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Show , 50 Cap. 10; De duplo incremen- to petcn~ HY CON"!- dcm mufculornm. IO. AL; BORELLII Si pof‘tca loco funis fupponatur Virga rigid; AB u non grauis , qua: perpendicularitcr innixa {010 Frabi~ ‘ li LB , in B comprimatur 31- pondere , vol 31 qualibci f potentia R in A per dircftionem AB ah A vet-{us B. ‘ Eodcm modo oitcndcrur , quod vis , qua virga com. prefiioni refiflit , dupla eflr potentix comprimentis R; Vice pauimcnti fubi'cituatur manus S , vel terminus B librx EB radiorum xqualium, cui in B virga BA cum pondcrc R filpcrincnmbat , aequilibreturque 2‘1 ponderc X; quia sequé bené , & eadcm cncrgia foli LB duritics impedit defccnfum , 8: rcfiftit prcflioni potenticg I R , ac cidcm mquilibmtur potential fubicfix manusS, ; autpondzis X; Ergo rciiltentia foli LB zequalis efi potentix prcmcnti R, & ab ciidcm duabus virga (Erin. gitur,‘ qmrc vis , quit virga AB comprcffioni rcfifiit ‘ oupicx eff pondcris , vcl porentim R : vt crat oflcn- ‘ ., acnduzn . {I‘D-DU" DE .MOTV ANIMALIV/W. "WI/4 P R O P O S. XXXIII. Idem alitcr dcmonftrarc . T:zb.3. Fig.1 I.' liftitm }70fiti53i11tclligantllr potentix contrari-x m0ucri a {ciiicct fimis AB contrahatur :3 potentia XZ : Vr terminus A ail‘endat quue ad H , ibidc mquc qUiC' icat; Be Ptccntur bifariam funis AB in C,& portio AH m 1); £1 fOICIIEid in dtms partes aaquales X 9 Z 9&1" dcm £31: CF xqualis DH: pate: afcmipotentiamx contmncrc mediemtem funis CA , 3C refiduam femipotentiam Z contrahcre reliquam funis mcdicraten u CB. "\fiii; i potentia X folitaria ( non confidcrata ‘ porrinti; Z ) fiiblfiuatul‘ refiflentia R, contrahendo {€mincm firms LA per fpatium detcrminatum AD; Ergo 6i Ergo per idem fpatium AD, & per candcm diretfiio- Cap. 10. ncm mouetur potential X femifunem contrahcndo ; 8: De duplo incrtmcnE0 potenti; cornn. dcm mn- fculomm. rcfiflcntia R afcendcndo,' ideoquc mqué vcioccs flint potentia X , 85 rciii'icntia R a 86 .eorum momenta funt :equalia in fine contrafhonis {emit-"unis , quando quicfcunrpotcntix xquilibratm s Igitur abioinm potentia X :equalis eff refificnticc R . Infupcr quia dum oom- plcturafiio porcntix X,rc1iqu;1 {cmipotcntia Z 11011.. otiatur, {ed fuam vim CXL‘I‘CCL‘, contraiicndo rciiqnum icmifuncm CB , scqué ac coritraéttis fucrat AC 2‘1 porentia X 3 & terminus B ciauo firmo S afiixus accede- c non potcfl vcrfus punétum medium funis C 3 Ergo in contrat‘tione cogitur punt‘tum G fcrri verius clauft firmumB per fpatium CF :equzzlc ipfi AD . Vcrunp non potefi puné‘tum medium flmis C afccnderc quue ad F, niti pondus R appenfum funiculo CD , dccurgiro :‘1 porcntiaX, cleuetur ex punc'to D ad H per ipatium aequaleipfi CF eicuationi iplins ccntri C,' 85; aiiundé aftio potentix Z non adiuuatur 51 potentia X , quialhmc abfumitur iricontrafiione funis AG 3 8c in- tmfiionc ponderis R ab A ad I) , nec pr'xtcrea quicquam agit tulis potentia X prmterquam confcruarc; dccurtdtioncm funis CD non fecus ac nodus, fcu vin- culum 1n eodcm ihne efl‘iccret . Igitur potentia Z noua, \& difiinéta afitione elcuat idem pondus R motu 33un veloci per eandem dircétionem , atquc comm.) momenta ftquantur in fine fecundae contraé‘tionis. Er- go potentia abfolum Z xqualis cit cidcm ponderi R tatautcm prius potential abfoluta X cidcm poten-,' rm? R ‘Uqlmlis ; Qyzproptcr du-x potentio: ubfolutx X, Zinnul fumptae , ciliccc potentia abfoiuta totius funis AB d"PIa cit tefiffcnriae abfolutm R , quod cm: oftendcndum . PROa ulnar. |
