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

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62622 L*IBER* S*TATICÆ*

Atquarti exempli demonſtratio pendet è proportione rectarum D G, H B
& triangulorum A C D, A C B; Et enim ut D G ad H B ſic erit, ſumpta com-
muni altitudine A C, rectangulum ſub D G in A C ad rectangulum ſub H B
in A C, hoc eſt (quia iſtorum dimidia ſunt) triangulum A C D ad triangu-
lum A C B.

Pari ratione quinti exempli demonſtratio, pendet ab analogia rectæ EK
cum I C ad L M & quadranguli A C D E ad triangulum A C B. Enimverò
cum L M ſit quarta in analogia rectarum A D, A C, H B rectangulum extre.
marum A D in L M æquatur mediarum rectangulo A C in H B. Hinc tres
rectæ E K, I C, L M pro baſibus parallelogrammorum nobis ſunto, quarum
altitudo ſit eadem A D, ideoque ut E K & C I ad L M ſic rectangula duo
E K in A D & CI in A D ad L M in A D ſed duo illa rectangula ſunt dupli-
cia ſuorum triangulorũ hoc eſt quadranguli A E D C; & rectangulum L M in
A D duplum eſt trianguli A B C quia æquale eſt rectangulo A C in H D ut
ſupra jam patuit; quamobrem erit quadrangulum A E D C ad triangulum
A B C ſicut E K & I C ad B H ſed ſic quoque eſt propter conſtructionem,
G N ad N F quare N eſt optatum gravitatis centrum.

Sexti exempli demonſtratio huic affinis eſt. C*ONCLVSIO*. Itaque dati
rectilinei cujuſcunque gravitatis centrum invenimus. Quod oportuit.

NOTATO.

Interim dum hæc pralo ſubjiciuntur nactus ſuns Federici Commandini Com-
mentarium in Archimedis quadraturam paraboles, ubi ad 6 propoſitionem recti-
lineorum gravitatis centrum invenire docet, modo ab horum utroque diverſo. Siquis
cognoſcendi ſit cupidus ipſum conſulat.

5 THEOREMA. 7 PROPOSITIO.

Securiculæ gravitatis centrum eſt in recta laterum paral-
lelorum biſectionem connectente.

D*ATVM*. A B C D ſecuricula eſt qualem in Geometricis definivimus,
duobus lateribus A B, D C parallela, recta ab E biſegmento A B, connexa cum
F biſegmento ipſius D E. Q*VAESITVM*. Quadrilateri A B C D gravitatis
centrum in jungente E F conſiſtere demonſtretur.

P*RAEPARATIO*. Tres rectæ D A, E F, C B, propter homologiam ſeg-
mentorum A E, E B, D F, F C eodem coïbunt in G.

DEMONSTRATIO.

Triangulum G D C ſuſpenſum ex rectâ G F faciet ſegmen-

103[Figure 103] ta GFC, G F D per 2 propoſ. ſitu ęquilibria; ideoq́ue triangu-
li G D C gravitatis centrum in recta G F conſiſtet. Sed G E B
triangulum triangulo G E A itidem ſitu æquilibre eſt, æqualia
igitur & ſitu ęquilibria utrimque deducta relinquent quadran-
gula A E F D, E F B C quoque ſitu æquilibria, & gravitatis
centrum in ipſa G E, neque tamen in ſegmento exteriore
E G, quamobrem in ipſâ E F. C*ONCLVSIO*. Itaque ſecu-
riculæ gravitatis centrum eſtin rectâ parallelorum laterum bi-
ſectrice.

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