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Colored diff for /texts/archimedes/xml/Attic/stevi_weegc_01_nl_1586.xml between version 1.46 and 1.57

version 1.46, 2003/09/08 14:47:21

version 1.57, 2003/09/09 14:32:45

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<s><emph type="other"/>IIVERVOLGH<emph.end/>. </s>

<s><emph type="other"/>II. VERVOLGH<emph.end/>. </s>

<s> <emph type="other"/>SO<emph.end/> anden pilaer (tpunt R vast sijnde als vooren) eenich gewicht ofte gewichten hingen, trechthefwicht sal oock bekent worden. </s><s>Laet by voorbeelt an X hanghen 6 lb, so sal Z moeten weghen I2 lb door het 3 voorstel, ende vervolghens Æ I2 lb. </s>

<s><emph type="other"/>VIIVERTOOCH. XVVOORSTEL<emph.end/>.</s>

<s><emph type="other"/>VII VERTOOCH<emph.end/>. <emph type="other"/>XV VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> twee punten inden as des pilaers, t'een vast t'ander verroerlick: Trechthefwicht an tverroerlic met den pilaer euestaltwichtich, heeft sulcken reden tot den pilaer als het asstick tusschen het swaerheyts middelpunt des pilaers, ende het vastpunt, tot het asstick tusschen tvastpunt ende t'verroerlick punt. </s>

<s><emph type="other"/>VERCLARING<emph.end/>. </s>

<s> <emph type="other"/>LAET<emph.end/> ons nemen de formen des I4 voorstels, al waer blijct dat ghelijck Æ 4 lb, tot tghewicht des pilaers 6 lb, alsoo TR tot RV. </s><s>Maer om d'oirsaeck hier af Wisconstelick <arrow.to.target n="marg118"/> te verclaren, soo is te weten dat ghelijck t'ghewicht Z, tottet ghewicht des pilaers, alsoo RT tot RY door het I voorstel; Maer Æ is euen an Z, ende RV is euen an RY door tghegeuen, ghelijck dan Æ tot den pilaer, alsoo TR tot RV. </s><s><emph type="other"/>TBESLVYT<emph.end/>. </s><s>Wesende dan twee punten inden as des pilaers t'een vast t'ander verroerlick, &c. </s>

<s>

<margin.target id="marg118"/>Mathematicè.

</s>

<s><emph type="other"/>TBESLVYT<emph.end/>. </s><s>Wesende dan twee punten inden as des pilaers t'een vast t'ander verroerlick, &c. </s>

<s><emph type="other"/>VIII VERTOOCH<emph.end/>. <emph type="other"/>XVI VOORSTEL<emph.end/>.</s>

<s><emph type="other"/>VIIIVERTOOCH. XVIVOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> twee punten inden as des pilaers, t'een vast t'ander verroerlick: Trechthefwicht an tverroerlick dat den pilaer in een ghestalt houdt, sal hem in alle ghestalten houden. </s>

<s> <emph type="other"/>TGHEGHEVEN<emph.end/>. </s><s>Laet ons den pilaer met sijn ghewichten des I4 voorstels wat verkeeren op tvastpunt R, ende dat Æ 4 lb noch sy rechthefwicht, alsoo dat dan alles van gestalt sy als hier neuen. </s><s><emph type="other"/>TBEGHEERDE<emph.end/>. </s><s>Wy moeten bewysen dattet rechthefwicht Æ den pilaer oock in die ghegheuen ghestalt houdt. </s><s><emph type="other"/>TBEWYS<emph.end/>. </s><s>Laet ons weeren Æ ende anhanghen Z 4 lb, ende door het voorstel den pilaer sal in die ghestalt bliuen: Maer Æ doet by V soo grooten ghewelt anden pilaer als Z by Y door het I3 voorstel, daerom gheweert Z, ende Æ anghehanghen, soo sal Æ den pilaer oock in die ghestalt houden. </s><s><emph type="other"/>TBESLVYT<emph.end/>. </s><s>Wesende dan twee punten inden as des pilaers t'een vast tander verroerlick, trechthefwicht an tverroerlick, dat den pilaer in een ghestalt houdt, sal hem in alle ghestalten houden, twelck wy bewysen moesten.</s>

