rectae
AX ad puncta X; summa rectarum IVX (in radiis) aequatur spacio
AFZ R
Rad. _ summa rectarum NVX (in parallelis ad A5) equatur spatio
PLOO
3 Llac.
Nlam eriangulum Z M N triangulo S A C simile cAt; d inde X N.
MN:: AS. C A. _ XN. MH:: C S. C A. unde XM =
M N X AS
CA 5d XN=
MNXCS
CA
Prolitum, Cx 2, ec 7 harum.
.e itu in reliquis; unde liquet
E18. 172.
F18. 1730
2)1 a.