Stevin, Simon - Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis

Scan	Original
101	101
102	102
103	103
104	104
105	105
106	106
107	107
108	108
109
110	110
111	111
112	112
113	113
114	114
115	115
116	116
117	117
118	118
119	119
120	120
121	121
122	122
123	123
124	124
125	125
126	126
127	127
128	128
129	129
130	130

123123*DE* H*YDROSTATICES ELEMENTIS*. minus inſidere pondus quàm A C ζ γ V R, fundo R V X S minus quàm
R V Z δ X S, item fundo S X Y T minus quam S X α ε Y T, denique ſundo
T Y D E minus quàm T Y β H D E, toti quoq; fundo A C D E minus inſide-
bit ponere omniũ horũ, hoc eſt, corpore circumſcripto A C ζ γ Z δ α ε β H D E.
Atqui fundo A C D E, qui in diagrammate quadrãtibus diſtinguitur, ſic in octo
æqualia ſegmenta divio palam eſt corporum dimidiæ columnæ A C H E D
hujus inſcripti illius circumſcripti ab ipſa differentiam dimidio minorem fore
quàm nunc ſit: quare hujuſmodi fundi ſectione infinita eo devenitur, ut differĕ-
tia ponderis (ſi qua tamen hîc ſit) fundo A C D E incumbĕtis a põdere dimidiæ
columnæ A C D E quolibet minimo põdere adhuc minor ſit. Vnde ita ediſſero.

Gravitas cujus à pondere fundo A C D E inſidente differentia minor eſt quolibet
pondere dato, æquatur ponderi fundo A C D E inſidenti.

Sed pondus dimidiæ columnæ A C H D E eſt gravitas minus differens à pondere
fundo A C D E inſidente quam quodlibet datum.

Itaque pondus dimidiæ columnæ A C H D E æquatur ponderi in baſe A C D E.

2 Exemplum.

D*ATVM*. Exponatur ſecundo A B vas plenum aquæ, fundumq́ue A C D E
quadrangulum ad horizontem in angulo obliquo inclinatum, ejusq́ue ſupre-
mum latus A C conſiſtar in A C F G aquæ ſuperficie ſumma. Iam aqua
ipſiusq́ue fundum dividatur conſimiliter antecedenti 1 exemplo, & A υ per-
pendicularis ſit àſummo fundi latere in planum, per inſimum latus E D ad ho-
rizontis paralleliſmum eductum, demiſſa. Q*VAESITVM*. Pondus aquæ
fundo A C D E ſubnixum dimidiæ columnæ cujus baſis A C D E, altitudo
A υ, æquari demonſtrato. P*RAEPARATIO*. Perpendicularis A υ à tribus
punctis ο, π, ρ in quatuor æquas partes diſſecator.

DEMONSTRATIO.

Fundo A C V R, cum nõ ſit in

171[Figure 171] aquę ſummitate, inſidet aliquod
pondus, minus tamen quàm co-
lumna aquea baſis A C V R, alti-
tudinis A ο, nam ſi per R V planũ
horizonti æquidiſtanter duce-
retur per 10 propof id hoc pon-
deris ſuſtineret, nuncverò cum
ſublimiori ſit loco minus ſuffert
quam columnam iſta baſi & al-
titudine, hoc eſt, A C ζ γ V R.
Simili deductione ut in primo exemplo
cætera proſequeris; unde tandem con-

172[Figure 172] cludes fundo A C D E inſidere corpus
æquale ipſi A C H D E, hoc eſt, colum-
næ baſis A C D E, altitudinis A υ (nam
A υ æqualis eſt perpendiculari ab H
in planum A C D E) tandem inquam
concludes fundo A C D E inſidere a-
queam molem magnitudine æqualem
columnæ cujus baſis A C D E, altitu-
do A υ.

Page concordance

Text layer

Text normalization

Search

Scan	Original
101	101
102	102
103	103
104	104
105	105
106	106
107	107
108	108
109
110	110
111	111
112	112
113	113
114	114
115	115
116	116
117	117
118	118
119	119
120	120
121	121
122	122
123	123
124	124
125	125
126	126
127	127
128	128
129	129
130	130

Scan	Original
101	101
102	102
103	103
104	104
105	105
106	106
107	107
108	108
109
110	110
111	111
112	112
113	113
114	114
115	115
116	116
117	117
118	118
119	119
120	120
121	121
122	122
123	123
124	124
125	125
126	126
127	127
128	128
129	129
130	130

Scan	Original
101	101
102	102
103	103
104	104
105	105
106	106
107	107
108	108
109
110	110
111	111
112	112
113	113
114	114
115	115
116	116
117	117
118	118
119	119
120	120
121	121
122	122
123	123
124	124
125	125
126	126
127	127
128	128
129	129
130	130