<s><emph type="other"/>IXVERTOOCH. XVIIVOORSTEL<emph.end/>.</s>

<s><emph type="other"/>TBEGHEERDE<emph.end/>. </s><s>Wy moeten bewysen dattet rechthefwicht Æ den pilaer oock in die ghegheuen ghestalt houdt. </s>

<s> <emph type="other"/>RVSTENDE<emph.end/> een pilaer op twee punten inden as: Ghelijck het asstick tusschen t'swaerheyts middelpunt ende tslinckerpunt, tottet asstick tusschen tswaerheyts middelpunt ende trechterpunt, alsoo tghewicht des pilaers rustende op trechterpunt, tottet ghewicht rustende op tslinckerpunt. </s>

<s><emph type="other"/>TBEWYS<emph.end/>. </s><s>Laet ons weeren Æ ende anhanghen Z 4 lb, ende door het voorstel den pilaer sal in die ghestalt bliuen: Maer Æ doet by V soo grooten ghewelt anden pilaer als Z by Y door het I3 voorstel, daerom gheweert Z, ende Æ anghehanghen, soo sal Æ den pilaer oock in die ghestalt houden. </s><s><emph type="other"/>TBESLVYT<emph.end/>. </s><s>Wesende dan twee punten inden as des pilaers t'een vast tander verroerlick, trechthefwicht an tverroerlick, dat den pilaer in een ghestalt houdt, sal hem in alle ghestalten houden, twelck wy bewysen moesten.</s>

<s><emph type="other"/>IX VERTOOCH<emph.end/>. <emph type="other"/>XVII VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>TBEWYS<emph.end/>. </s><s>TR is dobbel an TV door tghewstelde, <pb pagenum="38"/>ende opt tpunt van Æ rust 4 lb, ende van &OElig; 2 lb door I veruolgh des I4 voorstels, maer 4 lb is tot 2 lb oock dobbel, ghelijck dan TR tot TV, alsoo tghewicht rustende op tpunt van Æ, tot tghewicht rustende op tpunt van &OElig;.</s>

<s> <emph type="other"/>TGHEGHEVEN<emph.end/>. </s><s>Laet ABCD een pilaer sijn weghende 6 lb, ghedeelt als int I voorstel, rustende met de twee punten R, V, op de punten van &OElig;, Æ. </s><s><emph type="other"/>TBEGHEERDE<emph.end/>. </s><s>Wy moeten bewysen dat ghelijck het asstick TR, tottet asstick TV, also tghewicht rustende mettet punt V op tpunt van Æ, tottet tghewicht rustende mettet tpunt R op tpunt van &OElig;. </s><s> <emph type="other"/>TBEWYS<emph.end/>. </s><s>TR is dobbel an TV door tghewstelde, <pb pagenum="38"/>ende opt tpunt van Æ rust 4 lb, ende van &OElig; 2 lb door I veruolgh des I4 voorstels, maer 4 lb is tot 2 lb oock dobbel, ghelijck dan TR tot TV, alsoo tghewicht rustende op tpunt van Æ, tot tghewicht rustende op tpunt van &OElig;.</s>

<s> Maer om tghemeen nootsaeckelick veruolgh in allen te bewysen, laet ons voorttrecken VR tot in Z, also dat RZ euen sy an RV; aensiende daer naer R voor tvastpunt, so sal an Z moeten hanghen 4 lb, om de pilaer in die ghestalt te houden door het 3 voorstel. </s><s>Maer tghene an V den pilaer in die ghestalt houdt als Æ, doet daer an alsulcken gheweldt als Δ, door het I3 voorstel; An Æ dan rust een ghewicht euen an Δ. </s><s>Laet ons insghelicx voorttrecken, RV tot in Φ, also dat VΦ euen sy an VR, ansiende daer naer V voor vastpunt, soo sal an Φ moeten hanghen Δ 2 lb, om den pilaer in die ghestalt te houden door het 3 voorstel, maer tghene an R den pilaer in die ghestalt houdt als &OElig;, doet daeran alsulcke ghewelt als Δ door het I3 voorstel, An &OElig; dan rust een ghewicht euen an . </s><s>Nu anghesien <emph type="other"/>INSERT PI Π<emph.end/> euestaltwichtich is teghen den pilaer op tghemeen vastpunt R, so heeft den erm TR, sulcken reden tot den erm RZ, als <emph type="other"/>INSERT PI Π<emph.end/> tot den pilaer door I voorstel. </s><s>Insghelijcx nemende V voor tvastpunt, soo heeft den erm TV sulcken reden tot den erm VΦ, als Δ tot den pilaer, maer RZ is altijt euen an VΦ: Wy hebben hier dan twee eueredenheden <arrow.to.target n="marg119"/> elck van vier palen <arrow.to.target n="marg120"/>, welcker tweede palen an malcanderen euen sijn, ende welcker laeste palen an malcanderen oock euen sijn. </s>

