Full text: Musschenbroek, Petrus: Physicae experimentales, et geometricae de magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terrae, cohaerentia corporum firmorum dissertationes

611. PROPOSITIO CVIII.

Tab. XXVII. fig. 11. Infinita ſolida priſmatica datæ latitudinis
invenire, quæ utrimque fulta, æqualis ſint Cohærentiæ reſpectu
propriæ gravitatis.

Sit parabola A I H I. ejus axis A B, ordinatæ B I, F H, B I. di-
co quodlibet priſma longitudinis ejuſdem ac eſt ordinata quælibet
B I aut F H, & altitudinis B A vel F A, atque datæ conſtantis la-
titudinis ſatisfacere propoſito: nam ob naturam parabolæ eſt A B,
A F: : I B q . H F q . eſtque ſoliditas priſmatis ex longitudine I B, & altitudine A B, uti I B X A B. & ſoliditas alterius priſmatis = A F
X F H. ſed I B X A B. A F X H F: : I B c . H F c . momenta gravita-
tis horum priſmatum ſunt I B c X I B. H F c X H F. verum Cohæren-
tiæ eorundem ſunt A B q . A F q . quæ ſunt I B qq . H F qq . quæ ſunt uti
momenta gravitatis, adeoque demonſtrato Cohærentias eſſe uti ſunt
gravitates, erunt hæc ſolida æqualis Cohærentiæ.

Coroll. Hinc ungula ſolida parabolica erecta ex Cylindro ſuper
parabola A I B, eademve ad alteram diametri partem duplicata,
erecto, per planum baſi, utcunque inclinatum, & per verticem A
tranſiens, foret ſolidum reſpectu ſui ponderis in qualibet ſui parte
æqualiter reſiſtens: ſive ſuſtineretur in linea A B, ſive fulcris ſub
ejus perimetro circumpoſitis fulciretur: nam diametro A B diviſa
in quotlibet æquales partes, erectiſque planis per omnia diviſionum
puncta, & correſpondentes ordinatas parabolæ, haberentur toti-
dem priſmata, huic ungulæ inſcripta, quæ ſui ponderis reſpectu,
juxta hanc Propoſitionem, æqualis eſſent Cohærentiæ, & quæ
ungulæ ipſius ſoliditatem, aucto omnium numero, & diminuta
ſingulorum latitudine, facile exhaurirent: quemadmodum deduxit
Cl. Grandi.

612. PROPOSITIO CIX.

Tab. XXVII. fig. 12. Dato cuneo A B P C D, & pondere maxi-
mo, quod extremo C D appendi poſſit, cum Cunei baſis A B P pa-

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