Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ptotalis DEF erit Hyperbolæ circumſcriptus, cum totus cadat extra, & </
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libet ſectionis diameter, eaſdem ipſi applicatas, ad latcra anguli productas,
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bifariam ſecet: </
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<
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">eritque _MINIMV S_, nam
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quælibet alia linea, quæ per
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">ex 8. 2.
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conic.</
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vel per E (quod idem eſt) intra ipſum ducitur, minorem quidem cum altera
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">8. huius.</
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aſymptoto conſtituit angulum, ſed omnino ſecat Hyperbolen. </
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">Si ſecun- dum, duci poterunt ex G Hyperbolen contingentes GA, GC, & </
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conic.</
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gulus AGC erit quæſitus circumſcriptus: </
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<
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">quoniam ſi iungatur AC, & </
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riam ſecetur in N, iuncta GN diameter eſt ſectionis, ſimulque anguli; </
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<
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conic.</
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erit _MINIMV S_, vt per ſe patet, cum quæ ex G ducitur intra angulum AGC
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ſecet omnino Hyperbolen. </
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">ducantur GL, GM aſymptotis ęqui-
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diſtantes, & </
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">angulus LGM erit Hyperbolæ ABC circumſcriptus, cum cir-
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cumſcriptus ſit angulo aſymptotali DEF: </
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<
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">nam ducta GEN ſectionis diame-
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tro, applicataque quacunque LDANCFM; </
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<
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">in triangulis LGN, MGN eſt
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ND ad DL, vt NE ad EG, vel vt NF ad FM, ſuntq; </
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<
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"> ND, NF inter ſe
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">ex 8. 2.
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conic.</
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les, quare DL, FM ęquales erunt, & </
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ſcripti etiam anguli LGM diameter erit: </
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_NIMVS_: </
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<
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">nam recta, quę ex G intra ipſum ducitur, minorem angulum cum al-
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tera nunc ductarum conſtituens, ſi producatur, ſecat vnam aſymptoton (cum
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ei æquidiſtanter ductam ſecet in G) quare vlterius producta ſecabit
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Hyperbolen. </
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<
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poſſibilibus, circumſcriptus eſt _MINIMVS_ quæſitus angulus. </
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">Datę Hyperbolę, per punctum intra ipſam datum, MAXIMVM
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angulum inſcribere. </
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">Dato angulo, per punctum extra ipſum datum, cum dato ſemi-
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tranſuerſo latere, MINIMAM Hyperbolen circumſcribere.</
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">Oportet autem datum punctum eſſe in angulo, qui eſt ad verti-
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cem dato.</
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<
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ipſam ſit G, per quod ei oporteat _MAXIMV M_ angulum inſcribere.</
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">Ducantur ex G rectæ GH, GI aſymptotis æquidiſtantes. </
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HGI eſſe _MAXIMVM_ quæſitum.</
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">Nam iuncta DG, & </
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L, ipſa GL neceſſariò diuidet angu-
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lum HGI (vt ſatis patet) ſumptoque
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in ea quolibet puncto L, & </
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ta in Hyperbola, ad diametrũ BL, or-
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dinata ELF, Intera anguli HGI ſecã
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in H, I; </
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<
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tudinem, DL ad LE, vt GL ad LH,
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ſed DL ad LE eſt vt DL ad LF, cum
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LE, LF ſint æquales, & </
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<
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eſt vt GL ad LI, quare GL ad LH erit vt GL ad LI, ſiue LH ęqualis LI: </
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