Gravesande, Willem Jacob 's - Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1

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14781MATHEMATICA. LIB. I. CAP. XX. punctis B & b coincidentibus in Q, puncto medio arcus
LQA, a quo puncto ſemper æqualiter diſtant puncta B
& b.

Si AI ſit horizontalis arcus AQL, eſt ſemicirculus, &
11336. in hoc caſu amplitudo, manente celeritate, cum qua pro-
jectio fit, eſt omnium maxima, quando directio projectionis
cum borizonte efficit angulum ſemirectum.

Si celeritas mutetur, & corpus ſecundum eandem dire-
ctionem projiciatur, amplitudo in eodem plano mutatur in ea-
dem ratione cum altitudine A L; id eſt, amplitudines, manente
22337. eâdem directione, ſunt ut altitudines ad quas corpora, iiſ-
dem celeritatibus, in altum projecta adſcendere poſſunt;
ſunt ergo ut quadrata celeritatum .

33262.

Sit iterum La altitudo a qua cadendo corpus acquirit
44338. velocitatem cum qua projicitur per AB; punctum altiſſi-
55TAB XIII.
fig. 1. mum viæ percurſæ determinatur, ſi deſcripto ſemicirculo
cujus diameter eſt AL, per punctum B in quo a directio-
ne projectionis ſecatur ducatur horizontalis linea MBG,
& fiat BG æqualis BM; punctum quæſitum erit G.

Hujus patebit demonſtratio ſi ad ſequentia attendamus;
66339. ductâ AI horizontali, corpus ut dictum projectum cadet in
I, poſitâ AI quadrupla MB aut AR .

77134.

Dum corpus per AB projicitur motus hicce coincidit
cum duplici motu horizontali uno & æquabili, altero
verticali . Ultimo motu corpus adſcendit & 88246. dit, tempuſque adſcenſus æquale eſt tempori deſcenſus;
ideò aſcenſus terminatur ubi corpus motu horizontali dimi-
dium AI, id eſt MG, percurrit; punctum ergo altiſſimum
datur in verticali lineâ SC quæ per G tranſit. Dentur IE
verticalis, AB continuatam ſecans in E, ut & verticalis
BR; quia MG dupla eſt MB, id eſt AS dupla AR;
eſt etiam CS dupla BR, id eſt CG æqualis GS: Sed
AI dupla eſt AS; ergo EI dupla CS, & quadrupla CG;
etiam AE dupla AC. Dum Corpus motu projectitio per-
currit AE, cadit per EI; dum percurrit AC, cadendo quar-
tam partem EI id eſt CG percurrit ; tranſit idcirco 99255.

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Scan	Original
131	71
132	72
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136	73
137	74
138	75
139	76
140	77
141	78
142	78
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145	79
146	80
147	81
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149	82
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