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

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60602 LIBER STATICÆ

PRAGMATIA.

Quadrangulum rectâ A C in duo triangula dividun-
dum eſt, & cujusq́ue gravitatis centrum, per 3 propoſit. in-

97[Figure 97] veniendum: trianguli A B C eſto E, A C D vero F, re-
ctaq́ue E F jugum , hinc duo quadrãgula 1145 propoſ.
z. lib. Euclid. ma æquæalta cõſtituenda, ut G H I K & G H L M, æqua-
lia triangulis, illud quidem A C D hoc vero A C B, de-
2210. propoſ.
G. lib. Euclid. nique jugo F E in N ita ſecto, utradius N E ſit ad radium
N F: quemadmodum HI, ad HL: N quæſitum gravi-
tatis centrum eſſe dico.

2 Exemplum.

D*ATVM*. A B C D F inordinatum quinquangulum eſto.

Q*VÆSITVM*. Gravitatis centrum quærendum eſt.

PRAGMATIA.

Ductâ A C, centrum gravitatis trianguli A C B,
per 1 propoſitionem, inveniendũ ſit vero F: itemq́ue

98[Figure 98] quadranguli A C D E, per 1 hujus exemplum, ſitq́ue
G, & recta F G jugum, hinc duo quadrangula paral-
lelogramma æquealta conſtituenda, ut H I K L &
HIM N, quorum illud quadrangulo A C D E iſtud
vero triangulo A C B æquetur. Denique jugo G F
diviſo in O, ut radius O F ſitad radium O G; quem-
admodum I K ad IM: O quæſitum gravitatis cen-
trum eſſe ajo.

3 Exemplum.

D*ATVM*. A B C D E F inordinatum ſexangulum eſto.

Q*VÆSITVM*. Gravitatis centrum nobis quærendum eſt.

PRAGMATIA.

Ductâ A C gravitatis centrum trianguli A C B,

99[Figure 99] per 3 propoſit. quærendum, eſtq́ue G, nec non &
quinquanguli A C D E F, per 2 exemplum hujus,
eſtq́ue H. & recta G H jugum. Deinde duo quadran-
gula parallelogramma æquealta fabricanda ſunt, ut
I K L M æquale quinquãgulo A C D E F, & I K N O
æquale triangulo A C B: diviſoq́ue jugo H G in P,
ut P G radius illam rationem habe at ad P H radium;
quæ eſt K L ad K N: P quæſitum gravitatis centrum
eſſe dico. Atque iſta pragmatiæ ratio in reliquis mul-
tilateris planis planiſſime eadem eſt.

NOTATO

Etſi hactenus exempla fuere, in quibus datum planum in quadrangula pa-
rallelogramma æquealta mutatur, poſſe tamen abſque transfiguratione hujuſ-
modirem expediri: ejusq́ue rei nos varia exempla ſubjungere.

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