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talis;
ut à puncto D ductâ quâvis rectâ DYH (quæ rectam BK ſe-
cet in H, curvam DYX in Y) ſit perpetuò ſubtenſa DY æqualis re-
ctæ BH; oportet curvæ DYX tangentem ad Y rectam determi-
nare.
cet in H, curvam DYX in Y) ſit perpetuò ſubtenſa DY æqualis re-
ctæ BH; oportet curvæ DYX tangentem ad Y rectam determi-
nare.
Centro D per B ducatur circulus BRS;
cui occurrat recta YER
ad BK parallela; & connectatur DR; eſtque (propter ang. DYE
= ang. DHB; & DY = BH, ac DR = DB) triangulum RDY
triangulo DBH ſimile ac æquale; quare RY. YD : : (DH. HB)
: : YD. YE. unde ex præcedente determinabilis eſt recta curvam
DYX tangens in Y.
ad BK parallela; & connectatur DR; eſtque (propter ang. DYE
= ang. DHB; & DY = BH, ac DR = DB) triangulum RDY
triangulo DBH ſimile ac æquale; quare RY. YD : : (DH. HB)
: : YD. YE. unde ex præcedente determinabilis eſt recta curvam
DYX tangens in Y.
XIX.
Sint itidem rectæ DB, BK poſitione datæ;
nec non curva
BXX talis, ut à puncto Dprojectâ quâcunque rectâ DX (quæ re-
11Fig. 93. ctam BK ſecet in H, curvámque BXX in X) ſit perpetuò HX ipſi
BH æqualis; deſignetur oportet recta curvam BMX tangens in X.
BXX talis, ut à puncto Dprojectâ quâcunque rectâ DX (quæ re-
11Fig. 93. ctam BK ſecet in H, curvámque BXX in X) ſit perpetuò HX ipſi
BH æqualis; deſignetur oportet recta curvam BMX tangens in X.
Concipiatur curva DYY talis, ut perpetuò ſit DY = BH (talis
nempe, qualem attigimus in præcedente) hanc verò tangat recta YT
in Y, ipſi BK occurrens in R; tum _aſymptotis_ RB, RT per X de-
ſcripta cenſeatur _hyperbola_ NXN; ad quam utcunque projiciatur re-
22_a_) _Couſtr_. cta DN (lineas expoſitas ſecans, ut vides) Eſtque jam OM 33(_b_) _Converſ_
9. Lect. VI D I) & lt; (DL = ) ON; ergò _hyperbola_ NXN curvam BXX tangit ad X. Ducatur itaque recta XS _hyperbolam_ NXN contin-
gens, hæc ipſam curvam BXX quoque continget.
nempe, qualem attigimus in præcedente) hanc verò tangat recta YT
in Y, ipſi BK occurrens in R; tum _aſymptotis_ RB, RT per X de-
ſcripta cenſeatur _hyperbola_ NXN; ad quam utcunque projiciatur re-
22_a_) _Couſtr_. cta DN (lineas expoſitas ſecans, ut vides) Eſtque jam OM 33(_b_) _Converſ_
9. Lect. VI D I) & lt; (DL = ) ON; ergò _hyperbola_ NXN curvam BXX tangit ad X. Ducatur itaque recta XS _hyperbolam_ NXN contin-
gens, hæc ipſam curvam BXX quoque continget.
Cæterùm ſatìs pro hac vice nugati videmur;
ceſſemus aliquantiſper.