<s> Maer om tghemeen nootsaeckelick veruolgh in allen te bewysen, laet ons voorttrecken VR tot in Z, also dat RZ euen sy an RV; aensiende daer naer R voor tvastpunt, so sal an Z moeten hanghen Π 4 lb, om de pilaer in die ghestalt te houden door het 3 voorstel. </s><s>Maer tghene an V den pilaer in die ghestalt houdt als Æ, doet daer an alsulcken gheweldt als Π, door het I3 voorstel; An Æ dan rust een ghewicht euen an Π. </s><s>Laet ons insghelicx voorttrecken, RV tot in Φ, also dat VΦ euen sy an VR, ansiende daer naer V voor vastpunt, soo sal an Φ moeten hanghen Δ 2 lb, om den pilaer in die ghestalt te houden door het 3 voorstel, maer tghene an R den pilaer in die ghestalt houdt als &OElig;, doet daeran alsulcke ghewelt als Δ door het I3 voorstel, An &OElig; dan rust een ghewicht euen an Δ. </s><s>Nu anghesien Π euestaltwichtich is teghen den pilaer op tghemeen vastpunt R, so heeft den erm TR, sulcken reden tot den erm RZ, als Π tot den pilaer door I voorstel. </s><s>Insghelijcx nemende V voor tvastpunt, soo heeft den erm TV sulcken reden tot den erm VΦ, als Δ tot den pilaer, maer RZ is altijt euen an VΦ: Wy hebben hier dan twee eueredenheden <arrow.to.target n="marg119"/> elck van vier palen <arrow.to.target n="marg120"/>, welcker tweede palen an malcanderen euen sijn, ende welcker laeste palen an malcanderen oock euen sijn. </s><s> Maer alle twee eueredenheden elck van vier palen, welcker tweede palen an mal<pb pagenum="39"/>cander euen sijn, ende welcker laetste palen an malcander oock euen sijn, die hebben dander palen oock euerednich, daerom ghelijck TR tot TV, alsoo Π tot Δ; maer Π is euen an tghewicht des pilaers rustende met tpunt V op tpunt Æ, ende tghewicht Δ is euen an t'ghewicht des pilaers rustende met tpunt R op tpunt van &OElig;, daerom ghelijck TR tot TV, also tghewicht rustende mettet tpunt V op tpunt van Æ, tottet ghewicht rustende mettet punt R op tpunt van &OElig;. </s><s><emph type="other"/>TBESLVYT<emph.end/>. </s><s>Rustende dan een pilaer op twee punten inden as, &c. </s>

<s>

<margin.target id="marg119"/>Proportiones.

<margin.target id="marg120"/>Terminis.

</s>

<s> Maer alle twee eueredenheden elck van vier palen, welcker tweede palen an mal<pb pagenum="39"/>cander euen sijn, ende welcker laetste palen an malcander oock euen sijn, die hebben dander palen oock euerednich, daerom ghelijck TR tot TV, alsoo <emph type="other"/>INSERT PI Π<emph.end/> tot Δ; maer <emph type="other"/>INSERT PI Π<emph.end/> is euen an tghewicht des pilaers rustende met tpunt V op tpunt Æ, ende tghewicht Δ is euen an t'ghewicht des pilaers rustende met tpunt R op tpunt van &OElig;, daerom ghelijck TR tot TV, also tghewicht rustende mettet tpunt V op tpunt van Æ, tottet ghewicht rustende mettet punt R op tpunt van &OElig;. </s><s><emph type="other"/>TBESLVYT<emph.end/>. </s><s>Rustende dan een pilaer op twee punten inden as, &c. </s>

