DelMonte, Guidubaldo, In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata

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1
LEMMA. I.
Æquidiſtantes lineæ lineas in eadem proportione diſpe­
ſcunt.
Sintlineę AB CD, quas ſecent æqui­

diſtantes lineæ AC EF BD. Dico ita eſ­
ſe BE ad EA, vt DF ad FC. primùm
quidem AB CD vel ſunt
vel minùs. ſi ſunt æquidiſtantes, iam habe
tur intentum. Nam BE erit æqualis DF,
& EA ipſi FC. vnde ſequitur ita eſſe BE

ad EA, vt DF ad FC.
34. primi.
56[Figure 56] 57[Figure 57]
Si verò AB CD non fuerint æquidi­
ſtantes, concurrant in G, vt in ſecunda fi­

gura, & quoniam BD EF æquidi­
ſtantes, erit GB ad BE, vt GD ad
& componendo GE ad EB, vt GF ad
conuertendoquè BE ad EG, vt DF ad
FG, rurſus quoniam EF AC ſunt æquidi
ſtantes; erit GE ad EA, vt GF ad FC, e­
ritigitur ex æquali BE ad EA, vt DF ad FC.
2.ſexti.
18.quinti.
cor.4.quinti
58[Figure 58]
Secent verò ſeſe lineæ AB CD, vt in tertia figura, ſimi­
litudinem triangulorum BGD EGF, it a erit BG ad GE,
DG ad GF. & componendo BE ad EG, vt DF ad FG.
verò GE ad EA, vt GF ad FC. ergo ex æquali BE ad EA
erit, vt DF ad FC. quod demonſtrare oportebat.

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