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

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1241244 L*IBER* S*TATICÆ*

3 Exemplum.

D*ATVM*. Fundum regulare A B ellipſis eſto, cujus ſupremum punctum
A ſit in aquæ ſuperficie ſumma, B in ima, A C perpendicularis à ſummo A in
planum horizonti parallelum per imum B.

Q*VAESITVM*. Pondus aquæ fundo A B

173[Figure 173] incumbentis æquari dimidiæ columnæ, cu-
jus baſis A B, altitudo A C.

P*RAEPARATIO*. Circumſcribito ellipſi
A B parallelogrammum quadrangulum
D E F G ut D E in aquæ ſummo tangat ejus
ſummum A, & G F imum B; ſitq́ue F I
perpendicularis in F G æqualis lateri F E, &
horizonti parallela; jam reliqua latera G H,
H I claudant parallelogrammum F G H I &
connecto E I, D H.

Conſtruito deinde alteram figuram non tan-
tum forma ſimilem, ſed etiam magnitudine &

174[Figure 174] ponderitate ipſi æqualem, cujus latus F I hori-
zonti ad perpendiculum inſiſtat, ut in ſubjecto
diagrammate. ſitq́ue corpus hoc ſolidum ſub-
nixum fundo D E F G.

DEMONSTRATIO.

Quanto preſſu ſolidum D E F G H I afficit
ſuam hedram D E F G, tanto quoq, afficitaqua
primæ ſiguræ ſuum fundum D E F G, quod
paulò ante nobis demonſtratum eſt, & conſe-
quenter quantâ preſſione ellipſis A B ſecundæ
formæ afficitur, tantâ quoque omninò inerit ellipſi A B primæ formæ: Atqui
preſſio quam ellipſis ſecunda perpetitur, eſt ſemiſſis columnæ (ut jam mox de-
monſtraturi ſumus) cujus baſis ellipſis, altitudo æqualis rectę A C, nam per-
pendicularis à K in planum ellipſis A B demiſſa æqualis foret dictę A C; qua-
re aquę in primam ellipſin A B impreſſio, æquatur dimidiæ columnæ cujus ba-
ſis ipſa ellipſis ſit, altitudo autem A C.

Pondus autem ſecundæ ſiguræ inſidens ellipſi A B, æquari dimidiæ colum-
næ, cujus baſis iſta ipſa ſit ellipſis, & altitudo æqualis A C, hoc pacto arguo.
Ducito B K æqualem & parallelam rectæ F I, & ípſam ita circum ellipſin A B
circumducito ut tamen perpetuò contra F I parallela ſit, eâque converſione in-
ter duas hedras oppoſitas figurabit columnam A B K L, quæ plano D E I H
per duo puncta A, K ſimili ſitu atque tranſverſim in parallelarum ellipſium am-
bitu ſibi mutuo reſpondentia incidetur: ſed quęlibet columna cujus baſis eſt
planum regulare, ſectum plano per duo puncta in oppoſitis iſtis hedris tranſver-
ſim ὁμοταγῆ ab ipſo in duas æquas partes dirimitur: Quare ſegmentum 11Similiter
fita. lumnæ hujus infra planum D E I H, eſt ſemiſſis columnæ A B K L in ellipſi
A B tanquam baſe inſidentis. Columnam autem A B K L æquari columnæ
baſis A B, altitudinis A C, hinc palam eſt quia ipſius altitudo altitudini A C
æqualis ſit. Pondus itaque ſubnixum ellipſi A B ęquatur dimidiæ columnæ
cujus baſis ellipſis A B, altitudo æqualis rectæ A C.

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