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

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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.

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