Viviani, Vincenzo - De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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21634 factum, tunc ex dictis binis contingentibus, quæ ad partem axis ducitur ſem-
per altera contingente ad oppofitam axis partem minor erit, atq; hæc erit MA-
XIMA. Si verò punctum fuerit extra Ellipſim inter axes, tunc contingens
ad partem maioris axis ducta, minor erit altera contingente ad partem mino-
ris, pariterque hæc erit MAXIMA ad conuexam Ellipſis peripheriã. Quæ
omnia facili negotio demonſtrabuntur ſi animaduertatur, quod in quocunque
triangulo, cuius vnum latus altero ſit maius, hoc ipſum eſſe MAXIMIAM
linearum omnium à vertice anguli ab ipſis lateribus comprehenſi, ad puncta
baſis prædicti trianguli ducibilium, (tale enim triangulum eſt, quod a prædi-
ctis contingentibus tanquam lateribus, & à recta puncta contactuum iungen-
te, tanquam baſi efficitur, in quo idem maius latus, ſiue contingentium ma-
ior eò magis erit MAXIMA ad incluſam ſectionis peripheriam.) Si tandem
punctum fuerit in angulo ad verticem aſymptotalis, aut in aſymptotis eum
comprehendentibus, tunc vllam contingentium ducere imposſibile eſt, & du-
cibiles lineæ ad conuexam Hyperbolæ peripheriam ſemper augentur, ideoque
non datur MAXIMA; & cum eſt in altero angulorum, qui deinceps ſunt
aſymptotali, vel in ipſis aſymptotis Hyperbolen continentilem, tunc vnica
tantùm contingens linea ab eo duci poteſt, & hæc ad partem axis, quæ erit
MAXIMA ad eandem partem ducibilium; ſed ad oppoſitam, ipſæ ducibiles
ad Hyperbolæ conuexam peripheriam perpetuò pariter augentur. Sed in re
haud difficilis inueſtigationis ne ampliùs quæſo immoremur.

THEOR. XVI. PROP. XXIV.

Tranſuerſorũ laterũ in Hyperbola, MINIMVM eſt axis; in Elli-
pſi autẽ, MAXIMVM eſt axis maior, MINIMVM verò axis minor.

SIt Hyperbole A B C, cuius axis tranſuerſus D B, centrum E. Dico D
B omnium tranſuerſorum eſſe _MINIMVM._

Sit quodcunque aliud H

177[Figure 177] E A, & per B axi applicetur
G B F, quę axi perpendicu-
laris erit, ac ſectionem con-
tinget in B. Erit ergo per-
pendicularis E B _MINIMA_
ad peripheriam A B C: 1110. h. quare E B minor erit E A,
& duplum D B maius du-
plo H A: ex quo D B erit
tranſuerſorum _MINIMVM._

In Ellipſi verò A B C,
cuius centrum E, & B D ſit
axis maior, & A C minor: patet B D eſſe tranſuerſorum _MAXIMVM_, &
A C _MINIMVM_, ex primo Coroll. 86. primihuius. Quod erat, & c.

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