11292GEOMETRIÆ&
. Modòetiam ſi ad illa puncta non terminentur dico tamen, ls,
ad, E4, eſſe vt, 47, ad, ℟ & , etenim, ls, ad, 47, eſt vt, AC,
ad, FK, ideſt vt, LO, ad, uY, vel vt, E4, ad, ℟ & , vt probatum
eſt, ergo permutando, ls, ad, E4, erit vt, 47, ad, ℟ & , quod o-
ſtendere oportebat.
ad, E4, eſſe vt, 47, ad, ℟ & , etenim, ls, ad, 47, eſt vt, AC,
ad, FK, ideſt vt, LO, ad, uY, vel vt, E4, ad, ℟ & , vt probatum
eſt, ergo permutando, ls, ad, E4, erit vt, 47, ad, ℟ & , quod o-
ſtendere oportebat.
COROLLARIVM.
_E_T quoniam probatum eſt, l s, ad, 4 7, eſſe vt, E 4, ad, ℟ &
, ſeu
vt, LO, ad, u γ, vt autem, LO, ad, u γ, ita duæ homologæ, QP,
ad, 83, ideò duæ homologæ, ls, 47, ſunt inter ſe, vt duæ homologæ,
QP, 8R, & cum oppoſitæ tangentes, DL, dO, pu, g γ, ductæ ſint vt-
cumque, licet ad eundem angulum cx eadem parte cum ipſis, E4, ℟ & ,
ideò duæhomologæ, ls, 4 7, erunt vt quæcumq; aliæ duæ homologæ qui-
buſuis regulis aſſimptæ, vel vt ecrum incidentes, immo & ipſæ inciden-
tes, crunt inter ſe, vt quæuis aliæ duæ incidentes, oſtenſum. n. eſt, A
C, ad, FK, eſſe vt, LO, ad, u γ.
vt, LO, ad, u γ, vt autem, LO, ad, u γ, ita duæ homologæ, QP,
ad, 83, ideò duæ homologæ, ls, 47, ſunt inter ſe, vt duæ homologæ,
QP, 8R, & cum oppoſitæ tangentes, DL, dO, pu, g γ, ductæ ſint vt-
cumque, licet ad eundem angulum cx eadem parte cum ipſis, E4, ℟ & ,
ideò duæhomologæ, ls, 4 7, erunt vt quæcumq; aliæ duæ homologæ qui-
buſuis regulis aſſimptæ, vel vt ecrum incidentes, immo & ipſæ inciden-
tes, crunt inter ſe, vt quæuis aliæ duæ incidentes, oſtenſum. n. eſt, A
C, ad, FK, eſſe vt, LO, ad, u γ.
THEOREMA XLV. PROPOS. XLVIII.
SI ſint duæ ſimiles figuræ planæ, quarum ſint ductæ oppo-
ſitæ tangentes, quæ ſunt homologarum earundem regu-
læ, per quas extendantur duo plana vtcumque inuicem pa-
rallela ęquè ad eandem partem ijſdem inclinata, deinde ſum-
ptis duabus quibuslibet homologis illæ deſcribere intelli-
gantur figuras planas ſimiles, ductis primò planis æquidi-
ſtantes, ita vt ſint ſimiliter deſcriptæ, & deſcribentes earum
lineæ, vel latera homologa, idem autem contingat cæteris
homologis, etiam ſi omnes figuræ deſcriptæ ſeorſim in vna-
quaque propoſitarum figurarum non eſſent ſimiles; Solida,
quę ab ijſdem tanguntur oppoſitis planis, in quibus ex traie-
ctione planorum præfatis oppoſitis tangentibus æquidiſtan-
tium eædem figuræ produci poſſunt, erunt ſimilia, & figuræ
deſcriptæ eorundem homologæ figuræ, & earum regulę ipſa
oppoſita tangentia plana, quorum & dictorum ſolidorum fi-
guræ incidentes erunt primò propoſitæ figuræ.
ſitæ tangentes, quæ ſunt homologarum earundem regu-
læ, per quas extendantur duo plana vtcumque inuicem pa-
rallela ęquè ad eandem partem ijſdem inclinata, deinde ſum-
ptis duabus quibuslibet homologis illæ deſcribere intelli-
gantur figuras planas ſimiles, ductis primò planis æquidi-
ſtantes, ita vt ſint ſimiliter deſcriptæ, & deſcribentes earum
lineæ, vel latera homologa, idem autem contingat cæteris
homologis, etiam ſi omnes figuræ deſcriptæ ſeorſim in vna-
quaque propoſitarum figurarum non eſſent ſimiles; Solida,
quę ab ijſdem tanguntur oppoſitis planis, in quibus ex traie-
ctione planorum præfatis oppoſitis tangentibus æquidiſtan-
tium eædem figuræ produci poſſunt, erunt ſimilia, & figuræ
deſcriptæ eorundem homologæ figuræ, & earum regulę ipſa
oppoſita tangentia plana, quorum & dictorum ſolidorum fi-
guræ incidentes erunt primò propoſitæ figuræ.
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