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

Scan	Original
101	50
102
103
104
105	51
106	52
107	53
108	54
109	55
110	56
111
112
113
114	57
115	58
116	59
117	60
118	61
119	62
120	63
121	64
122
123
124
125	65
126	66
127	67
128	68
129	69
130	70

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.

Page concordance

Text layer

Text normalization

Search

Scan	Original
101	50
102
103
104
105	51
106	52
107	53
108	54
109	55
110	56
111
112
113
114	57
115	58
116	59
117	60
118	61
119	62
120	63
121	64
122
123
124
125	65
126	66
127	67
128	68
129	69
130	70

Scan	Original
101	50
102
103
104
105	51
106	52
107	53
108	54
109	55
110	56
111
112
113
114	57
115	58
116	59
117	60
118	61
119	62
120	63
121	64
122
123
124
125	65
126	66
127	67
128	68
129	69
130	70

Scan	Original
101	50
102
103
104
105	51
106	52
107	53
108	54
109	55
110	56
111
112
113
114	57
115	58
116	59
117	60
118	61
119	62
120	63
121	64
122
123
124
125	65
126	66
127	67
128	68
129	69
130	70