Full text: Viviani, Vincenzio: De maximis et minimis, geometrica divinatio

ptotalis DEF erit Hyperbolæ circumſcriptus, cum totus cadat extra, & quę-
libet ſectionis diameter, eaſdem ipſi applicatas, ad latcra anguli productas,
bifariam ſecet: eritque _MINIMV S_, nam [?] quælibet alia linea, quæ per G, vel per E (quod idem eſt) intra ipſum ducitur, minorem quidem cum altera
aſymptoto conſtituit angulum, ſed omnino ſecat Hyperbolen. Si ſecun- dum, duci poterunt ex G Hyperbolen contingentes GA, GC, & tunc an- gulus AGC erit quæſitus circumſcriptus: quoniam ſi iungatur AC, & bifa-
riam ſecetur in N, iuncta GN diameter eſt ſectionis, ſimulque anguli; qui erit _MINIMV S_, vt per ſe patet, cum quæ ex G ducitur intra angulum AGC
ſecet omnino Hyperbolen. Sitertium: ducantur GL, GM aſymptotis ęqui-
diſtantes, & angulus LGM erit Hyperbolæ ABC circumſcriptus, cum cir-
cumſcriptus ſit angulo aſymptotali DEF: nam ducta GEN ſectionis diame-
tro, applicataque quacunque LDANCFM; in triangulis LGN, MGN eſt
ND ad DL, vt NE ad EG, vel vt NF ad FM, ſuntq; ND, NF inter ſe ęqua- les, quare DL, FM ęquales erunt, & totę NL, NM ęquales, ſiue GEN circũ-
ſcripti etiam anguli LGM diameter erit: inſuper idem angulus LGM erit _MI-_
_NIMVS_: nam recta, quę ex G intra ipſum ducitur, minorem angulum cum al-
tera nunc ductarum conſtituens, ſi producatur, ſecat vnam aſymptoton (cum
ei æquidiſtanter ductam ſecet in G) quare vlterius producta ſecabit ipſam Hyperbolen. Datę igitur Hyperbolę per datum extra ipſam pũctum in locis
poſſibilibus, circumſcriptus eſt _MINIMVS_ quæſitus angulus. Quod, & c.

155.1.

ex 8. 2.
conic.
8. huius.
49. ſec.
conic.
29. ſec.
conic.
ex 8. 2.
conic.
35. h.

156. PROBL. XXVII. PROP. LXIX.

Datę Hyperbolę, per punctum intra ipſam datum, MAXIMVM
angulum inſcribere. Item.

Dato angulo, per punctum extra ipſum datum, cum dato ſemi-
tranſuerſo latere, MINIMAM Hyperbolen circumſcribere.

Oportet autem datum punctum eſſe in angulo, qui eſt ad verti-
cem dato.

SIt data Hyperbole ABC, cuius aſymptoti ſint DE, DF, & punctum intra
ipſam ſit G, per quod ei oporteat _MAXIMV M_ angulum inſcribere.

Ducantur ex G rectæ GH, GI aſymptotis æquidiſtantes. Dico angulum
HGI eſſe _MAXIMVM_ quæſitum.

Nam iuncta DG, & producta ad
L, ipſa GL neceſſariò diuidet angu-
lum HGI (vt ſatis patet) ſumptoque
in ea quolibet puncto L, & applica-
ta in Hyperbola, ad diametrũ BL, or-
dinata ELF, Intera anguli HGI ſecã
in H, I; erit ob triangulorum ſimili-
tudinem, DL ad LE, vt GL ad LH,
ſed DL ad LE eſt vt DL ad LF, cum
LE, LF ſint æquales, & DL ad LF
eſt vt GL ad LI, quare GL ad LH erit vt GL ad LI, ſiue LH ęqualis LI: vnde

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