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

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1261264 L*IBER* S*TATICÆ* colligendæ compendium infra damus) erit {499500/1000000}: Similiter mille ponduſcula
graviora {1/1000000}, {2/1000000}, {3/1000000}, & c. quorum noviſſimum {1000/100000}, in ſummam colle-
cta efficiunt {500500/1000000}. Quamobrem fundo inſidet põdus majus quàm {499500/1000000}, minus
autem quàm {500500/1000000} unius pedis cubici, atqui {499500/1000000} abeſt duntaxat {1/1000} ab {1/27}, quare
pondus quod inſidet fundo ACDE deficit à dimidio pede defectu minore
quam fit {1/10000}; ſic {500500/1000000} excedit {1/2} pedis ſemiſſem {1/1000}, itaq; ipſi non inſidet pon-
dus {1/1000} dimidium pedem excedens. Simile ratiocinium inſtitues in cæteris,
etiam poſitis quibuſliber quam minimis particulis. Quare evidens eſt difſeten-
tiam (ſi quæ tamen eſſet) inter aquam fundo ACDE inſidentem, & cubici
aquei pedis dimidium, minorem eſſe qualibet quæ animo concipi aut cogita-
tione comprehendi poſſit. Vnde ſyllogiſmum inſtituo.

Pondere, quod ab aquæ dimidio pede abeſt, aliud minore ab eo differentia distans
exhiberi poteſt:

Sed pondere aqueo fundo A C D E inſidente, nullum ab aquæ pede dimidio minus
differens exhiberi poteſt:

Itaque pondus aquæ inſidens fundo A C D E, à dimidio aquæ pede nihil differt.

C*ONCLVSIO*. Itaque fundi regularis, cujus ſummum punctum in aquæ
conſiſtit, & c.

CAuſa cur ſemiſſis iſte inter duos numeros perpetuò magis vicinos, nun-
quam tamen concurrentes conſiſtar, hujuſmodi theoremate exprimitur.

Numeris quotcunqueab unitate deinceps continuatis,
dimidius noviſsimi numeri quadratus cedat ſummæom-
nium, eandemq́ue noviſsimo numero multatam excedit.

SEd ut fidem exſolvam, & compendium in tanta numerorum multitudine
addenda nunc explicem, ita habe. primùm partium iſtarum nomen unum
eſſe & commune, quare hoc poſthabito ipſarum numeris animũ intendamus,
ii igitur ab unitate continuò progreſſu unitate mutuò ſe ſuperant. Itaque ad fa-
ctum à noviſſimo in ſui ſemiſſem multiplicato, is ipſe ſemiſſis additus dabit
optatam ſummam. Exemplum hujuſmodi eſto; quæritur ſumma numerorum
1, 2, 3, 4, 5, 6. Factus à noviſſimo 6 in ſuũ ſemiſſem 3 ad eundem 3 additus dabit
21 optatam ſummam. Vel ſi noviſſimus ſit impar, ut 1, 2, 3, 4, 5, 6, 7: 7 in ſuum ſe-
miſſem 2 {1/2} ductus facit 24 {1/2}, qui cum ſemiſſe 3 {1/2} compoſitus dat 28 optatũ ſum-
mæ totius numerum. At cum noviſſimus iſle impar erit, quî partium numeratio
declinetur, unitatead noviſſimum addito eodemq́; noviſſimo per hujus ſemiſ-
ſem multiplicato commodius abſolves. utſi in eodem exemplo 1, 2, 3, 4, 5, 6, 7,
quæratur ſumma; adde 1 ad 7 fit 8, cujus ſemiſsis 4 cum noviſsimo 7 multipli-
catus dabit 28 ut priùs. atque ita in cæteris.

NOTATO.

Luia ſupraſcriptus columnæ ſemißis, æquatur integræ item columnæ cujus baſis ſit
fundum datum, altitudo autem ſemißis perpendicularis à ſummo fundi puncto, in pla-
num per imum eius punctum borizonti parallelum demiſſæ; 11 pr opoſhoc modo quoque
enuntiari poterit.

Si fundi regularis ſupremum punctũ ſit in ſumma

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