<s><emph type="other"/>VERVOLGH<emph.end/>. </s>

<s> <emph type="other"/>SOO<emph.end/> de twee punten daer den pilaer op rust, waren inde hanghende <arrow.to.target n="marg121"/> linien door R en V, de selue ghewichten die hier vooren op elck rustende punt waren, soudender nu oock op sijn. </s><s>Laet by boorbeelt door de punten R, V, hanghende linien ghetrocken worden, ende punten inde selue ghestelt als Y , Ghenomen nu dat Y ende de punten sijn daer den pilaer op rust, tis kennelick dat op Y rusten sal 2 lb, ende op 4 lb, waer uyt alsulcken vertooch openbaer is.</s>

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<margin.target id="marg121"/>Perpendicularibus.

</s>

<s><emph type="other"/>10. VERTOOCH<emph.end/>. <emph type="other"/>XVIII. VOORSTEL<emph.end/>.</s>

<s>I 0. <emph type="other"/>VERTOOCH. XVIII. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>RVSTENDE<emph.end/> een pilaer op eenighe twee punten, ghelijck het asstick tusschen tswaerheyts middelpunt ende de hanghende door t'slinckerpunt, tottet asstick tusschen t'swaerheydts middelpunt ende de hanghende door trechterpunt, also tghewicht des pilaers rustende op trechterpunt, tottet ghewicht rustende op t'slinckerpunt. </s>

<s> <emph type="other"/>TGHEGHEVEN<emph.end/>. </s><s>Laet ABCD een pilaer wesen, diens as EF, ende swaerheydts middelpunt G, ende de twee punten daer d'een pilaer op rust <emph type="other"/>HI<emph.end/>, waer duer ghetrocken sijn de hanghende linien KL, MN, sniende den as in O, P; Ick seg dat ghelijck GO tot GP, alsoo de swaerheydt rustende op tpunt I, tot de swaerheydt rustende op H, waer af tbewys openbaer is door tvervolgh des voorgaenden I7 voorstels, </s>

<s> <emph type="other"/>TGHEGHEVEN<emph.end/>. </s><s>Laet ABCD een pilaer wesen, diens as EF, ende swaerheydts middelpunt G, ende de twee punten daer d'een pilaer op rust HI, waer duer ghetrocken sijn de hanghende linien KL, MN, sniende den as in O, P; Ick seg dat ghelijck GO tot GP, alsoo de swaerheydt rustende op tpunt I, tot de swaerheydt rustende op H, waer af tbewys openbaer is door tvervolgh des voorgaenden I7 voorstels, </s>

<s> nochtans om alhier wat breder vande nootsakelicheyt te segghen, so laet ons achten al of H ter plaets van O waer, twelck soo ghenomen tghewicht alsdan op H rustende, heeft sulcken reden tottet ghewicht op P rustende, ghelijck GP, tot GO, duer het I7 voorstel; Laet ons voort nemen dattet tpunt H vast blijuende, den pilaer in haer ghegheuen ghestalt neerghetrocken worde, soo verre als van H tot O, ende duer de begheerte, de swaerheydt an H rustende blijft de selue. </s><s>Sghelijcx salmen bethoonen de swaerheyt dieder op P rust, oock te rusten op I, daerom ghelijck GO tot GP, also de swaerheyt rustende op I, tot de swaerheyt rustende op H. </s><s><emph type="other"/>TBESLVYT<emph.end/>. </s><s>Rustende dan een pilaer op eenighe twee punten, &c. </s>

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<s> <emph type="other"/>TBLIICT<emph.end/> uyt het voorgaende dat soomen begheerde te weten de reden van tghewicht rustende op I, tottet ghewicht rustende op H, datmen trecken soude de hanghende linien KL, MN, sniende den as EF in O, P, ende de reden van GO tot GP soude de begheerde sijn waer uyt oock openbaer is, dat des pilaers swaerheyt bekent wesende, soo is oock tghewicht bekent rustende op yder punt als H ende I.</s>

<s> <emph type="other"/>TOTHIERTOESIIN<emph.end/> </s>

<s> <emph type="other"/>TOT HIER TOE SIIN <lb/>DE GHEDAENTEN DER RECHT<lb/>WICHTEN VERCLAERT: INT <lb/>

volghende sullen de eyghenschappen der scheefwichten <lb/>bescreuen worden, wiens ghemeene grondt dit <lb/>volghende vertooch begrijpt.<emph.end/>

