6244
ſimplicibus triplicatas ſubſtituendo rationes, eſt γ Q.
QB &
gt;
YP .
PB. & his æquales rationes adjungendo eſt QN. γ Q + γ Q. QB& gt;
PN . YP + YP. PB; hoc eſt QN. QB & gt; PN. PB. compo-
nendóque BN. QB & gt; BN. P B. ergo QB & lt; PB. unde rurſus
liquet rectam X Qipſis AB; ZP interjacere: Q. E. D.
PB. & his æquales rationes adjungendo eſt QN. γ Q + γ Q. QB& gt;
PN . YP + YP. PB; hoc eſt QN. QB & gt; PN. PB. compo-
nendóque BN. QB & gt; BN. P B. ergo QB & lt; PB. unde rurſus
liquet rectam X Qipſis AB; ZP interjacere: Q. E. D.
XVII.
Conſimili prorſus argumentatione conſtabit obliquio-
rum incidentium refractos ultra punctum Z ipſam KN interſe-
care.
rum incidentium refractos ultra punctum Z ipſam KN interſe-
care.
XVIII.
Quinimò rurſus exertiùs apparet non niſi binos refractos
in eodem puncto convenire.
in eodem puncto convenire.
XI X.
Addo cum ipſo KN concurrentes refractos circa punctum
Z conglomerari, præſertim illos, qui ad partes F (obliquius) inci-
dentes pertinent.
Z conglomerari, præſertim illos, qui ad partes F (obliquius) inci-
dentes pertinent.
Nam accipiantur, exempli causâ, ſibi pares N S, ST ;
&
ſit BP
11Fig. 61. quarta proportionalis in ratione YB ad BN; & BQ quarta proportionalis
in ratione YB ad BS; & BR itidem quarta talis in ratione YB ad
BT; & à punctis P, Q, R erectæ perpendiculares ipſam NKZ
ſecent in Z, X, & V. patet (è mox oſtenſis) omnium ſpatio NS
incidentium refractos cum NK concurrere intra ZX; nec non omnes
ipſi ST incidentium refractos intra XV cum eodem convenire. por-
rò rectæ BP , BQ, BR ſe habent invicem ut _Cubi_ rectarum BN,
BS, BT, ( vel ſunt in ipſarum BN, BS, BT _ratione triplicata_ : nam
BP. YB : : BN cub. BY cub. & YB . BQ : : YB cub. BS cub.
adeóque ex æquo BP. BQ : : BN cub . BS cub. & conſimili ratione
BP. BR : : BN cub. BT cub.) undè faciiè monſtrabitur eſſe PQ
multo minorem quàm QR; xel ZX quàm XV (verbis parco multis
in re ſatis manifeſta) . quare dicti refracti circa punctum Z ſpiſſiùs
ipſum NK decuſſabunt.
11Fig. 61. quarta proportionalis in ratione YB ad BN; & BQ quarta proportionalis
in ratione YB ad BS; & BR itidem quarta talis in ratione YB ad
BT; & à punctis P, Q, R erectæ perpendiculares ipſam NKZ
ſecent in Z, X, & V. patet (è mox oſtenſis) omnium ſpatio NS
incidentium refractos cum NK concurrere intra ZX; nec non omnes
ipſi ST incidentium refractos intra XV cum eodem convenire. por-
rò rectæ BP , BQ, BR ſe habent invicem ut _Cubi_ rectarum BN,
BS, BT, ( vel ſunt in ipſarum BN, BS, BT _ratione triplicata_ : nam
BP. YB : : BN cub. BY cub. & YB . BQ : : YB cub. BS cub.
adeóque ex æquo BP. BQ : : BN cub . BS cub. & conſimili ratione
BP. BR : : BN cub. BT cub.) undè faciiè monſtrabitur eſſe PQ
multo minorem quàm QR; xel ZX quàm XV (verbis parco multis
in re ſatis manifeſta) . quare dicti refracti circa punctum Z ſpiſſiùs
ipſum NK decuſſabunt.
XX.
Ex his demùm conficitur omnibus bene trutinatis, oculo
(O) centrum habenti in refracto NK uſpiam conſtituto, puncti A
imaginem ad ipſum conditione præditum toties inſinuatâ punctum Z
conſiſtere. Sit enim CD pupillæ (in plano ABC jacens) _Diameter;_
_axi Optico_ KN perpendicularis; & per ejus extrema C, D tranſeant
refracti IM LR ipſi KN occurrentes punctis X, V. ex oſtenſis patet
omnium intra ſpatium MN incidentium radiorum refractos intra ten-
minos ZX principalem refractum interſecare; neque non omnes
(O) centrum habenti in refracto NK uſpiam conſtituto, puncti A
imaginem ad ipſum conditione præditum toties inſinuatâ punctum Z
conſiſtere. Sit enim CD pupillæ (in plano ABC jacens) _Diameter;_
_axi Optico_ KN perpendicularis; & per ejus extrema C, D tranſeant
refracti IM LR ipſi KN occurrentes punctis X, V. ex oſtenſis patet
omnium intra ſpatium MN incidentium radiorum refractos intra ten-
minos ZX principalem refractum interſecare; neque non omnes