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

Duabus datis rectis lineis terminatis, non modò ad rectum, ſed
ad quemlibet angulum conſtitutis, & per vnius ipſarum terminum
alia alteri ipſarum æquidiſtanter ducta, ad contrarias tamen par-
tes, & in infinitum producta: oportet per extremum terminum al-
terius, rectam ducere æquidiſtanti occurrentem, quæ cum bina
ſimilia triangula ad verticem conſtituat, ipſorum aggregatum ſit
MINIMA quantitas.

ſimulque noſtram Problematis enodationem his verbis enunciauimus;

Diuidatur ſecanda linea, ita vt ſegmentum ipſius propè termi-
natam parallelam, ad ſegmentum reliquum ſit in ratione diametri
cuiuslibet quadrati ad exceſſum diametri ſuper latus: nam pũctum
interſectionis erit quæſitum.

ac demum de inuentione binorum æqualium ex triangulis aggregatorum,
tam ſupra, quàm infra punctum MINIMI aggregati eundem Cl. Ado-
leſcentem commonefecimus. Sed iam Appendicem aggrediamur.

385. LEMMA I. PROP. I.

Si fuerint duo ordines quotcunque triangulorum æqualem al-
titudinem habentium; erit aggregatum baſium triangulorum pri-
mi ordinis, ad aggregatum baſium triangulorum ſecundi, vt ag-
gregatum triangulorum primi, ad aggregatum triangulorum ſe-
cundi ordinis.

SIt vnus ordo triangulorum A B C, C D E, E F G, G H I, alter verò
triangulorum ordo L M N, N O P, P Q R, & omnia ſint æqualis alti-
tudinis, vtriuſque autem ordinis triangula ſint ad eaſdem partes, & ipſorum
baſes in directum diſponãtur, quarum baſium aggregatum, in primo ſit A I,
& in ſecundo ſit L R. Dico aggregatum A I, ad aggregatum L R eſſe vt
aggregatum triangulorum primi ordinis ad aggregatum tr iangulorũ ſecũdi.

Quoniam iunctis rectis A H,
C H, E H; & L Q, N Q: erit
triangulum A B C ęquale trian-
gulo A H C, (cum ſint ſuper ea-
dembaſi A C, & habeant ex hy-
potheſi eandem altitudinem) & C D E ęquale C H E, ac E F G
æquale E H G; vnde communi
addito G H I, erunt omnia ſimul
primi ordinis æqualia vnico A
H I: item oſtẽdetur omnia ſimul
ſecundi ordinis æqualia eſſe vni-
co L Q R; ſed triangulum A H I ad L Q R eſt vt baſis A I ad L R, cum po-

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