6545LIBERI.
DB, ideſt vt, HO, ad, ON, at, vt ſupra, oſtendemus, HO, ad,
ON, eſſe vt, HG, ad, NR, ergo, PL, ad, BF, erit vt, HG,
ad, NR, erat autem, EL, ad VG, vt, PL, ad, HG, ergo, EL,
ad, VG, erit vt, BF, ad, NR, quia verò, BF, ad, NR, eſt vt,
DF, ad, OR, (nam, BF, NR, ſunt ſimiliter diuiſæ in punctis,
D, O,) ideſt vt, FL, ad, RG, ergo, EL, ad, VG, erit vt, FL,
ad, RG, ergo reliqua, EF, ad, VR, erit vt tota, EL, ad, VG,
ideſt vt, BF, ad, NR. Idem oſtendemus de quibuslibet ductis ip-
ſis, EF, VG, parallelis, quę diuidant, BF, NR, ſimiliter ad ean-
dem partem, nempè eas, quæ inter ipſas, BF, NR, & circuitum
figurarum, AE, MV, eodem ordine ſumptæ continentur, eſſe vt
ipias, BF, NR, ergo, BF, NR, ſunt incidentes ſimilium figura-
11B. Def. 10. rum, MV, AE, & ductarum tangentium, quod oſtendere opus erat.
ON, eſſe vt, HG, ad, NR, ergo, PL, ad, BF, erit vt, HG,
ad, NR, erat autem, EL, ad VG, vt, PL, ad, HG, ergo, EL,
ad, VG, erit vt, BF, ad, NR, quia verò, BF, ad, NR, eſt vt,
DF, ad, OR, (nam, BF, NR, ſunt ſimiliter diuiſæ in punctis,
D, O,) ideſt vt, FL, ad, RG, ergo, EL, ad, VG, erit vt, FL,
ad, RG, ergo reliqua, EF, ad, VR, erit vt tota, EL, ad, VG,
ideſt vt, BF, ad, NR. Idem oſtendemus de quibuslibet ductis ip-
ſis, EF, VG, parallelis, quę diuidant, BF, NR, ſimiliter ad ean-
dem partem, nempè eas, quæ inter ipſas, BF, NR, & circuitum
figurarum, AE, MV, eodem ordine ſumptæ continentur, eſſe vt
ipias, BF, NR, ergo, BF, NR, ſunt incidentes ſimilium figura-
11B. Def. 10. rum, MV, AE, & ductarum tangentium, quod oſtendere opus erat.
COROLLARIVM.
INnoteſcit exhoe conſequenter duarum ſimilium figurarum, &
ea-
rundem oppoſitarum tangentium, quæ ſuntregulæ homologarum,
tum incidentes ſimiliter diuidi ab homologis earundem figurarum, pro-
ductis, ſi opus ſit, tum quaſcumque alias, quæ cum homologis angulos
continent æquales, vt exempli gratia ipſæ, NR, BF. Et vlterius ip-
ſas homologas eſſe tum vt quaſuis incidentes, tum vt eiſdem parallelas,
ideſt ex. gr. CI, ad, TS, mdum erit vt, PE, ad, HG, ſiue vt, BF, ad,
NR, ſed etiam vt, BF, ad quamcumque aliam parallolam ipſi, NR,
ductam inter parattelas, MN, VR, nam illa erit æqualis ipſi, NR.
Patet igitur duarum ſimilium figurarum homologas nedum eſſe vt ea-
rum, & oppoſitarum earundem tangentium, quæ ſunt regulæ homolo-
garum, incidentes, ſed etiam vt quaſuis alias inter eaſdem tangentes
ductas ipſis incidentibus æquidiſtantes, ſiue ad homologas ſimilium figu-
rarum æqualiter inclinatas.
rundem oppoſitarum tangentium, quæ ſuntregulæ homologarum,
tum incidentes ſimiliter diuidi ab homologis earundem figurarum, pro-
ductis, ſi opus ſit, tum quaſcumque alias, quæ cum homologis angulos
continent æquales, vt exempli gratia ipſæ, NR, BF. Et vlterius ip-
ſas homologas eſſe tum vt quaſuis incidentes, tum vt eiſdem parallelas,
ideſt ex. gr. CI, ad, TS, mdum erit vt, PE, ad, HG, ſiue vt, BF, ad,
NR, ſed etiam vt, BF, ad quamcumque aliam parallolam ipſi, NR,
ductam inter parattelas, MN, VR, nam illa erit æqualis ipſi, NR.
Patet igitur duarum ſimilium figurarum homologas nedum eſſe vt ea-
rum, & oppoſitarum earundem tangentium, quæ ſunt regulæ homolo-
garum, incidentes, ſed etiam vt quaſuis alias inter eaſdem tangentes
ductas ipſis incidentibus æquidiſtantes, ſiue ad homologas ſimilium figu-
rarum æqualiter inclinatas.
THEOREMA XXII. PROPOS. XXV.
SI quæcunque ſimiles figuræ planæ à rectis lineis deſcti-
bantur, quæ ſint earundem homologæ, & inter ſe æqua-
les; ſuperponantur autem ad inuicem ipſæ figuræ, ita vt ea-
ſdem deſcribentes rectæ lineæ ſibi congruant, figuræq; ſint
fimiliter poſitæ, illæ quoque erunt ad inuicem congruentes.
bantur, quæ ſint earundem homologæ, & inter ſe æqua-
les; ſuperponantur autem ad inuicem ipſæ figuræ, ita vt ea-
ſdem deſcribentes rectæ lineæ ſibi congruant, figuræq; ſint
fimiliter poſitæ, illæ quoque erunt ad inuicem congruentes.
Sint ſimiles figuræ planæ, ABXC, EFPG, quæcunq;
deſcri-
ptæ ab earundern homologis, & æqualibus rectis lineis, BC,
ptæ ab earundern homologis, & æqualibus rectis lineis, BC,