Reg.8. Inventis longitudinibus AH, HX; ſi jam deſideretur
poſitio rectæ AH,ſecundum quam Projectile, data illa cum veloci
tate emiſſum, incidit in punctum quodvis K:ad puncta A& K
erigantur rectæ AC, KFhorizonti perpendiculares, quarum AC
deorſum tendat, & æquetur ipſi AIſeu 1/2HX.Aſymptotis AK,
KFdeſcribatur Hyperbola, cujus conjugata tranſeat per punctum
C,centroque A& intervallo AHdeſcribatur Circulus ſecans Hy
perbolam illam in puncto H;& Projectile ſecundum rectam AH
emiſſum incidet in punctum K. Q.E.I.Nam punctum H,ob
datam longitudinem AH,locatur alicubi in Circulo deſcripto. A
gatur CHoccurrens ipſis AK& KF,illi in E,huic in F;& ob
158[Figure 158]
parallelas CH, MX& æquales AC, AI,erit AEæqualis AM,
& propterea etiam æqualis KN.Sed CEeſt ad AEut FHad
KN,& propterea CE& FHæquantur. Incidit ergo punctum
Hin Hyperbolam Aſymptotis AK, KFdeſcriptam, cujus conju
gata tranſit per punctum C,atque adeo reperitur in communi in
terſectione Hyperbolæ hujus & Circuli deſcripti. Q.E.D.No
tandum eſt autem quod hæc operatio perinde ſe habet, ſive recta
AKNhorizonti parallela ſit, ſive ad horizontem in angulo quo
vis inclinata: quodque ex duabus interſectionibus H, Hduo pro
deunt anguli NAH, NAH; & quod in Praxi mechanica ſufficit
tate emiſſum, incidit in punctum quodvis K:ad puncta A& K
erigantur rectæ AC, KFhorizonti perpendiculares, quarum AC
deorſum tendat, & æquetur ipſi AIſeu 1/2HX.Aſymptotis AK,
KFdeſcribatur Hyperbola, cujus conjugata tranſeat per punctum
C,centroque A& intervallo AHdeſcribatur Circulus ſecans Hy
perbolam illam in puncto H;& Projectile ſecundum rectam AH
emiſſum incidet in punctum K. Q.E.I.Nam punctum H,ob
datam longitudinem AH,locatur alicubi in Circulo deſcripto. A
gatur CHoccurrens ipſis AK& KF,illi in E,huic in F;& ob
158[Figure 158]parallelas CH, MX& æquales AC, AI,erit AEæqualis AM,
& propterea etiam æqualis KN.Sed CEeſt ad AEut FHad
KN,& propterea CE& FHæquantur. Incidit ergo punctum
Hin Hyperbolam Aſymptotis AK, KFdeſcriptam, cujus conju
gata tranſit per punctum C,atque adeo reperitur in communi in
terſectione Hyperbolæ hujus & Circuli deſcripti. Q.E.D.No
tandum eſt autem quod hæc operatio perinde ſe habet, ſive recta
AKNhorizonti parallela ſit, ſive ad horizontem in angulo quo
vis inclinata: quodque ex duabus interſectionibus H, Hduo pro
deunt anguli NAH, NAH; & quod in Praxi mechanica ſufficit
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