<emph type="italics"/>principijs huius)<emph.end type="italics"/> affert nunc exemplum alterius demon&longs;trationis, quæ non <lb/>
ex communibus, vt præcedens Bry&longs;onis, &longs;ed ex proprijs principijs o&longs;tendit <lb/>
affectionem de &longs;ubiecto proprio. </s> <s id="s.001001">E&longs;t autem illud exemplum toties decan<lb/>
tatum de triangulo habente tres angulos æquales duobus rectis angulis; id<lb/>
circo operæpretium e&longs;&longs;e puto explicare demon&longs;trationem, 32. primi Eucli<lb/>
dis, quæ i&longs;tud ex proprijs principijs demon&longs;trat, & quam hoc loco Ari&longs;to<lb/>
teles innuit, hoc enim modo ip&longs;ius Ari&longs;t. mentem probè penetrare poteri<lb/>
<figure id="id.009.01.055.1.jpg" place="text" xlink:href="bianc_locam_009_la_1615/009-01-figures/009.01.055.1.jpg"/><lb/>
mus. </s> <s id="s.001002">&longs;it ergo <expan abbr="triãgulum">triangulum</expan> A B C. </s> <s id="s.001003">Dico ag<lb/>
gregatum <expan abbr="tri&utilde;">trium</expan> ip&longs;ius angulorum A, B, C, <lb/>
e&longs;&longs;e æquale aggregato ex duobus angu<lb/>
lis rectis (vt autem melius intelligas, quæ <lb/>
&longs;equuntur, lege prius ea, quæ dicta &longs;unt <lb/>
in lib. 1. Priorum &longs;ecto 3. cap. 1.) produ<lb/>
catur latus B C, <expan abbr="v&longs;q;">v&longs;que</expan> in D, vt fiat angulus <lb/>
externus A C D; Iam &longs;ic, quoniam <expan abbr="pro-bat&utilde;">pro<lb/>
batum</expan> e&longs;t in 13. primi, duos angulos, quos <lb/>
facit linea A C, cum linea B D, &longs;cilicet angulos A C B, A C D, e&longs;&longs;e pares <lb/>
duobus rectis: & quia pariter in prima parte huius propo&longs;. </s> <s id="s.001004">32. probatum <lb/>
e&longs;t ab Euclide duos angulos A B, e&longs;&longs;e æquales externo angulo A C D: &longs;i ter<lb/>
tius angulus reliquus A C B, &longs;umatur bis, &longs;emel cum duobus angulis A, B, <lb/>
& &longs;emel cum externo A C D, <expan abbr="add&etilde;tur">addentur</expan> æqualia æqualibus, & propterea tres <lb/>
anguli A, B, A C B, &longs;imul &longs;umpti, erunt æquales duobus A C D, A C B, &longs;imul <lb/>
&longs;umptis; &longs;ed his duobus &longs;unt æquales duo recti, ergo cum quæ &longs;unt æqualia <lb/>
vni tertio, &longs;int etiam æqualia inuicem, erit aggregatum trium angulorum <lb/>
A, B, A C B, æquale aggregato duorum rectorum; quod erat demon&longs;tran<lb/>
dum. </s> <s id="s.001005">Medium <expan abbr="itaq;">itaque</expan> huius demon&longs;trationis, &longs;i res ad trutinam Logicam ex<lb/>
pendatur, e&longs;t, quod partes aggregati <expan abbr="tri&utilde;">trium</expan> <expan abbr="angulor&utilde;">angulorum</expan> A, B, A C B, &longs;unt æqua<lb/>
les partibus aggregati <expan abbr="duor&utilde;">duorum</expan>, & ideo <expan abbr="aggregat&utilde;">aggregatum</expan>, aggregato æqua<lb/>
le e&longs;t. </s> <s id="s.001006">quod medium e&longs;t in genere cau&longs;æ materialis. </s> <s id="s.001007">quod verò partes illius <lb/>
&longs;int æquales partibus huius, probatur, per dignitatem <expan abbr="illã">illam</expan>, quæ &longs;unt æqualia <lb/>
vni tertio, &longs;unt etiam inter &longs;e. </s> <s id="s.001008">partes porrò aggregati trium angulorum <lb/>
erant hæ, anguli A, B, vna; altera verò angulus A C B; partes verò aggre<lb/>
gati duorum rectorum erant A C B, A C D, quibus partibus, illæ &longs;unt æqua<lb/>
les, & ideo totum toti æquale. </s> <s id="s.001009">quod medium e&longs;t omnino intrin&longs;ecum, & ex <lb/>
proprijs ip&longs;ius trianguli, &longs;iue ex proprijs angulorum ip&longs;ius, cum &longs;int ip&longs;ius <lb/>
partes. </s> <s id="s.001010">quod pariter medium ex parte pa&longs;&longs;ionis, quæ demon&longs;tratur, e&longs;t ex <lb/>
proprijs, cum &longs;int partes illius materiales. </s> <s id="s.001011">per materiam autem oportet <lb/>
hoc loco intelligere materiam intelligibilem, ide&longs;t quantitatem à qualita<lb/>
tibus ab&longs;tractam, & terminatam, de qua pluribus agemus infra in tractatu <lb/>
de natura mathematicarum. </s> <s id="s.001012">Hinc videas eos magnopere decipi, qui pu<lb/>
tant, hanc demon&longs;trationem e&longs;&longs;e per extrin&longs;eca, eò quod ad demon&longs;tran<lb/>
dum producatur linea B C, in D, putantes lineam illam productam C D, <lb/>
e&longs;&longs;e demon&longs;trationis medium; lineæ <expan abbr="namq;">namque</expan> huiu&longs;modi, quæ in demon&longs;tra<lb/>
tionibus geometricis con&longs;truuntur, nunquam &longs;unt media propria demon<lb/>
&longs;trationum, &longs;ed tantummodo a&longs;&longs;umuntur ad probandum medium iam ex<lb/>
cogitatum e&longs;&longs;e veram cau&longs;am conclu&longs;ionis. </s> <s id="s.001013">Hinc etiam manife&longs;tè colligas