<s> <emph type="other"/>DEGHEDAENTENDERRECHT<emph.end/><lb/></s>

<s> <emph type="other"/>WICHTENVERCLAERT<emph.end/>: <emph type="other"/>INT<emph.end/> </s>

<s>

<margin.target id="marg122"/> sullen de eyghenschappen der scheefwichten bescreuen worden

</s>

<s> <emph type="other"/>TOTHIERTOESIIN<emph.end/> </s>

<s> <emph type="other"/>DEGHEDAENTENDERRECHT<emph.end/><lb/></s>

<s> <emph type="other"/>WICHTENVERCLAERT<emph.end/>: <emph type="other"/>INT<emph.end/> </s>

<s>

<margin.target id="marg123"/>volghende sullen de eyghenschappen der scheefwichten bescreuen worden, wiens ghemeene grondt dit volghende vertooch begrijpt.

</s>

<s><emph type="other"/>XI. VERTOOCH<emph.end/>. <emph type="other"/>XIX. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>XI<emph.end/>. </s><s><emph type="other"/>VERTOOCH<emph.end/>. </s><s><emph type="other"/>XIX<emph.end/>. </s><s><emph type="other"/>VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> een driehouc wiens plat <arrow.to.target n="marg124"/> rechthouckich op den sichteinder <arrow.to.target n="marg125"/> is, met sijn grondt daer af euewidich, ende op elck der ander sijden een rollende cloot met malcanderen euewichtich: </s>

<s>

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<margin.target id="marg125"/>Horizontem.

</s>

<s> Ghelijck des driehoucx rechter sijde tot de slincker, also t' des cloots op de slincker sijde, tottet staltwicht des cloots op de rechter sijde. </s>

<s> <emph type="other"/>TGHEGHEVEN<emph.end/>. </s><s>Laet ABC een driehouck wesen diens plat sy rechthouckich op den sichteinder, ende den grondt AC euewydich vanden sichteinder, ende op de sijde AB, die dobbel sy an BC, ligghe een cloot D, ende op de sijde BC een cloot E, euewichtich ende euegroot met den cloot D. </s><s><emph type="other"/>T'BEGHEERDE<emph.end/>. </s><s>Wy moeten bewysen dat ghelijck de sijde AB 2, tot BCI, alsoo t'staltwicht des cloots E, tottet staltwicht des cloots D. </s>

<s> T' <emph type="other"/>BEGHEERDE<emph.end/>. </s><s>Wy moeten bewysen dat ghelijck de sijde AB 2, tot B<emph type="other"/>CI<emph.end/>, alsoo t'staltwicht des cloots E, tottet staltwicht des cloots D. </s><s>T' <emph type="other"/>BEREYTSEL<emph.end/>. </s><s>Laet ons maecken rondtom den driehouck ABC eenen crans van veerthien clooten, euegroot, euewichtich, ende euewijt van malcanderen, als E, F, G, H, I, K, L, M, N, O, P, Q, R, D, al ghesnoert an een lini, streckende door haer middelpunten <arrow.to.target n="marg126"/>, also dat sy op die middelpunten drayen mueghen; Datter oock twee clooten passen op de sijde BC, ende vier op BA, dat is ghelijck lini tot lini, also clooten tot clooten; laet oock an S, T, V, drie vastpunten staen, ouer welcke de lini ofte t'snoer der clooten slieren mach, also dat de twee deelen des snoers die bouen den driehouck staen, euewydich <arrow.to.target n="marg127"/> sijn vande sijden AB, BC; Inder voughen dat alsmen den crans an d'een ofte d'ander sijde neertrect, soo rollen de clooten op de linien AB, BC. </s>

