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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 82, page id 797435492:0130
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F18, 2220
218. 123.
P F C F. Z II.
habeatur decerminatus; Tuccedit ut breriter etiam ipslimum in sin-
sulo cali retracto punctum ostendamus, ad quod illa consistie. in cu-
jus rei gratiam hoc quali Lemma prxsternemus.
VI. In circulo A NI B, cujus centrum C, sint Semidiametro C A
perpendiculares NF, R F; item Semidiametro C B sint perpendicu.
lares N C, XHI; line auteM CF, F F ipsiS CC, OHI proportion
les; _ arcnS N R, NIX indetinire parri; seu quali minimi dicta
conditione praediti; dicimus arcum N R ad arcum NX rationem ha-
bere conslatam c rarionibus ipsarum C F: ad CC, _ NC ad NE; vel esse
ArC. N R, NX:: C F X NC. CGX N E. Nam per N ducaturV Y
tangens circulum, ipsisque FR, HX occurrens punctis Y, V. eAt
itaque (proxter Summami ex LIypocheli parricatem dictorum arcuum)
arc N R. CN:: NT. CH:: FF. F:N, itEM C.H. AEC N X:
C PI. NV:: VO. GH. quaPEOPEer erit arC NR. C N - CN.
AFC NZ = (EF. ENI F NO. GH = F P. CHI-+ NG. FH
=) CF. CO -, NC. FNT. hOC esArCNR. ATCNZ =CF
C6-]. NO, FH: G. E. D. (vel arCNR. NX = C F XNO.
C OX FN.)
VII. Sit jam radii cujulris calis MNIP, retringentem intersecantis
punctis H, P, retractus N a (retringentem nempe, denuo secans
in ∞) huic autem indetinice ricinus (_ quali proximus) adjacear
radius ORS, cujus itidem refractus R0 (retringenci nempe rursIs
Occurrens in ∞), priorem N u decussans in Z. Bisecentux autem
subrensx NIP, N ∞ punCtisD, E: Dicorationem NL ad O Z com.
poni cracionibus N G ad NI E, SE C F ad CC.
Nam ducantur recta C F (HXC ipSaM R S quoque SCcanS in F) _
CG, nec non Clad Ro perpendicularis, e in protracta C ( su-
matur C II = CI; _ per lI ducatur X Y ad N as parallela, seu per.
pendicularis ad CH; unde est X Y = R5; _ arC NX = Y v: e
AsC X Y = arC R0; adeoque arc NR F: ∞ ∞ = 2 arCN Z. FA.
que prxterea C6. CF: : R. I:: C L. C P:: CFI. CF; adeoque
permutatim C C3. CFI:: C F. C. F. ergo (jurta praecedentem) est
arC. NR. NX = NC. N F + CF. CO. ad haec ob iltam (qua
DOnituF) arCUUM NI R, SP, _o exiquitate, exit DEC NR. 00::
Subrenta NR. 80:: NZ, Z0:: NZ. Z∞. ergo (inverse compo-
nendo, vel diridendo, cum e consequenres sub duplando) arc NR.
arc N P F. a 8
N
L
aequi relur modo dictum)
dec