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

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6565DE INVENTIONE GRAVITATIS CENTRO. deinceps in cæteris ſimili machinatione, quorum ſegmentorum ratio per ar-
tem cognoſci poſsit. C*ONCLVSIO*. Quamobrem datis planę ſuperficiæ
& ſegmenti ejuſdem gravitatis centris & C.

7 THEOREMA. 10 PROPOSITIO.

Parabo. æ gravitatis centrum eſt in diametro.

D*ATVM*. Parabola A B C, axis A D. Q*VÆSITVM*. Centrum gravita-
tis in A D conſiltere demonſtrato. P*RAEPARATIO*. E F, G H, I K baſi
B C parallelæ interſecent diametrum A D in punctis L, M, N, & eædem in-
tercipiant rectas E O, G P, I Q, K R, H S, F T axi A D parallelas.

DEMONSTRATIO.

Cum enim parallelæ E F, B C, claudantur E O, F T, parallelis, E F T O
parallelogrammum erit, cujus oppoſita latera E F, O T in L & D bifariam
dividuntur, quare centrum gravitatis per 1 propoſ. in L D conſiſtet. Eadem ra-
tione centrũ gravitatis quadranguli G H S P erit in L M, itemq́; ipſius IKR Q
in M N. Quamobrem gravitatis centrum rectilinei I K R H S F T O E P G Q
è tribus iſtis parallelogrammis cõflati in DN,

107[Figure 107] ſeu D A conſiſtet. Sed quò frequentiora hu-
juſmodi parallelogramma in parabolam in-
ſcribuntur, eò minor erit inſcriptæ figuræ à
parabola defectus. Quamobrem infinita hac
parallelogrammorum inſcriptione eo adſcen-
ditur ut ejus à parabola defectus quacunque
minima propoſita ſuperficie minor ſit, conſe-
quens igitur eſt, ſumpta A D gravitatis dia-
metro, æquilibritatem ſitus ſtgmenti A D C
ab æquilibritate ſitus ſegmenti A D B, mi-
nori intervallo abeſſe quam vel minimæ quæ
dari poſſit ſuperficiei planę differentia: unde
concludo.

Ponderum inaqualium ſitu gravium differentiâ minus pondus exhiberi poteſt:
Atqui ponderum horum A D C, A B D ſitu gravium differentiâ pondus minus
exhiberinullum poteſt.

Ponderum igitur A D C, A B D ſitu gravium differentia nulla eſt.

A D igitur crit diameter gravitatis, & propterea parabolæ A B C gravitatis
centrum in ipſa. C*ONCLVSIO*. Itaque paraboles gravitatis centrum eſt in
diametro. Quod demonſtraſſe oportuit.

8 THE OREMA. 11 PROPOSITIO.

Parabolarum diametri à gravitatis centro in homologa
fegmenta dirimuntur.

D*ATVM*. Sunto A B C D & a b c d, diſſimiles parabolæ, harum diame-
@ri A D, & a d, denique gravitatis centra E & e.

Q*VAESITVM*. Segmenta A E, E D, ſegmentis a e, e d proportionalia
@ſſe demonſtrator. P*RÆPARATIO*. Rectas A B, A C, à vertice

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