<s> <emph type="other"/>T'BEREYTSEL<emph.end/>. </s><s>Laet ons maecken rondtom den driehouck ABC eenen crans van veerthien clooten, euegroot, euewichtich, ende euewijt van malcanderen, als E, F, G, H, I, K, L, M, N, O, P, Q, R, D, al ghesnoert an een lini, streckende door haer middelpunten <arrow.to.target n="marg126"/>, also dat sy op die middelpunten drayen mueghen; Datter oock twee clooten passen op de sijde BC, ende vier op BA, dat is ghelijck lini tot lini, also clooten tot clooten; laet oock an S, T, V, drie vastpunten staen, ouer welcke de lini ofte t'snoer der clooten slieren mach, also dat de twee deelen des snoers die bouen den driehouck staen, euewydich <arrow.to.target n="marg127"/> sijn vande sijden AB, BC; Inder voughen dat alsmen den crans an d'een ofte d'ander sijde neertrect, soo rollen de clooten op de linien AB, BC. </s><s><emph type="other"/>T'BEWYS<emph.end/>. </s><s>Soo t'staltwicht der vier clooten D, R, Q, P, niet euen en waer met het staltwicht der twee clooten E, F, t'een of t'ander sal swaerder sijn, latet wesen (soot mueghelick waer) der vier D, R, Q. </s><s>P; Maer de vier clooten O, N, M, L, sijn euewichtich met de vier clooten G, H, I, K, de sijde dan der acht clooten D, R, Q, P, O, N, M, L, is swaerder na de ghestalt dan de sijde der ses clooten E, F, G, H, I, K: maer want het swaerste altijdt het lichtste ouerweeght, de acht clooten sullen neerwaert rollen, ende d'ander ses rijsen: </s><s> Latet soo wesen, ende D <pb pagenum="42"/>sy gheuallen daer nu O is, ende E, F, G, H, sullen sijn daer nu P, Q, R, D, ende I, K, daer nu E, F, sijn. </s><s>Maer dit soo wesende, den crans der clooten sal alsulcken ghestalt hebben als sy te vooren dede, ende sullen om de selue redenen de acht clooten ter slincker sijde wederom staltwichtigher sijn dan de ses clooten ter rechter, waer duer de acht clooten wederom neer sullen rollen, ende d'ander ses rijsen, welcke valling ter eender, ende rijsing ter ander, om dat de reden altijdt de selue is, altijdt ghedueren sal, ende de clooten sullen uyt haer seluen een maken, t'welck valsch is. </s><s> Het deel dan des crans D, R, Q, P, O, N, M, L, is euestaltwichtich met het deel E, F, G, H, I, K: Maer van sulke euewichtighe ghetrocken euewichtighe, de resten sijn euewichtich, laet ons dan van dat deel trecken de vier clooten O, N, M, L, ende van dit de vier clooten G, H, I, K, (welcke euen sijn ande voornoemde O, N, M, L,) de resten D, R, Q, P, ende E, F, sullen euestaltwichtich sijn, Maer wesende dese twee euestaltwichtich met die vier, E sal tweemael staltswaerder sijn als D. </s><s>Ghelijck dan de lini BA 2, tot de lini BCI, also t'staltwicht des cloots E, tottet staltwicht des cloots D.</s>

<s>

<margin.target id="marg126"/>Centra.

<margin.target id="marg127"/>Parallela.

</s>

<s><emph type="other"/>T'BESLVYT<emph.end/>. </s><s>Wesende dan een driehouck wiens plat, &c.</s>

<s><emph type="other"/>LAET<emph.end/> ABC een driehouck sijn als vooren, wiens sijde AB dobbel sy an BC, ende laet op AB ligghen een cloot D, ende op de sijde BC een cloot E euewichtich anden helft van D, ende an F sy een vastpunt daer ouer de lini DFE. </s><s>(te weten uyt het middelpunt <arrow.to.target n="marg128"/> des cloots D ouer F tot int middelpunt des cloots E) slieren mach, alsoo dat DF euewydich blijue van AB, ende FE van BC. </s><s>Dit also sijnde, anghesien de vier clooten P, Q, R, D, hier vooren, euestaltwichtich waren met de twee clooten E, F, so sal desen cloot D, euestaltwichtich sijn teghen de cloot E: want ghelijck die P, Q, R, D, tot E, F, also dese D tot E: Daerom ghelijck de lini AB, tot BC, alsoo den cloot D tot den cloot E.</s>

<s> T' <emph type="other"/>BEWYS<emph.end/>. </s><s>Soo t'staltwicht der vier clooten D, R, Q, P, niet euen en waer met het staltwicht der twee clooten E, F, t'een of t'ander sal swaerder sijn, latet wesen (soot mueghelick waer) der vier D, R, Q. </s><s>P; Maer de vier clooten O, N, M, L, sijn euewichtich met de vier clooten G, H, I, K, de sijde dan der acht clooten D, R, Q, P, O, N, M, L, is swaerder na de ghestalt dan de sijde der ses clooten E, F, G, H, I, K: maer want het swaerste altijdt het lichtste ouerweeght, de acht clooten sullen neerwaert rollen, ende d'ander ses rijsen: </s>

