Valerio, Luca - De centro gravitatis solidorum

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PROPOSITIO VIII.

Si ſint tres magnitudines ſe ſe æqualiter exce
dentes; & aliæ eiuſdem generis illis multitudine
æquales, binæque ſumptæ in duplicata primarum
proportione; erit vtriuſque ordinis minor pro
portio compoſitæ ex primis ad compoſitam ex ſe
cundis, quam compoſitæ ex ſecundis ad compoſi
tam ex tertijs.

Sint tres magnitudines A, B, C, quarum C maxima
æque ſuperet B, atque
B, ipſam A. & totidem
eiuſdem generis D, E,
F, ſitque F ad E du
plicata proportio ipſius
C ad B: & E ad D,
duplicata ipſius B ad
A. Dico AD, ſimul
ad BE, ſimul mino
tem eſſe proportionem
quam BE, ſimul ad
CF, ſimul. Eſto enim
recta quæpiam GH,
ad aliam rectam ſibi in
directum poſitam HK,
vt magnitudo A ad ip
ſius F duplam (hoc
enim fieri poteſt) &

73[Figure 73]
ſuper baſim GK; conſtituatur triangulum GLK, atque
in eo deſcribatur parallelogrammum GHMN: & vt eſt

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