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

1361364 L*IBER* S*TATICÆ* tra A B interſecet A D in I, & ſegmento A B H I incumbat pondus aquæ 24
pedum cubicorum. diviſis 24 per 3, quæ femiſſis eſt lateris A B, quotus erit 8:
tumq́ue invenito duos numeros in ratione A F 3 ad A E 4 quorum planus ſit
dictus octonarius; numeriq́ue iſti erunt √ 6 & √ 10 {2/3}, poſterior hic definiet
quantitatem A G: namque G H parallela ex G contra A B auferet planum
A B H I cui per 1, propoſ. molcsaquea 24 pedum innitetur.

NOTATO.

Tribus deinceps continuis propoſitionibus, ex ſententia Breviarii, agendum nobis de
centris gravitatis preſſuum in fundis collectorum Vbi jure funda borizonti parallela
primum ſibi locum depoſcerent, ſed quia ipſorum gravitatis centra (quæ ex ſecundi li-
bri doctrina pateſcunt) à centris preſſuum diverſa non ſint, brevitatis ſtudio novum
nullum de iis theorema inſtituimus. Quare initio ducto à fundis in clinatis, ita or dimur.

12 THEOREMA. 18 PROPOSITIO.

Si parallelogrammiad horizonrem inclina ti recta ſupre-
mum ejus latus, in ſumma aquæ ſuperficie conſiſtens, &
imum ſibi oppoſitum biſecet, hæc à preſſus gravitatis cen-
tro ita tribuitur ut pars ſumma reliquæ ſit dupla.

1 Exemplum.

D*ATVM. * Exponatur aqua A B, fundumq́ue ACDE figura parallelo-
gramma ad horizontem annuens, cujus ſuperũ

195[Figure 195] latus A C ſit in aquæ ſuperficie ſumma, tumq́;
ſuperum inferumq́ue latus A C, E D, biſecen-
tur in F & G, quæ jungat F G in puncto H ita
diviſa ut ſegmentum F H reliqui H G ſit du-
plum.

Q*VAESITVM. * H preſſus quo fundum affi-
citur gravitatis eſſe centrum demonſtrator.

196[Figure 196]

P*RAEPARATIO. * Acta CI ſubtendat an-
gulum C D I æquicrurum; ut priſima A C I D E
ſit dimidia columna, cujus baſis A C D E, alti-
tudo perpendicularis ab A uſque ad planum per
E D horizonti parallelum.

Figurato item alterum corpus K L M N O P
ſimile priori A C I D E, planumque K L M N
plano A C E, & M O horizonti perpendi-
cularis lateri D I homologa ſunto, itemq́ue Q R
ipſi F G: hinc ab S medio lateris O P agantur S Q, S R, atque trianguli Q S R
gravitatis centrum T, unde V X horizonti perpendieularis ſit.

DEMONSTRATIO.

Iam per 11 propof. qua to preſſu corpus K L M N O P afficit fundum
K L M N, tanto afficit aqua A B fundum A C D E; quare preſſuum gravita-
tis centra in fundis K L M N, A C D E ſimili erunt ſitu. Cæterùm T quod

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