Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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390378IO. BAPT. BENED.
De incommenſur abilitate, in longitudine perpendicu-
laris trianguli æquilateri cum eiuſdem latere.
ID quod à me poſtulas eſt omnino impoſſibile, velles enim duos numeros inueni
re inter ſe ita ſe habentes, vt ſe habent perpendicularis in triangulo æquilatero
cum vno eius laterum, quod vero hoc fieri non poſſit, conſidera in figura præcedenti
triangulum æquilaterum .d.l.q. cuius perpendicularis ſit .d.o. quæ diuidit .l.q. per
æqualia in .o. vnde ex .4. ſecundi Euclidis, quadratum .l.q. (ideſt .d.q.) quadruplum
erit quadrato .o.q. & ex penultima primi ęquale quadratis .d.o. et .o.q.
quare erit ſeſ-
o.q.
quod ſi ita fuiſſent, ſequeretur ternarium numerum eſſe quadratum ex .22. octaui.
ma decimi .d.o. eſſe incommenſurabilem ipſi .l.q. ſeu .d.q. in longitudine.
nere ſuperparticulari, cum ſit ſeſquitertia, vnde quadratum ipſius .d.o. numeris da-
ri non poteſt, eo quod ſi dabilis fuiſſet, ſequeretur, quod inter quadratum ipſius. l .
q.
& ipſius .d.o. eſſet aliquis numerus medius proportionalis ex .16. octaui, vnde ex
octaua eiuſdem vnitas diuiſibilis eſſet, quod fieri non poteſt.
431[Figure 431]
De triangulo & Pentagono æquilatero