Full text: Clavius, Christoph: Geometria practica

GEOMETR. PRACT. circulus æqualis ſitrectangulo ſub AB, BEF, erit quo que ſector A B C D, re- ctangulo ſub AB, BC, æqualis. quod erat demonſtrandum.

194.1.

Note:
33. ſexti.
15. quinti.
1. ſexti.
14. quinti.

Eadem ratione procreabitur ſector A B F D A, ex ſemidiametro A B, in ſe-
miſſem arcus BFD.

2. Sit deinde ſegmentum BCD. Inuento centro A, arcus B C D, & co- gnitis per aliquam menſuram lateribus trianguli A B D, & arcu B C D, in eadem
menſura, vt Num. 1. diximus, inueſtigetur tam area ſectoris ABCD, quam trian-
guli ABD. Hæc enim detracta ex illa relinquet aream ſegmenti propoſiti BCD.

194.1.

25. tertij.

3. Sit præterea figura lenticularis duobus arcubus G H I, GKI. contenta. Ducta recta GI, inquiratur, vt Nu. 2. docuimus, vtriuſque ſegmenti GHI, GKI,
area. Summa enim ex duabus hiſce areis conflata, erit area propoſitæ figuræ
GHIK. Quod ſi ſegmenta GHI, GKI, ſint æqualia, ſatis erit vnius areaminue-
ſtigare. Hæc namque duplicata dabit propoſitæ figuræ GHIK, aream.

4. Non aliter metiemur figuras ex varijs circulorum ſegmentis coagmen-
tatas, ſiue omnes circumferentiæ extrorſus vergant, ſiue introrſum, ſiue partim
introrſum, & partium extrorſum. Vtin tribus his figuris, ſi arcubus ſubten-
dantur chordæ, metiemur in prima quadrilaterum ABCD, vt cap. 1. vel 3. do cui-
mus: & ſegmenta AEB, BFC, CGD, DHA, vthoccap. Num. 2. traditũ eſt. Sie-
nim hæc ſegmenta quadrilatero adijciantur, quod omnia extrorſum tendant,
conſlabitur area figuræ A E B F C G D H, ex quatuor arcubus compoſitæ.

194.1.

230-01

In ſecunda autem metiemur pentagonum ABCDE, per ea, quæ cap. 4. ſcri-
pta ſunt: Ex quo ſi dememus quinque ſegmenta introrſum vergentia, quæ qui-
dem ex ijs, quæ Num. 2. huius cap. ſcripſimus, cognoſcentur, reliqua fiet area ſi-
guræ A F B G C H D I E K, ex quinque arcubus conflatæ.

In tertia denique pentagono A B C D E, adij ciemus tria ſegmenta, A F B,
A G E, C H D, extrorſum vergentia, & ex compoſito numero duo ſegmenta
B I C, D K E, introrſum vergentia tollemus, vt area relinquatur figuræ AFBIC-
HDKEG, ex quinque arcubus compoſitæ. Atque hoc modo agrum quantum-
uis irregularem metirilicebit.

5. Sit denique in prima figura huius cap. ſegmentum circuli LMON, com-
prehenſum duabus rectis L M, N O, & duobus arcubus LN, MO. Exploretur
vt Num. 2. declaratum eſt, area vtriuſque ſegmenti P L M, P N O. Minor enim
area P N O, detracta ex maiori PLM, reliquam ſaciet aream propoſiti ſegmenti
L M O N.

6. Vt quartus hic liber concludatur, lubet hic appẽdicis loco regulas quaſ-
dam alias à noſtro inſtituto non alienas ſubiungere.

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