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Geometriae Planae Elementa Theorico-Practica : Methodo breviore conscripta & Praelectionibus publicis In Gymnasio Aquisgranensi Explanata
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(85)que & angulorum ad centrum (28) va-lor prodit, dividendo 360 per numerumarcuum, adeóque & laterum. q. e. d.307. COROL. In figura ordinata an-guli ad centrum omnes aequales sunt.Quilibet autem in triangulo aequilaterocontinet gr. 120: in quadrato 90: in pen-tagono 72: in hexagono 60 &c.308. THEOR. In quavis figura or-dinata angulus polygoni cum angulo adcentrum duos rectos efficit.DEMONST. CAD†ADC†ACD= 180 gr. (103) ADC=BAC(35) er-go CAD†BAC†ACD=180 gr. (22)CAD†BAC=BAD (20) igitur BADA CD=180 gr. (22) q. c. d.309. COROL. Iginir BAD = 180gr. ACD (21) id est, si ex 180 gr.subtrahitur angulus ad centrum, proditangulus polygoni. Itaque angulus po-lygoni in triangulo aequilatero continetgr. 60: in quadrato 90: in pentagono108: in hexagono 10 &c.310. THEOR. Latus hexagoni ordi-nati aequale est radio illius circuli, cui in-ſcribi poteſt.DEMONST. Ductis ex centro radiisAC & BC, in triangulo ACC angulusC=60 gr. (307) unde A+B=120 gr.(105) quia ergo AC=BC (9) erit A120= 60=C.= B (127) ergo A=B-ItaqueF 2