4426
GP _a_, HP δ ità diſponantur, ut latera PG, PH ſibi congruant (un-
de major angulus GP _a_ minorem HP δ comprehendet) tum centro P
per δ deſcribatur circulus E δ F ipſas PG, P _a_ ſecans punctis F, E; item
connexâ EH, centro H per δ tranſeat circulus HMN ipſas HP, HE
ſecans punctis N, M; denuò connexa E δ cum PG conveniat in L.
Eſtque jam ang. _a_ P δ. ang. δ PH: : ſector EP δ. ſector δ PF & gt;
triang. EP δ. triang. δ PL: : Eδ. δ L : : triang. EH δ. δ HL & gt;
ſector MH δ. ſector δ HN : : ang. EH δ. ang. δ HP. eſt igi-
tur ang. _a_ P δ. ang. δ PH & gt; ang. EH δ. ang. δ HP. ergóque
compoſitè ang. _a_ PG. ang. δ PH & gt; ang. EHP. ang. δ HP. per-
mutandóque ang. _a_ PG. ang. EHP & gt; ang. δ PH. ang. δ HP. eſt
autem HP. PE : : HP. P δ : : I. R : : GP. P _a_. adeoque EH ad
_a_ G parallela; vel ang. EHP = ang. _a_ GP. ergò erit ang. _a_ PG.
ang. _a_ GP & gt; ang. δ PH. ang. δ HP. hoc eſt ang. _a_ BG, _a_ BP
& gt; ang. δ BH. ang. δ BP. vel componendo ang. GBP. ang. _a_ BP
& gt; ang HBP. ang. δ BP. Quod erat demonſtrandum.
de major angulus GP _a_ minorem HP δ comprehendet) tum centro P
per δ deſcribatur circulus E δ F ipſas PG, P _a_ ſecans punctis F, E; item
connexâ EH, centro H per δ tranſeat circulus HMN ipſas HP, HE
ſecans punctis N, M; denuò connexa E δ cum PG conveniat in L.
Eſtque jam ang. _a_ P δ. ang. δ PH: : ſector EP δ. ſector δ PF & gt;
triang. EP δ. triang. δ PL: : Eδ. δ L : : triang. EH δ. δ HL & gt;
ſector MH δ. ſector δ HN : : ang. EH δ. ang. δ HP. eſt igi-
tur ang. _a_ P δ. ang. δ PH & gt; ang. EH δ. ang. δ HP. ergóque
compoſitè ang. _a_ PG. ang. δ PH & gt; ang. EHP. ang. δ HP. per-
mutandóque ang. _a_ PG. ang. EHP & gt; ang. δ PH. ang. δ HP. eſt
autem HP. PE : : HP. P δ : : I. R : : GP. P _a_. adeoque EH ad
_a_ G parallela; vel ang. EHP = ang. _a_ GP. ergò erit ang. _a_ PG.
ang. _a_ GP & gt; ang. δ PH. ang. δ HP. hoc eſt ang. _a_ BG, _a_ BP
& gt; ang. δ BH. ang. δ BP. vel componendo ang. GBP. ang. _a_ BP
& gt; ang HBP. ang. δ BP. Quod erat demonſtrandum.
_Corol_. 1. Ang. _a_ BG. ang. _a_ BP > ang. δ BH. ang. δ BP.
2. Ang. _a_ BG. ang. PBG > ang. δ BH. PBH.
2. Ang. _a_ BG. ang. PBG > ang. δ BH. PBH.
Opportunum eſt hoc Theorema conciliandis cum experientia pro-
poſitis refractionum legibus. Ut demirari ſubeat nuperrimum Opticæ
ſcriptorem, virum alioqui diffuſè doctum, hujuſmodi ratiocinio leges
iſtas impugnàſſe: “In majoribus tamen angulis inclinationis (Ipſiſ-
"ſima ſunt ejus verba) falſum eſſe conſtat (principium nempe no-
"ſtrum;) in his enim angulus refractionis major eſt ſubtriplo an-
"guli inclinationis; quod mihi aliiſque ex luculentis experimentis
"compertum eſt. Hæc, inquam, ille ταντοεπ@. Quaſi verò dixiſſet;
numeri 6 & 4 ſimul accepti non conficiunt 10, quia numerum effici-
unt majorem quam 8. planè ſimilis eſt diſcurſus; non ovum ovo ſi-
milius. Nam in refractionibus ex. gr. ad vitrum factis ſi ponatur ad
quamvis inclinationem (puta graduum 15.) quòd ſit angulus refra-
ctionis ſubtriplus anguli inclinationis (quem ille vocat, incidentiæ nos
angulum appellare ſolemus) neceſſariò, ſicuti modò demonſtratum
eſt, è principio noſtro conſequetur, quòd ad aliam quamcunque ma-
jorem inclinationem refractionis angulus major erit ſubtriplo anguli
inclinationis; nominatim acceptâ graduum 30 inclinatione juxta di-
ctum principium inſtitutus calculus angulum præbebit reſractum
19. 24'; angulúmque proinde refractionis 10. 36', qui 30 graduum
trientem exuperat. Quare cùm Clariſſimus vir Hypotheſin hanc
poſitis refractionum legibus. Ut demirari ſubeat nuperrimum Opticæ
ſcriptorem, virum alioqui diffuſè doctum, hujuſmodi ratiocinio leges
iſtas impugnàſſe: “In majoribus tamen angulis inclinationis (Ipſiſ-
"ſima ſunt ejus verba) falſum eſſe conſtat (principium nempe no-
"ſtrum;) in his enim angulus refractionis major eſt ſubtriplo an-
"guli inclinationis; quod mihi aliiſque ex luculentis experimentis
"compertum eſt. Hæc, inquam, ille ταντοεπ@. Quaſi verò dixiſſet;
numeri 6 & 4 ſimul accepti non conficiunt 10, quia numerum effici-
unt majorem quam 8. planè ſimilis eſt diſcurſus; non ovum ovo ſi-
milius. Nam in refractionibus ex. gr. ad vitrum factis ſi ponatur ad
quamvis inclinationem (puta graduum 15.) quòd ſit angulus refra-
ctionis ſubtriplus anguli inclinationis (quem ille vocat, incidentiæ nos
angulum appellare ſolemus) neceſſariò, ſicuti modò demonſtratum
eſt, è principio noſtro conſequetur, quòd ad aliam quamcunque ma-
jorem inclinationem refractionis angulus major erit ſubtriplo anguli
inclinationis; nominatim acceptâ graduum 30 inclinatione juxta di-
ctum principium inſtitutus calculus angulum præbebit reſractum
19. 24'; angulúmque proinde refractionis 10. 36', qui 30 graduum
trientem exuperat. Quare cùm Clariſſimus vir Hypotheſin hanc
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