152132GEOMETRIÆ
vt figura tertiæ ad figuram quartæ.
Et ſi fuerint quatuor fi-
guræ planæ proportionales, ita vt quæ ſunt termini eiuſdem
proportionis ſint figuræ ſimiles, deſcriptæ ab eorundem li-
neis, vel lateribus homologis; lineæ, vel latera homologa
deſcribentia erunt proportionalia.
guræ planæ proportionales, ita vt quæ ſunt termini eiuſdem
proportionis ſint figuræ ſimiles, deſcriptæ ab eorundem li-
neis, vel lateribus homologis; lineæ, vel latera homologa
deſcribentia erunt proportionalia.
Sint quatuor rectæ lineæ proportionales, AB, CD, FG, HM,
prima verò, & ſecunda deſcribant fig. planas ſimiles, AXB, CVD,
89[Figure 89]&
, FG, HM, ſimiles figuras pla-
nas, FOG, HNM, licet prędictis
diſſimiles eſſent, & ſint deſcribentes
figurarum deſcriptarum lineæ, vel
latera homologa. Dico, AXB, ad,
CVD, eſſe vt, FOG, ad, HNM.
Sit, R, tertia proportionalis ipſa-
rum, AB, CD, & , I, tertia pro-
portionalis ipſarum, FG, HM; eſt
igitur, AXB, ad, CVD, vt, AB,
ad, R, . i. in ratione dupla eius, quam habet, AB, ad, CD, . i. eius,
11Coroll. 2.
antec. quam habet, FG, ad, HM, . i. vt, FG, ad, I, quę eſt, vt, FOG,
ad, HNM, ergo vt, AXB, ad, CVD, ita erit, FOG, ad, H
NM.
prima verò, & ſecunda deſcribant fig. planas ſimiles, AXB, CVD,
nas, FOG, HNM, licet prędictis
diſſimiles eſſent, & ſint deſcribentes
figurarum deſcriptarum lineæ, vel
latera homologa. Dico, AXB, ad,
CVD, eſſe vt, FOG, ad, HNM.
Sit, R, tertia proportionalis ipſa-
rum, AB, CD, & , I, tertia pro-
portionalis ipſarum, FG, HM; eſt
igitur, AXB, ad, CVD, vt, AB,
ad, R, . i. in ratione dupla eius, quam habet, AB, ad, CD, . i. eius,
11Coroll. 2.
antec. quam habet, FG, ad, HM, . i. vt, FG, ad, I, quę eſt, vt, FOG,
ad, HNM, ergo vt, AXB, ad, CVD, ita erit, FOG, ad, H
NM.
Sit nunc figura, AXB, ad, CVD, ſibi ſimilem, vt, FOG, ad,
HNM, ſibi ſimilem, licet iſtæ eſſent prædictis diſſimiles, & eas de-
ſcribentes ſint earum lineæ, vel latera homologa. Dico, AB, ad,
CD, eſſe vt, FG, ad, HM, ſit adhuc, R, tertia proportionalis ip-
ſarum, AB, CD, & , I, tertia proportionalis ipſarum, FG, HM,
22Coroll. 2.
antec. eſt ergo, vt figura, AXB, ad, CVD, ita, AB, ad, R, vt verò fi-
gura, FOG, ad, HNM, ita, FG, ad, I, eſt verò, vt, AXB, ad,
CVD, ita, FOG, ad, HNM, ergo vt, AB, ad, R, ſic, FG, ad,
I, eſtautem, AB, ad, R, dupla rationis ipſius, AB, ad, CD, & ,
FG, ad, I, dupla rationis ipſius, FG, ad, HM, ergo vt, AB, ad,
CD, ita, FG, ad, HM, quæ oſtendere opus erat.
HNM, ſibi ſimilem, licet iſtæ eſſent prædictis diſſimiles, & eas de-
ſcribentes ſint earum lineæ, vel latera homologa. Dico, AB, ad,
CD, eſſe vt, FG, ad, HM, ſit adhuc, R, tertia proportionalis ip-
ſarum, AB, CD, & , I, tertia proportionalis ipſarum, FG, HM,
22Coroll. 2.
antec. eſt ergo, vt figura, AXB, ad, CVD, ita, AB, ad, R, vt verò fi-
gura, FOG, ad, HNM, ita, FG, ad, I, eſt verò, vt, AXB, ad,
CVD, ita, FOG, ad, HNM, ergo vt, AB, ad, R, ſic, FG, ad,
I, eſtautem, AB, ad, R, dupla rationis ipſius, AB, ad, CD, & ,
FG, ad, I, dupla rationis ipſius, FG, ad, HM, ergo vt, AB, ad,
CD, ita, FG, ad, HM, quæ oſtendere opus erat.
SCHOLIV M.
_P_Ropoſitionis proximè ſubſequentis nimia fortaſſe prolixitas faſti-
dium potius Lectori, quam delectationem pariet, veruntamen, qui
hoc veretur, ac tantum otij, aut tolerantiæ habere nequit, vt illius ſa-
tis tongam texturam percurrere Valeat, ipſam ſupponat, ac prætereat,
ijs enim præcipuè à me dirigitur, quibus nec otium deeſt, nec
dium potius Lectori, quam delectationem pariet, veruntamen, qui
hoc veretur, ac tantum otij, aut tolerantiæ habere nequit, vt illius ſa-
tis tongam texturam percurrere Valeat, ipſam ſupponat, ac prætereat,
ijs enim præcipuè à me dirigitur, quibus nec otium deeſt, nec
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