<s> Latet soo wesen, ende D <pb pagenum="42"/>sy gheuallen daer nu O is, ende E, F, G, H, sullen sijn daer nu P, Q, R, D, ende I, K, daer nu E, F, sijn. </s><s>Maer dit soo wesende, den crans der clooten sal alsulcken ghestalt hebben als sy te vooren dede, ende sullen om de selue redenen de acht clooten ter slincker sijde wederom staltwichtigher sijn dan de ses clooten ter rechter, waer duer de acht clooten wederom neer sullen rollen, ende d'ander ses rijsen, welcke valling ter eender, ende rijsing ter ander, om dat de reden altijdt de selue is, altijdt ghedueren sal, ende de clooten sullen uyt haer seluen een maken, t'welck valsch is. </s>

<s> Het deel dan des crans D, R, Q, P, O, N, M, L, is euestaltwichtich met het deel E, F, G, H, I, K: Maer van sulke euewichtighe ghetrocken euewichtighe, de resten sijn euewichtich, laet ons dan van dat deel trecken de vier clooten O, N, M, L, ende van dit de vier clooten G, H, I, K, (welcke euen sijn ande voornoemde O, N, M, L,) de resten D, R, Q, P, ende E, F, sullen euestaltwichtich sijn, Maer wesende dese twee euestaltwichtich met die vier, E sal tweemael staltswaerder sijn als D. </s><s>Ghelijck dan de lini BA 2, tot de lini B<emph type="other"/>CI<emph.end/>, also t'staltwicht des cloots E, tottet staltwicht des cloots D.</s>

<s> T' <emph type="other"/>BESLVYT<emph.end/>. </s><s>Wesende dan een driehouck wiens plat, &c.</s>

<s> <emph type="other"/>AETA<emph.end/>BC een driehouck sijn als vooren, wiens sijde AB dobbel sy an BC, ende laet op AB ligghen een cloot D, ende op de sijde BC een cloot E euewichtich anden helft van D, ende an F sy een vastpunt daer ouer de lini DFE. </s><s>(te weten uyt het middelpunt <arrow.to.target n="marg128"/> des cloots D ouer F tot int middelpunt des cloots E) slieren mach, alsoo dat DF euewydich blijue van AB, ende FE van BC. </s><s>Dit also sijnde, anghesien de vier clooten P, Q, R, D, hier vooren, euestaltwichtich waren met de twee clooten E, F, so sal desen cloot D, euestaltwichtich sijn teghen de cloot E: want ghelijck die P, Q, R, D, tot E, F, also dese D tot E: Daerom ghelijck de lini AB, tot BC, alsoo den cloot D tot den cloot E.</s>

<s>

<margin.target id="marg128"/>Centro.

</s>

<s>I. <emph type="other"/>VERVOLGH<emph.end/>.</s>

<s><emph type="other"/>I. VERVOLGH<emph.end/>.</s>

<s> <emph type="other"/>LAET<emph.end/> ons nu d'een sijde des driehouckx als BC (ande welcke AB dobbel is) rechthouckich stellen op AC als hier neuen; Ende den cloot D die dobbel is an E, sal noch met E euestaltwichtich sijn, want ghelijck AB tot BC, also den cloot D tot den cloot E. </s>

<s><emph type="other"/>II VERVOLGH<emph.end/>.</s>

<s><emph type="other"/>III<emph.end/> <emph type="other"/>VERVOLGH<emph.end/>.</s>

<s> <emph type="other"/>LAET<emph.end/> ons nu inde plaets van t'punt F, stellen een caterol als hier neuen, also dat de scheefheflini van D naer F euewydich blijue van AB, ende inde plaets vanden cloot E sy eenich wicht van form soot valt, maer euewichtich anden cloot E: t'selue is noch euestaltwichtich met D, Daerom ghelijck AB tot BC, alsoo noch den cloot D tottet ghewicht E. </s>

<s><emph type="other"/>III. VERVOLGH<emph.end/>.</s>

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