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

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92923 L*IBER* S*TATICÆ* pendicularetam hoc quam ſequentibus 3 & 4 exemplis in opere ſufficiat, atta-
men quò evidentius ſit centrum ipſum ſumpſimus) tumq́ue ſegmento ABD
incumbat pondus H 2000 ℔ cujus gravitatis diameter IK eſto ut K termi-
netur in axe C D; quæritur potentia quæ ex C, attollat datum pondus H.

CONSTRVCTIO.

Oneris H & machinæ D A C B ſimulutriuſque gravitatis centrum inve-
nies, diviſa K G in L, ut ſegmentorum G L, L K ratio ſit eadem quæ 2000 ℔
ad 400 ℔, hoc eſt, 5 ad 1, perpendicularis per L educta eſt gravitatis diameter;
præterea F C dicis gratia duodecupla aſſumatur ipſius F L, unde concludo, ut
FC 12 ad FL 1, ſic 2400 ℔ videlicet vectis & oneris conjunctum pondus, ad
200 ℔ quæ ex C ſuſpenſæ iſtis æquipondiæ forent iſtoc duntaxat ſitu, poſito

133[Figure 133] enim M centro gravitatis H, & aſſurgente ſegmento A B D, non opus erit
200 ℔ pondere, cujus illuſtrandi gratia perpendicularis N O per centrum M
plano A B D horizonti parallelo terminetur in O, tributa igitur O G in P ut
P G itidem quintupla ſit reliqui P O, atque eo ſitu perpendicularis per P edu-
cta totius ponderis erit pendula gravitatis diameter, eſto autem F C q́uintupla
rectæ F P, unde concludes, ut F C 15 ad F P 1, ſic 2400 ℔ ad 160 ℔ quæ tunc
ſitus æquiponderantiam tuebuntur.

3 Exemplum.

Verumenimverò quia haſtarum ſimiliumve ſcaporum humeris geſtatorum
ratio antecedenti exemplo non ſit admodum adſimilis, hanc ipſam tertio para-
digmate perſequemur.

D*ATVM. * Palangrarius humero B geſtet haſtile librarum 12, cujus axis ſit
C D, centrum gravitatis E, atque ab haſtilis & humeri contactu acta B F ho-
rizonti perpendicularis ſecet axem DC in G, manus haſtile rectà deprimens
ſtatuitior in puncto axis H, ſitq́ue G H dupla G E.

Q*VAESITVM. * Quanta potentia manus ſit inquirere.

CONSTRVCTIO.

Quandoquidem G H dupla eſt ſegmenti G E, etiam pondus ab E, quod
eſt haſtilis univerſi duplum erit ejus quod ad H collocatur, videlicet manus;

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