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

239. THEOR. XIV. PROP. XIX.

Si à puncto, quod eſt in angulo aſymptotali, ductæ ſint re-
ctæ lineæ aſymptotis æquidiſtantes, & Hyperbolæ occurrentes,
atque ex vnius eductarum occurſu agatur recta, quæ ſectionem,
vel in ipſo tangens puncto, vel alibi ſecans, producta ſecet
quoque eam aſymptoton, cui altera eductarum æqui diſtat; re-
cta linea iungens hoc idem punctum cum puncto contactus, vel
interſectionis nouiter ductæ lineæ cum Hyperbola, æquidiſtabit
rectæ, quę ab occurſu eiuſdem lineæ cum prædicta aſymptoto
ad datum punctum educitur.

0204-01

SIt Hyperbole A B C, in cuius angulo aſymptotali E D F ſumptum ſit
quodlibet punctum G, vel extra Hyperbolen, vt in prima, ſecunda,
& tertia; vel intra, vt in quarta, quinta, & ſexta figura, à quo ductæ
ſint aſymptotis æquidiſtantes G A, G C, ſectioni occurrentes in A, C; & ex altero occurſuum C ducta ſit quæcunque alia C B E, quæ, vel ſe-
ctionem contingat in C, vt in prima, & quarta figura, vel alibi ſecet in
B, vt in reliquis, & producta conueniat cum aſymptoto D E, quæ rectæ
G A ęquidiſtat. Dico, ſi iungantur A B, E G ipſas inter ſe æquidiſtare.

Nam ducta B H parallela ad F D, productiſque A G, C G vſque ad
aſymptotos in F, L; & E B C ad aliam aſymptoton D F in I. Erit iuncta
A B iunctæ H F parallela, eſt autem E B æqualis C I; quare, ob paral- lelas B H, C L, I D, erit quoque E H æqualis ipſi L D, ſiue ęqualis G F;

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