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

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40401 L*IBER* S*TATICÆ*

10 C*ONSECTARIUM*.

Eſto exemplat 9 conſectarii fimile, eo

69[Figure 69] tantũ diſſimile, quod F H ultra F I, ver-
ſus C declinet, quodq́; H F C angulus
R P O angulo ſit æqualis, quapropter
põderi G in columnam A M tantumdĕ
potentiæ eſt, quantũ ponderi Q: & pro-
pter cauſas 9 cõſect. cõmemoratas (quas
brevitatis causâ omittimus) G tantam
vim columnæ A B adfert: quantam Q
columnæ L M. Itaque ut T P ad P R: ita
S ad Q, per 9 conſectarium: at qui I F
æquatur T P, & F H ipſi P R, pondusq́;
K ponderi S, & G ipſi Q. Quemadmo-
dum igitur I F ad F H: ita K ad G.

11 C*ONSECTARIUM*.

ESto & 10 conſectarii ſimile exemplũ,

70[Figure 70] eo tantũ diſſimile quod P R in alterũ
latus à P T declinet & P R ad F H pa-
rallela ſit, ut Q & G columnæ A M æ-
qualem vim inferant, & , propter cauſas 9
conſectario dictas, quantum potentię eſt
ponderi G in columnam A B, tantundĕ
& põdus Q obtinet in columnam L M.
Vtigitur I F ad F H: ita, per 6 conſecta-
rium, K ad G. Atqui T P æquatur I F, &
P R ipſi F H, & pondus S ponderi K, &
Q ipſi G. Quemadmodum igitur TP ad
P R: ita S ad Q. Similiter aliorum
omnium ſituum proportio ex contrario demonſtrabitur.

12 C*ONSECTARIUM*.

HAncautem proportionem etiam in illis

71[Figure 71] locum obtinere ubi axis horizõti paral-
lelus eſt, ita demõſtratur. A B columna eſto,
ejusq́; axis C D ad horizontem parallelus, E
punctũ firmum, F mobile, G põdus obliquè
extollens, quod columnam eo in ſitu ſervat,
cujus obliqua linea F H, I vero pondus rectè
extollens, columnam itidem eodem ſervans
in ſitu, ejusq́; linea recta F K. His poſitis, diſ-
ſimilis ratio eſto (ſi fieri poteſt) K F ad F H,
atq; I ad G: exempli gratià, ratio K F ad F H
ſit 1 ad 2: ratio verò I ad G 3 ad 7. Et hoc ita
poſito, prioris exempli columna demittitor,
aut poſterioris extollitor, uſq; dum ratio K F
ad F H, ſit 3 ad 7: tunc G contra columnam
æquilibre erit, per antecedentia conſectaria,
ut columna ſive altius elata, ſive humilius de-
preſſa contra G æquilibris manſura ſit: At-
qui illud @@ ἀδύναπις eſſe manifeſtum

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