Full text: Clavius, Christoph: Geometria practica

LIBER SEPTIMVS. rectæ B E, G H, ipſi A D, æquidiſtantes, eritque G H, ęqualis perpendiculari A D. Quoniamigitur rectangulum BCFE, duplum eſt trianguli ABC; Item duplum rectanguli BEHG: erit rectangulum BEHG, quod continetur ſub per-
pendiculari GH, vel AD, & dimidio baſis BG, æquale triangulo ABC.

291.1.

322-01
41. primi.
36. primi.
34. primi.
41. primi.
36. primi.

Secetvr iam perpendicularis AD, vel G H, bifariam in I, agaturque per I,
ipſi BC, parallela KL. Dico triangulum idem ABC, æquale quoque eſſe rectã-
gulo BCLK, in 1. & 2. figura, Item rectangulo BCLM, in 3. figura, comprehen-
ſo nimirum ſub ID, vel IG, ſemiſſe perpendicularis AD, vel HG. Quoniam enim triangulum ABC, dimidium eſt rectanguli E C, eiuſdemque dimidium et-
iam eſt rectangulum BL; quod rectangula BL, LE, ſuper æquales baſes æqua- lia ſint: æqualia inter ſe erunt triangulum A B C, & rectangulum B L. Et quia rectangulum B F, contentum ſub perpendiculari A D, vel B E, & baſe trianguli
BC, duplum eſt trianguli ABC; erit triangulum ſemiſsiillius rectanguli ęquale. Area igitur cuiuslibet trianguli æqualis eſt, & c. quod erat oſtendendum.

291.1.

41. primi.
36. primi.
41. primi.

292. PROBL. 2. PROPOS. 2.

Regularis fi-
gura quæcun-
que cuirectã-
gulo @qualis
ſit.

AREA cuiuslibet figuræ regularis æqualis eſt rectangulo contento ſub
perpendiculari à centro figuræ ad vnum latus ducta, & ſub dimidia-
to ambitu eiuſdem figuræ.

Sit figura regularis quæcunque ABCDEF, & centrum eius punctum G, à
quo ducatur GH, perpendicularis ad vnum latus, nempe ad AB: Sit quoq; re-
ctangulum I K L M, contentum ſub I K, quæ æqualis ſit perpendiculari G H, & ſub KL, recta, quæ æqualis ponatur dimidiæ parti ambitus figuræ ABCDEF. Di-
co huic rectangulo æqualem eſſe figuram regularem ABCDEF. Ducantur enim
ex G, ad ſingulos angulos lineæ rectæ, vt tota figura in triangula reſoluatur, quæ
omnia æqualia inter ſe erunt, vt in corollario propoſ. 8. lib. 1. Eucl. demonſtra-
tum eſt à nobis: propterea quòd omnia latera triangulorum à puncto G, ex-
euntia ſint inter ſe æqualia, habeantq; baſes æquales, nempè latera figuræ regu-
laris. Hinc enim effi citur, omnes angulos ad G, æquales eſſe, ac proinde, ex di- cto corollario, triangula ipſa inter ſe quo que eſſe æqualia. Quoniam igitur re- ctangulum contentum ſub GH, perpendiculari, & medietate baſis AB, æquale
eſt triangulo ABG, ſi ſumantur tot huiuſmodi rectangula, in quot triangula di-
uiſa eſt figura regularis, erunt omnia ſimul figuræ ABCDEF, ęqualia; propterea

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