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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 111, page id 797435492:0345
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B F C T. XI.
III. Curra A X Z calis SIE, UE P Z secanti CS (vel CT) equetur;
spitium A C P Z hoc est Summa secan ium ad arcum A MI perrinen
tium, es ad C B applicatarum) xequarur duplo sectori AC N.
Nam (a) spatium A F M Z Segmenti AFM auplum est; _ rect. FI8. 766.
angulum FC PM Friang ali EC M. erSO torum spatium A C P Z. (4) 10. Lect.
torius sectoris AC M duplum est.
Etiam hoc e 16. hujus duodecima Lectionis aperte constat.
IV. Curra C VV calis (IC, UEPV Tangenti AS XquetuE; exit
sparium C V P (hoc est summa cangentium ad arcum A M pertiven-
rium, e ad rectam C B appliCaTArUI) Xquale semissi quadrati ex
Subcensa A M.
Maniteste consectatur ex septima undecimae Lectionis.
V. ACCePTCO== CP; _ ducta D O ad C F parallela CquXe
hyperbolae L F OcCurraE in O) eric spatium Byperb. licum PLOC du-
ctum in radium C B (Peu eylindricum ad BaFin P LOO. alticudine
E18, 266.
BC)duplum summa quadratorum ex rectis CS, Peu P X ad arcum F18. 166.
AMl perriventibus, _ ad rectam C B applicaris.
NTam quia PL. 2O:: (B2. BF. hoc est::) BC + CF.
BC - CP; erit componendo PL. + 9O. O:: 2BC. BC
C P. item est 2O. BC:: BC. BC - ). C P; ergO (PaTESKa-
tiones adjungendo) cAtP L - ) - (0. 90-+ OO. BC == 2 BC.
BC - CP - ]. BC. BC = CP; hOc est PL . OO. BC::
2BCg. BC9 --C P  (hoc est::) 2BCg. PMg. verum
cAtP Z g. BC g:: B C9. PM g. rel(antecedentes duplando) 2PX9
BC9:: 2BCg. PM9. ergo PL s OO. BC:: 2PX9. BC g. Vel PLKBC)
OOxBC. BCq:: 2PX9. BCg. Quare PL X BC- I OO X BC ==2P84
itaque BC in omnes PL. ].. O ducta adae quat omnia coridem PX9.
unde constat Propolitum.
VI. Einc Spatium a 3 aL u (hoc eA (nmNS seCAntIUM in arCH A M
ad ab applicatarum) xquatur subduplo spatio hyperbolico P L. O.
Plam lumacur arcus M eI indetinite parvus, sc huic aequalis recta pur
ducarurque recta N R ad A C parallela. FStquE M HI. MR :: (MC.
CF:: CS. C A: : PZ. C A ::) PX 9. PXXC A. adeoque
MIHIX PZZ C A == M R X P Z9. TeU PIV X pit X C A = MRX
PX g. atqui (ex praecedente) omnium M R x P X glumma spatii
PLOO in C A ducti subdupla est. Frgo omnia toridem H V X u ab
in C. A ducta eidem subduplo rquantur. Quare spatium. ay u (Om
nibus
Fi8. 1078