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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 61, page id 797435492:0281
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I. B C F VII.
Est enim F C P, ac indeD C O; e hinCC E N.
ZVII. Consectatur hinc; si Fuer ine quatuor linex HIBLI, OBC, FBF.
F B F sele interlecances in B, ac ita versus se relatae, ut duct à vtcunque
rectâ D H ad posirione datam D B parallela (in linea nempe DDD fijo, 68.
terminat a) vel a delignato puneto D projecta DHI; lIE PerPAVODC
inter D II, D F: eodem ordine media proporcionalis Arichmetice, quo
DFincer caldemmedia Ceomerrice; linex E B6, E BF, sese mu-
tuo contingunt.
Enimvero linea C B LL extra lineam P BF. toram cadere manisectum
epexcedente.
XVIII. Ex isthinc etiam (quod srictim transcurrens moneo) di.
verlis innumeris syperbolarum, aut superboliformium generibus corm F18. 70.
venientes rectae a siuxrcroi detiniuneur. Sint nempe rectae VD, BD.
policione datx; sine item alix dua rectae AB, VI; ducta vero li-
bere recta P C ad D B parallela, (IE P B CONStAnEeF InCEF PC, P F e0-
dem ordine media proportionalis Arichmetice, quo P F intex casdem
media Geometrice; quia jam (4) recta L C, Le semper caridem ob-
rinent rationem, cR linea o0 e recta; veriun linea V. F F est hyperbo, (a) 12 buje.
la vel hyperboliformis aligua ( COUNIS quidem vel Apolloniana
hyperbola, si P F Sic inter ipsaS P C, P F simplicirer media, sed alia
dirersi generis quxdam hrpeiboliformis, ( P S Cic alterius cujuspiam
ordinis media) atqui pacet epenulcima praemissa lineam e e  eodem
ordine respondenci linex V LE asymptoion esse. Quod an ressyu HE
nelcio, nohis cerre raze zortuit, hic snoralle.
XIX. A puncto altignato B ad datam. polirione rectam A C ductxe
sint re tXtres BA, BC, BO; cum in OC producta sumacur sumprum Bis. 77.
quodpiam D; per B recta (puta B R) duci porest (ad alterurras ipsi-
us B O DorreS) calis, ut a D project d qu’acunque recta, ceu D N; (IF
hujus a rectis B Z, B R intercepta pars (F F.) minor ejuldem d rectis
BA, B C INTETCCDEa PaKTE (N M).
Nam. prim, li B R ulera angulum AB C jaceat resrectu puncti
D; Aac QR = C R; _ connectatur BR; tum utcunque ducacur
DE, rectas secans, ur vides; e manifectum eAt, C Tupra MON n Pc 7. ZC5
AratiS FORC, FE = L NM.
Sin B C cirra angulum A B C cadaE rexIuS D; (a) ducatur recta
B. FI Ealis, UF Q B Z, B EI intercepEx minores sine intercepris a BC,
B A; _ TUIaTuEZIR = O C; e connectatur BH; cum carluS Fig. 73.
utcunque ducta DHI, quae rectas intexlecet, ut exhibet Schema; quo-
miaTa
E
Per
VL. 8L. CE.