Full text: Clavius, Christoph: Geometria practica

LIBER SEPTIMVS. cundum varias diametros deſcribantur circuli per A, tranſeuntes, abſcindent
quoq; ij circuli ex recta AB, latera quadratorum illis circulis æqualium. Habes
ergo viam facilem inueniendi quadratum circulo dato æquale, ſiue quadratri-
cemn oſtram adhibeas, ſiue demonſtrata ab Archimede ſequaris.

327.1.

Facilis inuen-
tio quadrati-
circulo æqua-
lis ex Archi-
mede.
coroll. 2.
ſexti.
coroll. 20.
ſexti.
11. quinti.
9. quinti.

328. IV.

DATO quadrato circulum æqualem deſcribere.

Sit datum quadratum lateris AE, cui circulus æqualis eſt deſcribendus. In
proxima figura ex recta AB, abſcindatur recta A E, dato lateri quadrati æqualis: Et ex E, ducatur ad AB, perpendicularis E F, ſecans A C, in F. Eritque circulus
diametri AF, quadrato lateris AE, æqualis, vt ex proximè demonſtratis liquet.

329. COROLLARIVM.

Ex his, quæ demonſtrata ſunt, conſtruemus circulum cuicunq; figuræ re-
ctilineæ æqualem. Et contra cuicunque circulo figuram rectilineam æqualem
conſtituemus, quæ alteri datæ figuræ rectilineæ cuicunque ſimilis ſit. Nam ſi da-
tæ figuræ rectilineæ deſcribamus quadratum æquale, & huic quadrato circu- lum æqualem per hanc 4. propoſ. conſtituamus; erit idem hic circulus datæ fi-
guræ rectilineæ æqualis.

329.1.

14. ſecundi.

Rvrsvs ſi per propoſitionem 3. dato circulo quadratum ęquale conſtru-
amus, huic autem quadrato conſtituamus figuram rectilineam æqualem, & ſi- milem alteri datę figuræ rectilineæ; erit eadem hæc figura rectilinea conſtituta,
dato circulo æqualis. quod eſt propoſitum.

329.1.

25. ſexti.

330. V.

DATÆ rectæ lineæ circumferentiam circuli reperire æqualem.

In ſecunda figura propoſ. 3. ſit rectæ O, exhibenda æqualis circumferentia. Eius quartæ parti capiatur in latere Quadratricis A D, recta æqualis A I, ac per I,
ipſi D E, agatur parallela I H. Eritque circumferentia circuli ex diametro A H,
deſcripti æqualis datę rectæ O, propterea quod quarta pars eius circum-
ferentiæ æqualis eſt rectæ AI, vt oſtenſum eſt ac proinde tota circũ-
ferentia æqualis erit quadruplæ rectæ AI, hoc eſt, æqua-
lis rectæ O, cuius quarta pars poſita eſt recta
AI. Datæ ergo rectæ circumfentiã æ-
qualem reperim 9 . Quod faci-
endum erat.

331. FINIS LIBRI SEPTIMI.

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer