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Colored diff for /texts/archimedes/xml/Attic/stevi_weegc_01_nl_1586.xml between version 1.17 and 1.18

version 1.17, 2003/09/04 13:28:11

version 1.18, 2003/09/04 17:24:06

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<pb/>

<s>Simon Steuin wenscht </s>

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

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

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

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

<s> <emph type="other"/>AT<emph.end/> Ghetal Grootheyt ende Ghewicht, in yder wesentlicke saeck * onscheydelicke ancleuinghen sijn, vol diepe ende nutte eyghenschappen, en betuyghen niet alleen verscheyden gheleerden, maer tis duer d'eruaring in allen an elcken bekent. </s><s>Tis oock openbaer, dat d'eerste twee tot grooten voordeele der menschen, ter form van beschreuen consten gherocht sijn, namelick * Telconst ende Meetconst, maer niet also t'Ghewicht, om dat sijn oirsproncklicke eyghenschappen den voorighen verborghen bleuen. </s>

<s> <emph type="other"/>DAT<emph.end/> Ghetal Grootheyt ende Ghewicht, in yder wesentlicke saeck * onscheydelicke ancleuinghen sijn, vol diepe ende nutte eyghenschappen, en betuyghen niet alleen verscheyden gheleerden, maer tis duer d'eruaring in allen an elcken bekent. </s><s>Tis oock openbaer, dat d'eerste twee tot grooten voordeele der menschen, ter form van beschreuen consten gherocht sijn, namelick * Telconst ende Meetconst, maer niet also t'Ghewicht, om dat sijn oirsproncklicke eyghenschappen den voorighen verborghen bleuen. </s>

<s>

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<s> E Beghinselen der Weeghconst, welcke van swaerheyt sijn duer t'ghedacht van natuerlicke stof gheweert, sullen in twee boucken begrepen worden. </s><s>Des eersten boucx eerste deel sal van 14 * bepalinghen wesen: T'ander van 28 * voorstellen, van de ghedaenten der ghewichten, die tweederhande sijn, als Rechtwichten, ende Scheefwichten. </s><s>Der Rechtwichten sijn twee * afcomsten, te weten Rechtdaelwichten, ende Rechthefwichten, beschreuen inde achtien eerste voorstellen. </s><s>Der Scheefwichten sijn oock twee afcomsten, als Scheefdaelwichten, ende Scheefhefwichten, verclaert inde rest der voorstellen.</s>

<s>DE Beghinselen der Weeghconst, welcke van swaerheyt sijn duer t'ghedacht van natuerlicke stof gheweert, sullen in twee boucken begrepen worden. </s><s>Des eersten boucx eerste deel sal van 14 * bepalinghen wesen: T'ander van 28 * voorstellen, van de ghedaenten der ghewichten, die tweederhande sijn, als Rechtwichten, ende Scheefwichten. </s><s>Der Rechtwichten sijn twee * afcomsten, te weten Rechtdaelwichten, ende Rechthefwichten, beschreuen inde achtien eerste voorstellen. </s><s>Der Scheefwichten sijn oock twee afcomsten, als Scheefdaelwichten, ende Scheefhefwichten, verclaert inde rest der voorstellen.</s>

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<s>HE<emph type="other"/>TE<emph.end/>ERST<emph type="other"/>EB<emph.end/>OVCK <lb/>VAND<emph type="other"/>EB<emph.end/>EGHINSELEN <lb/>DE<emph type="other"/>RW<emph.end/>EEGCONST, <lb/> Beschreuen door Simon Steuin. </s>

<s><emph type="other"/>HET EERSTE BOVCK<emph.end/> <lb/><emph type="other"/>VANDE BEGHINSELEN<emph.end/> <lb/><emph type="other"/>DER WEEGCONST<emph.end/>, <lb/> Beschreuen door Simon Steuin. </s>

<s>TEERST<emph type="other"/>ED<emph.end/>EEL <lb/>

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

vande Bepalinghen. </s>

<s> I. BEPALING. </s><s><arrow.to.target n="marg43"/> </s>

<s> <emph type="other"/>I. BEPALING<emph.end/>. </s><s><arrow.to.target n="marg43"/> </s>

<s>

<margin.target id="marg43"/>Definitio.

</s>

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

<s> <emph type="other"/>HELIICK<emph.end/> de Meetconst <arrow.to.target n="marg44"/> ansiet der formen grootheden niet hare swaerheden, houdende die alleenelick voor ofte oneuen, diens grootheden euen ofte oneuen sijn; Alsoo ansiet ter contrarie de Weegconst haer swaerheden, niet haer grootheden, houdende die voor euen ende oneuen, diens ghewichten euen ofte oneuen sijn: Ende ghelijck diens voornamelicke wercking bestaet int ondersoucken der Redenen Eueredenheden, ende Ghedaenten <arrow.to.target n="marg45"/> haerder grootheden, Also desens int ondersoucken der Redenen Eueredenheden, ende ghedaenten haerder swaerheden ofte ghewichten, welcker bescriuing t'voornemen is deses handels.</s>

<s> <emph type="other"/>GHELIICK<emph.end/> de Meetconst <arrow.to.target n="marg44"/> ansiet der formen grootheden niet hare swaerheden, houdende die alleenelick voor ofte oneuen, diens grootheden euen ofte oneuen sijn; Alsoo ansiet ter contrarie de Weegconst haer swaerheden, niet haer grootheden, houdende die voor euen ende oneuen, diens ghewichten euen ofte oneuen sijn: Ende ghelijck diens voornamelicke wercking bestaet int ondersoucken der Redenen Eueredenheden, ende Ghedaenten <arrow.to.target n="marg45"/> haerder grootheden, Also desens int ondersoucken der Redenen Eueredenheden, ende ghedaenten haerder swaerheden ofte ghewichten, welcker bescriuing t'voornemen is deses handels.</s>

<s>

<margin.target id="marg44"/>Geometria

<margin.target id="marg45"/>* Rationum, proportionum & qualitatum.

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

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

<s> Swaerheydt eens lichaems, is de macht sijnder daling in ghestelde plaets. </s>

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

<s> <emph type="other"/>DE<emph.end/> swaerheydt ofte lichticheydt die wy ghemeenelick segghen een lichaem te hebben, en is niet sijn eyghen wesentlicke ghedaente, maer veroirsaect uyt sijn ghemeenschap met een ander (wiens breeder verclaring wy gheschict hebben) want veel Stoffen <arrow.to.target n="marg46"/> die swaer sijn inde locht, worden licht beuonden int water, ende de lichte inde locht, sijn el<pb pagenum="2"/>ders swaer; daerom als wy segghen een haudt te weghen hondert pondt, wy verstaen daer by de macht sijnder daling in gestelde plaets, dat is in dien Grondt <arrow.to.target n="marg47"/> daert in gheweghen was. </s><s><emph type="other"/>DOOR<emph.end/> t verkerde deser bepaling is te verstaen, dat lichticheyt eens lichaems de macht is sijnder rijsing, maer in ghestelde plaets, want eyghentlick is alle lichaem swaer.</s>

<s> <emph type="other"/>DE<emph.end/> swaerheydt ofte lichticheydt die wy ghemeenelick segghen een lichaem te hebben, en is niet sijn eyghen wesentlicke ghedaente, maer veroirsaect uyt sijn ghemeenschap met een ander (wiens breeder verclaring wy gheschict hebben) want veel Stoffen <arrow.to.target n="marg46"/> die swaer sijn inde locht, worden licht beuonden int water, ende de lichte inde locht, sijn el<pb pagenum="2"/>ders swaer; daerom als wy segghen een haudt te weghen hondert pondt, wy verstaen daer by de macht sijnder daling in gestelde plaets, dat is in dien Grondt <arrow.to.target n="marg47"/> daert in gheweghen was. </s><s><emph type="other"/>DOOR<emph.end/> t verkerde deser bepaling is te verstaen, dat lichticheyt eens lichaems de macht is sijnder rijsing, maer in ghestelde plaets, want eyghentlick is alle lichaem swaer.</s>

<s>

<margin.target id="marg46"/>Materia.

</s>

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

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

<s> <emph type="other"/>BEKENDE<emph.end/> swaerheyt is diemen door bekent ghewicht uytet. </s>

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<s> <emph type="other"/>ALS<emph.end/> wanneermen seght een lichaem ofte swaerheydt te weghen ses , ofte acht marck, oft drie oncen, &c. </s><s>Om datse door sulcke bekende ghewichten gheuytet wort, wy noemense Bekende swaerheydt.</s>

<s><emph type="other"/>IIII<emph.end/>. <emph type="other"/>BEPALING<emph.end/>.</s>

<s><emph type="other"/>IIII. BEPALING<emph.end/>.</s>

<s> <emph type="other"/>SWAERHEYDTS<emph.end/> middelpunt is, an twelck het lichaem door ons ghedacht hanghende, alle ghestalt houdt diemen hem gheeft. </s>

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

<s> <emph type="other"/>LAETA<emph.end/>BC een cloot sijn, diens stof ouer al eueswaer is, welcke wy met haer middelpunt D door ons ghedacht nemen te hanghen ande lini ED; Ende is kennelick dat dien cloot ghekeert wordende, sal houden alle ghestalt diemen haer gheeft, want soomen B keerde daer A is, B sal daer blijuen, ende voort yder deel op sijn plaets, want soo dat niet en gheschiede, de stof soude an deen sijde swaerder sijn als an d'ander, twelck teghen tghestelde waer. </s><s>D dan naer luyt deser bepaling is Swaerheydts middelpunt des cloots ABC; Ende alsoo salmen verstaen dat binnen alle lichamen soo wel ongeschicter form ende van stof oneenuaerdigher swaerheydt als gheschicter ende eenvaerdigher, is eenich sulcken punt, waer an tlichaem also hanghende, alle ghestalt houdt diemen hem gheeft, welck punt ghenoemt wort sijn Swaerheydts middelpunt. </s><s> Ende op dattet door eenighe sijne eyghenschappen kennelicker sy, sullender noch dit toe segghen: Het swaerheydts middelpunt der oirdentlicke lichamen als Pilaren, Clooten, Lancworpighe Clooten <arrow.to.target n="marg48"/>, der Vijf gheschicte lichamen, &c. ouer al eue<pb pagenum="3"/>wichtigher Stof sijnde, is tselue der Form ofte grootheydt, datmen anders Meetconstich middelpunt noemt. </s><s>Maer die niet ouer al euewichtigher Stof en sijn, en hebben dese twee punten niet nootsaeckelick tot een selfde plaets. </s><s>Wat de naelden <arrow.to.target n="marg49"/>, ende ongheschicte lichamen belangt, sy en hebben gheen formens ofte grootheydts middelpunt, maer alleen des swaerheydts. </s><s>Het ghebuert oock in veel lichamen als Rynghen, Haecken, Beckens, ende dier ghelijcke, dat haer swaerheydts middelpunt niet en valt inde stof des lichaems, maer binnen tlichaem uyt de stof. </s><s><emph type="other"/>DAER<emph.end/> wort inde bepaling gheseydt <arrow.to.target n="marg50"/> reden datmen int bepalen moet nemen, tghene den aert van tbepaelde best verclaert, twelck Pappus (daer hy int 8 bouck het swaerheydts middelpunt bepaelt) door tghedacht oock bequamelick ghedaen heeft. </s><s>Men soudet oock mueghen aldus bepalen: <arrow.to.target n="marg51"/> Wat Euestaltwichticheyt is sal door de Bepaling verclaert worden.</s>

<s> <emph type="other"/>LAET<emph.end/> ABC een cloot sijn, diens stof ouer al eueswaer is, welcke wy met haer middelpunt D door ons ghedacht nemen te hanghen ande lini ED; Ende is kennelick dat dien cloot ghekeert wordende, sal houden alle ghestalt diemen haer gheeft, want soomen B keerde daer A is, B sal daer blijuen, ende voort yder deel op sijn plaets, want soo dat niet en gheschiede, de stof soude an deen sijde swaerder sijn als an d'ander, twelck teghen tghestelde waer. </s><s>D dan naer luyt deser bepaling is Swaerheydts middelpunt des cloots ABC; Ende alsoo salmen verstaen dat binnen alle lichamen soo wel ongeschicter form ende van stof oneenuaerdigher swaerheydt als gheschicter ende eenvaerdigher, is eenich sulcken punt, waer an tlichaem also hanghende, alle ghestalt houdt diemen hem gheeft, welck punt ghenoemt wort sijn Swaerheydts middelpunt. </s><s> Ende op dattet door eenighe sijne eyghenschappen kennelicker sy, sullender noch dit toe segghen: Het swaerheydts middelpunt der oirdentlicke lichamen als Pilaren, Clooten, Lancworpighe Clooten <arrow.to.target n="marg48"/>, der Vijf gheschicte lichamen, &c. ouer al eue<pb pagenum="3"/>wichtigher Stof sijnde, is tselue der Form ofte grootheydt, datmen anders Meetconstich middelpunt noemt. </s><s>Maer die niet ouer al euewichtigher Stof en sijn, en hebben dese twee punten niet nootsaeckelick tot een selfde plaets. </s><s>Wat de naelden <arrow.to.target n="marg49"/>, ende ongheschicte lichamen belangt, sy en hebben gheen formens ofte grootheydts middelpunt, maer alleen des swaerheydts. </s><s>Het ghebuert oock in veel lichamen als Rynghen, Haecken, Beckens, ende dier ghelijcke, dat haer swaerheydts middelpunt niet en valt inde stof des lichaems, maer binnen tlichaem uyt de stof. </s>

<s><emph type="other"/>DAER<emph.end/> wort inde bepaling gheseydt <arrow.to.target n="marg50"/> reden datmen int bepalen moet nemen, tghene den aert van tbepaelde best verclaert, twelck Pappus (daer hy int 8 bouck het swaerheydts middelpunt bepaelt) door tghedacht oock bequamelick ghedaen heeft. </s><s>Men soudet oock mueghen aldus bepalen: <arrow.to.target n="marg51"/> Wat Euestaltwichticheyt is sal door de Bepaling verclaert worden.</s>

<s>

<margin.target id="marg48"/>* Sphæroidalium.

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<margin.target id="marg51"/>Swaerheydts middelpunt eens lichaems, is door twelck alle plat, tlichaem deelt in euestaltwichtighe deelen.

</s>

<s>V. <emph type="other"/>BEPALING<emph.end/>.</s>

<s><emph type="other"/>V. BEPALING<emph.end/>.</s>

<s> <emph type="other"/>SWAERHEYTS<emph.end/> middellini eens lichaems, is de oneindelicke hanghende door sijn swaerheydts middelpunt. </s>

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<s> <emph type="other"/>ALS<emph.end/> inde form der 4 bepaling, de oneindelicke hanghende lini door tswaerheydts middelpunt D, daer an de swaerheyt door ons ghedacht hangt, ghelijck DE ouer beyden sijden oneindelick voortghetrocken, noemen wy de Swaerheydts middellini des lichaems ABC.</s>

<s><emph type="other"/>VI<emph.end/>. <emph type="other"/>BEPALING<emph.end/>.</s>

<s><emph type="other"/>VI. BEPALING<emph.end/>.</s>

<s> <emph type="other"/>SWAERHEYTS<emph.end/> middelplat eens lichaems, is alle plat hem deelende door sijn swaerheydts middelpunt. </s>

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<s> <emph type="other"/>ALS<emph.end/> eenich plat sniende den Cloot der 4 bepaling door sijn middelpunt D, wort des selfden Swaerheyts middelplat gheseyt, ende alsoo met allen anderen. </s><s>Sijn eyghenschap is tlichaem alsins te deelen in twee euestaltwichtighe stucken.</s>

<s><emph type="other"/>VII<emph.end/>. <emph type="other"/>BEPALING<emph.end/>.</s>

<s><emph type="other"/>VII. BEPALING<emph.end/>.</s>

<s> <emph type="other"/>ALLE<emph.end/> rechte lini begrepen tusschen twee swaerheyts middellinien, noemen wy dier swaerheden Balck. </s>

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<s> <emph type="other"/>LAETA<emph.end/> ende B twee lichamen wesen, ende haer swaerheydts middellinien CD ende EF, tusschen de welcke ghetrocken sijn, eenighe linien soot valt als GH, AB, IK, yder van dien, ende alle ander alsoo begrepen tusschen twee swaerheydts middellinien, noemen wy den Balck der swaerheden <emph type="other"/>AB<emph.end/>. </s>

<s><emph type="other"/>VIII<emph.end/>. <emph type="other"/>BEPALING<emph.end/>.</s>

<s><emph type="other"/>VIII. BEPALING<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> den Balck ghedeelt met de swaerheyts middellini daer de twee swaerheden euestaltwichtich an sijn, wy noemen de deelen Ermen. </s>

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<s> <emph type="other"/>LAETAB<emph.end/>, twee lichamen wesen, diens balck sy CD, welcke ghedeelt is in E, met de swaerheydts middellini FG, daer de twee swaerheden euestaltwichtich an hanghen; de twee deelen des balcx als EC ende ED worden Ermen ghenoemt. </s>

<s><emph type="other"/>IX<emph.end/>. <emph type="other"/>BEPALING<emph.end/>.</s>

<s><emph type="other"/>IX. BEPALING<emph.end/>.</s>

<s> <emph type="other"/>ENDE<emph.end/> die swaerheydts middellini der twee swaerheden, heeten wy Handthaef. </s>

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<s> <emph type="other"/>ALSE<emph.end/>, der 8 bepaling wort Vastpunt gheseyt.</s>

<s><emph type="other"/>XI<emph.end/>. <emph type="other"/>BEPALING<emph.end/>.</s>

<s><emph type="other"/>XI. BEPALING<emph.end/>.</s>

<s> <emph type="other"/>ENDE<emph.end/> die twee swaerheden noemen wy Evestaltwichtighe. </s>

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<s> <emph type="other"/>ALSA<emph.end/> ende B, inde form der 8 bepaling, tsy haer eyghenwichten euen ofte oneuen sijn, wy noemen die Euestaltwichtighe, ouermidts sy naer de ghestalt euewichtich sijn, want A doet anden balck door tghestelde soo grooten ghewelt als B, ende B als A. </s><s>Dese Euestaltwichticheydt dient nootsaeckelick verstaen, ende onderscheyden vande Eueneyghenwichticheydt, anghesien dit al wat anders is als dat, want om by voorbeelt daer af te spreken, tghewicht ande cortste sijde des onsels hanghende, is somtijts thienmael swaerder als tander, nochtan hebben sy een ghelaet van euewichticheyt, maer ten is niet eyghen, dan alleenlick na de ghestalt. </s>

<s><emph type="other"/>XII<emph.end/>. <emph type="other"/>BEPALING<emph.end/>.</s>

<s><emph type="other"/>XII. BEPALING<emph.end/>.</s>

<s> <emph type="other"/>HEFWICHT<emph.end/> is t'ghene oirsaeck is van eens swaerheydts verheffing, ende Daelwicht van eens swaerheydts daling. </s>

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<s> Maer E der derde ende vierde Form, Daelwicht, om dattet het lichaem an sijn gehechte sijde B doet dalen, ofte in die ghedaelde gestalt houdt. </s>

<s><emph type="other"/>XIII<emph.end/>. <emph type="other"/>BEPALING<emph.end/>.</s>

<s><emph type="other"/>XIII. BEPALING<emph.end/>.</s>

<s> <emph type="other"/>ENDE<emph.end/> de rechte lini vande verheven swaerheyt naer thefwicht, noemen wy Heflini, maer vande ghdaelde swaerheyt naer het daelwicht, Daellini, ende alsulcke linien in t'gemeen, Trecklini. </s>

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<s> <emph type="other"/>ALS<emph.end/> de rechte lini CB der I2 bepaling noemen wy inde I ende 2 form Heflini, maer inde 3 ende 4 Daellini. </s><s>Ende sulcke linien (die bouen de voorgaende ons oock euewidich vanden sichtender connen ontmoeten) in t'ghemeen Trecklini.</s>

<s><emph type="other"/>XIIII<emph.end/>. <emph type="other"/>BEPALING<emph.end/>.</s>

<s><emph type="other"/>XIIII. BEPALING<emph.end/>.</s>

<s> <emph type="other"/>ENDE<emph.end/> als de Heflini ofte Daellini rechthouckich is op den Sichteinder <arrow.to.target n="marg52"/>, soo noemen wy die Rechtheflini, Rechtdaellini, ende hare ghewichten Rechthefwicht, Rechtdaelwicht: Maer opden Sichteinder scheefhouckich wesende, alsdan Scheefheflini, Scheefdaellini, ende hare ghewichten Scheefhefwicht, Scheefdaelwicht. </s>

<s>

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<s> <emph type="other"/>WY<emph.end/> begheeren datmen toelate euen ghewichten an euen ermen oock euestaltwichtich te sijne. </s>

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

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

<s> <emph type="other"/>ENDE<emph.end/> ande wisconstighe <arrow.to.target n="marg68"/> lini alle ghewicht te connen hanghen ofte daer op te connen rusten, sonder dat sy breke ofte buyghe. </s>

<s>

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

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

<s> <emph type="other"/>ENDE<emph.end/> de swaerheydt hoogher ofte leegher hangende, altijt van een selfde gewicht te blijven. </s>

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<s> <emph type="other"/>ALS<emph.end/> de swaerheydt A neerghetrocken sijnde tot B, aldaer euen soo swaer te wesen, ofte sulcken macht an CD te doen, als sy ter plaets van A dede.</s>

<s><emph type="other"/>IIII<emph.end/>. <emph type="other"/>BEGHEERTE<emph.end/>.</s>

<s><emph type="other"/>IIII. BEGHEERTE<emph.end/>.</s>

<s> <emph type="other"/>ENDE<emph.end/> datmen by des pilaers beschreuen plat t'welck hem door de langde des as deelt, verstaen sal den voorghestelden pilaer. </s>

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

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

<s> <emph type="other"/>MEN<emph.end/> can tvoorgaende oock bethoonen, blyuende de twee swaerheden hanghende an eenen lichamelicken balck, in deser voughen: Laet den pilaer ABCD ghesneen sijn in twee deelen, met een plat door den as EF, ende den as des ondersten deels EC sy GH, ende EC sy doorsneen met een plat IK euewydich vanden grondt ED, sniende den as GH in L, ende het swaerheydts middelpunt van het deel IKDE sy M int middel van GL, ende van het deel IKCF sy N int middel van LH, ende des heels ABCD sy O in middel van EF, ende OP sy swaerheydts middellini des heels ABCD, ende MQ van IKDE, ende NR van IKCF. </s><s> Dit soo sijnde tis kennelick dat des heels pilaers rechter sijde, euewichtich is teghen haer slincker. </s><s><emph type="other"/>LAET<emph.end/> ons nu het onderste deel EFCD neertrecken, also dat het blyue hanghende ande linien ML [MQ] ende NR, als hier neuens. </s><s>Ende is openbaer dat den lichamelicken balc ABFE noch in haer eerste ghestalt sal blyuen. </s><s>Laet ons nu achten dat het deel IKDE, ghesneen sy van IKCF, ende dat elck deel vallen mach daert wil, maer sy hanghen an haer swaerheyts <pb pagenum="15"/>middelpunten M, N, sy houden dan haer eerste ghegheuen ghestalt door de bepaling, daerom ABFE blijft oock noch in sijn eerste ghedaente. </s>

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<s> <emph type="other"/>VYT<emph.end/> het verkeerde des voorgaenden voorstels volcht, dat hebbende de swaerste swaerheydt sulcken reden tot de lichtste, als den langsten erm tot den cortsten, dat die twee swaerheden euestaltwichtich sijn.</s>

<s>I. <emph type="other"/>EYSCH<emph.end/>. <arrow.to.target n="marg86"/> <emph type="other"/>II<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s>I. <emph type="other"/>EYSCH<emph.end/>. <arrow.to.target n="marg86"/> <emph type="other"/>II. VOORSTEL<emph.end/>.</s>

<s>

<margin.target id="marg86"/>Problema.

</s>

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<s> <emph type="other"/>TGHEGHEVEN<emph.end/>. </s><s>Laet d'een swaerheydt sijn den pilaer ABCD weghende 6 lb, ghedeelt als den pilaer int beghin des eersten voorstels; Ende an Q hanghe een ghewicht Y van 12 lb. </s><s><emph type="other"/>TBEGHEERDE<emph.end/>. </s><s>Wy moeten d'handthaef vinden. </s><s> <emph type="other"/>TWERCK<emph.end/>. </s><s>De swaerheydts middellini des pilaers is IT, ende van tghewicht Y is BQ, ende TQ is balck, <pb pagenum="16"/>de selue salmen in tween deelen, alsoo dat de sticken de reden hebben als 12 lb van Y, tot 6 lb vanden pilaer, weluerstaende tcortste stick naer de swaerheydts middellini vande swaerste swaerheydt Y, twelck vallen sal in X, inder voughen dat NX de begheerde hanthaef is.</s>

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

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

<s> <emph type="other"/>TGHEGHEVEN<emph.end/>. </s><s>Laet ABCD wederom den pilaer sijn, ghedeelt als vooren, hanghende nu Y 6 lb an X. </s><s><emph type="other"/>TBEGHEERDE<emph.end/>. </s><s>Wy moeten d'handthaef vinden. </s><s> <emph type="other"/>TWERCK<emph.end/>. </s><s>De swaerheydts middellini des pilaers is IT, ende van Y is NX, ende TX is balck: de selue salmen in tween deelen, alsoo dat de sticken de reden hebben als 6 lb van Y, tot 6 lb des pilaers, twelck vallen sal in V, indervoughen dat VL de begheerde handthaef sijn sal.</s>

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<s> E swaerheydts middellini van MLBCY, is NX, ende van MLAD is SG, ende SX is balck, de selue salmen in tween deelen, also dat de stucken de reden hebben als 8 lb van MLBCY, tot 4 lb van MLAD: welverstaende tcortste stick naer de swaerheyts middellini van tswaerste deel, twelck vallen sal in V, inder voughen dat VL wederom de begheerde handhaef sijn sal als vooren. </s>

<s><emph type="other"/>IIII<emph.end/>. <emph type="other"/>VOORBEELT<emph.end/>.</s>

<s><emph type="other"/>IIII. VOORBEELT<emph.end/>.</s>

<s> <emph type="other"/>TGHEGHEVEN<emph.end/>. </s><s>Laet ABCD wederom den pilaer sijn, ghedeelt als vooren, hanghende Y 6 lb an X, ende Z 24 lb an R. </s><s><emph type="other"/>TBEGHEERDE<emph.end/>. </s><s>Wy moeten d'handthaef vinden. </s><s> <emph type="other"/>TWERCK<emph.end/>. </s><s>De <pb pagenum="17"/>swaerheydts middellini van ABCDY, is LV door het 3 voorbeelt, ende van Z is RE, daerom is RV balck: de selue salmen in tween deelen, alsoo dat de stucken de reden hebben als 12 lb van ABCDY, tot 24 lb van Z: wel verstaende tcortste stic naer de swaerheyts middellini van tswaerste deel, twelck vallen sal in S, inder voughen dat SG de begheerde handthaef sijn sal. </s>

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<s><emph type="other"/>II<emph.end/>. <emph type="other"/>EYSCH<emph.end/>. <emph type="other"/>III<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s><emph type="other"/>II. EYSCH. III. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> ghegheuen twee euestaltwichtighe swaerheden, d'een bekent dander onbekent, ende d'hanthaef: Die onbekende bekent te maken. </s>

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<s> <emph type="other"/>TGHEGHEVEN<emph.end/>. </s><s>Laet A ende B twee euestaltwichtighe swaerheden sijn, welcker A hanghende an C weeght 3 lb, maer B hanghende an D is onbekent, ende EF sy d'handthaef. </s><s><emph type="other"/>TBEGHEERDE<emph.end/>. </s><s>Wy moeten tghewicht van B bekent maken. </s><s><emph type="other"/>TWERCK<emph.end/>. </s><s>Men sal ondersoucken wat reden den erm ED heeft, tot den erm EC, wort beuonden, neem ick, als van 3 tot 1, daerom seg ick, ED 3, gheeft EC 1, wat A 3 lb ? comt voor B 1 lb. </s>

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

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

<s> <emph type="other"/>TGHEGHEVEN<emph.end/>. </s><s>Laet inde form des 2 voorbeelts van het 2 voorstel den pilaer ABCD voor d'een swaerheyt weghen 6 lb, ende dander onbekende swaerheyt sy tghewicht daer an hanghende Y, ende d'hanthaef sy XN. </s><s><emph type="other"/>TBEGHEERDE<emph.end/>. </s><s>Wy moeten tghewicht van Y bekent maken. </s><s>[ Figuur ingevoegd ] <emph type="other"/>TWERCK<emph.end/>. </s><s>Anghesien TI swaerheydts middellini is des pilaers, ende QB van Y, so sal TQ balck sijn, diens cortsten erm XQ, ende langsten XT; Daerom salmen ondersoucken wat reden den erm XQ, heeft tot XT, wort beuonden neem ick, als van 1 tot 2. </s><s>Ich seg dan, XQ 1, gheeft XT 2, wat den pilaer 6 lb ? comt voor Y 12 lb. </s><s>Der ghelijcke voorbeelden mochten wy hier stellen op dander formen des 2 voorstels, ten waer die door de voorgaende kennelick ghenouch sijn. </s><s><emph type="other"/>TBEWYS<emph.end/>. </s><s>Laet B int eerste voorbeelt, soot mueghelick waer, swaerder sijn dan 1 lb, de swaerste swaerheydt dan en sal niet sulcken reden hebben tot de lichtste, als den langsten erm tot den cortsten; twelck teghen het I voorstel is; B dan en is niet swaerder dan 1 lb. </s><s>Sghelijcx salmen oock bethoonen dat sy niet lichter en is, sy weeght dan effen 1 lb, twelck wy bewysen moesten. </s><s><emph type="other"/>TBESLVYT<emph.end/>. </s><s>Wesende dan ghegheuen twee euestaltwichtighe swaerheden, d'een bekent dander onbekent, ende d'hanthaef: Wy hebben die onbekende bekent ghemaect, naer den eysch. </s>

<s><emph type="other"/>III<emph.end/>. <emph type="other"/>EYSCH<emph.end/>. <emph type="other"/>IIII<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s><emph type="other"/>III. EYSCH. IIII. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> ghegheuen twee bekende euestaltwichtighe swaerheden met de langde van d'eenen erm: de langde des anderen erms te vinden. </s>

<s> <emph type="other"/>TGHEGHEVEN<emph.end/>. </s><s>Laet A ende B twee euestaltwichtighe swaerheden sijn, welcker A hanghende an C weeght 3 lb, ende B hanghende an D 1 lb, ende de langde des erms DE sy 6 voeten.</s><s><emph type="other"/>TBEGHEERDE<emph.end/>. </s><pb pagenum="20"/><s>Wy moeten de langde des anderen erms vinden. </s><s> <emph type="other"/>TWERCK<emph.end/>. </s><s>Men sal segghen A 3 lb, gheeft B 1 lb, wat DE 6 voeten ? comt voor EC 2 voeten. </s><s>Ende der ghelijcke voorbeelden mochten wy stellen op de formen der voorbeelden des voorstels, ten waer die duer tvoorgaende kennelick ghenouch sijn. </s><s><emph type="other"/>TBEWYS<emph.end/>. </s><s>Laet EC, soot mueghelick waer, langher sijn dan 2 voeten; den langsten erm sal dan minder reden hebben tot den corsten, dan de swaerste swaerheyt tot de lichtste, twelck teghen het eerste voorstel is, EC dan en is niet langher dan 2 voeten; Sghelijcx salmense oock bewysen niet corter te sijn, sy is dan effen van twee voeten, twelck wy bewysen moesten. </s><s><emph type="other"/>TBESLVYT<emph.end/>. </s><s>Wesende dan ghegheuen twee euestaltwichtighe swaerheden met de langde van d'eenen erm, wy hebben de langde des anderen erms gheuonden, naer den eysch.</s>

<s><emph type="other"/>IIII<emph.end/>. <emph type="other"/>EYSCH<emph.end/>. V. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s><emph type="other"/>IIII. EYSCH<emph.end/>. V. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> ghegheuen een pilaer: te vinden een ghewicht in ghestelde reden tot des pilaers ghewicht. </s>

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<s><emph type="other"/>IIVERTOOCH<emph.end/>. <emph type="other"/>VIVOORSTEL<emph.end/>.</s>

<s><emph type="other"/>IIVERTOOCH. VIVOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> een hanghende pilaer ghesneen door sijn swaerheydts middelpunt, met een plat euewydich vanden gront, ende wesende tvastpunt in dat plat bouen het swaerheyts middelpunt: Den as des pilaers blijft euewydich vanden sichteinder. </s><s><arrow.to.target n="marg92"/></s>

<s>

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<s><emph type="other"/>IIIVERTOOCH<emph.end/>. <emph type="other"/>VIIVOORSTEL<emph.end/>.</s>

<s><emph type="other"/>IIIVERTOOCH. VIIVOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> tvastpunt het swaerheydts middelpunt des hanghenden pilaers, hy houdt alle gestalt diemen hem gheeft. </s>

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<s> als in dees tweede form, <pb pagenum="23"/>ende laet FE voortghetrocken worden tot in L, sniende AB in M, ende en laet den pilaer soot mueghelick waer niet in die ghestalt blijuen, dan het stick MLDA, ofte MLCB neervallen; Maer dees twee deelen sijn ghelijck euegroot, ende daerom oock eueswaer, het eene dan van euewichtighe sal swaerder sijn dan t'ander, twelc ongheschickt is: Den pilaer dan blijft in die ghestalt, ende sghelijcx in allen anderen diemen hem soude mueghen gheuen. </s><s><emph type="other"/>TBESLVYT<emph.end/>. </s><s>Wesende dan tvastpunt het swaerheydts middelpunt des pilaers, hy houdt alle ghestalt diemen hem gheeft, twelck wy bewysen moesten. </s>

<s><emph type="other"/>IIIIVERTOOCH<emph.end/>. <emph type="other"/>VIIIVOORSTEL<emph.end/>.</s>

<s><emph type="other"/>IIIIVERTOOCH. VIIIVOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> den pilaer ghesneen door sijn swaerheyts middelpunt, met een plat euewydich vanden gront, ende wesende tvastpunt in dat plat beneden het swaerheydts middelpunt: Den pilaer (natuerlick verstaen) keert om tot dat sijn swaerheydts middelpunt is in sijn swaerheydts middellini. </s>

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

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

<s> D' <emph type="other"/>HANTHAEF<emph.end/> oneindelick voortghetrocken, deelt alle balcken tweer swaerheden in haer ermen. </s>

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<s> Uyt het voorgaende is ghenouch blijckelick den ghemeenen voortganck in allen anderen, als van pilaren welcker vastpunt is buyten de lini als FG, ende der ghewichten vastpunten op ander plaetsen dan <emph type="other"/>DC<emph.end/>; Maer ouermits wy hier voornamelick trachten de oirsaecken vande ghedaenten des s grondelick te openbaren (daer af inde Weeghdaet breeder sal gheseyt worden) so en gheuen wy van sulcke ongheschicte ghestaltheden gheen besonder voorbeelden.</s>

<s>6. <emph type="other"/>EYSCH<emph.end/>. <emph type="other"/>II<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s>6. <emph type="other"/>EYSCH. II. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> ghegheuen een bekende pilaer, ende bekende swaerheden daer an hanghende: Te vinden het vastpunt daer op hy alle ghestalt houdt diemen hem gheeft. </s>

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<s> <emph type="other"/>TWERCK<emph.end/>. </s><s>Men sal <pb pagenum="29"/>trecken GI balck der ghewichten <emph type="other"/>FH<emph.end/>, daer naer salmen vinden haer ermen door het voorstel, dat is ghelijck <emph type="other"/>FI<emph.end/> lb, tot H 4 lb, also den erm KI, tot KG, daer naer salmen trecken EK balck des pilaers ter eender, ende der ghewichten <emph type="other"/>FH<emph.end/> ter ander sijden, de selue EK ghedeelt in L, also dat den erm EL sulcken reden hebbe tot LK, als 5 lb van <emph type="other"/>FH<emph.end/>, tot I0 lb des pilaers, L sal tbegheerde punt sijn op twelck sy alle ghestalt sullen houden diemen haer gheeft, waer af tbewys openbaer is door het voorstel.</s>

<s><emph type="other"/>VII<emph.end/>. <emph type="other"/>EYSCH<emph.end/>. <emph type="other"/>XII<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s><emph type="other"/>VII. EYSCH. XII. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> ghegheuen een bekende pilaer, met sijn vastpunt ende bekende ghewichten daer an hanghende die den as euewydich houden vanden sichteinder:<arrow.to.target n="marg111"/> Te vinden een ghewicht hanghende ter begheerder plaets des pilaers, dat den as in ghegheuen ghestalt houde. </s>

<s>

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

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

<s> <emph type="other"/>LAETA<emph.end/>BCD een pilaer sijn weghende 6 lb, diens vastpunt E, ende handthaef EF, ende G een ghewicht van 2 lb, diens vastpunt H, ende I een ghewicht van I lb, diens vastpunt K, ende den as LM sy euewydich vanden sichteinder <arrow.to.target n="marg113"/> NO, ende P sy een punt inden pilaer voor de begheerde plaets. </s>

<s>

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<s> Wesende dan ghegheuen een bekenden pilaer met sijn vastpunt, &c. </s>

<s><emph type="other"/>VI<emph.end/>. <emph type="other"/>VERTOOCH<emph.end/>. <emph type="other"/>XIII<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s><emph type="other"/>VI. VERTOOCH. XIII. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>EEN<emph.end/> daelwicht ende een hefwicht an hem euen, doen met euen houcken an euen ermen euen ghewelden. </s>

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<s> <emph type="other"/>TGHEGHEVEN<emph.end/>. </s><s>Laet A des handthaefs vastpunt, ende AB met AC twee euen ermen sijn, ende an B hanghe het scheefdaelwicht D, diens scheefdaellini BE, ende an C sy het scheefhefwicht F, euen an D, diens scheefheflini sy CG, ende den houck KCG, sy euen anden houck KBE. </s><s><emph type="other"/>TBEGHEERDE<emph.end/>. </s><s>Wy moeten bewysen dat het scheefdaelwicht D, ende het scheefhefwicht F, ande euen ermen AB, AC, euen ghewelden doen. </s><s><emph type="other"/>TBEREYTSEL<emph.end/>. </s><s>Laet an C een scheefdaelwicht H hanghen euen an D, diens scheefdaellini CI, also dat den houck ACI, euen sy anden houck ABE. </s><s><emph type="other"/>TBEWYS<emph.end/>. </s><s>Laet ons weeren F, ende is kennelick dat de macht van D teghen H, is de ermen AB, AC, in die ghegheuen ghestalt te houden, want D is euen an H, ende den erm AB an AC, ende den houck ACI, anden houck ABE. </s><s>Laet nu D weeren, ende F wederom anhanghen, ende de macht van F is oock de ermen AB, AC, in die ghegheuen ghestalt te houden, ouermits H euen is an F. </s><s><emph type="other"/>TBESLVYT<emph.end/>. </s><s>Een daelwicht dan ende een hefwicht an hem euen, doen met euen houcken an euen ermen euen ghewelden, twelck wy bewysen moesten. </s>

<s> <emph type="other"/>VIII<emph.end/>. <emph type="other"/>EYSCH<emph.end/>. <emph type="other"/>XIIII<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>. </s>

<s> <emph type="other"/>VIII. EYSCH. XIIII. VOORSTEL<emph.end/>. </s>

<s> <emph type="other"/>WESENDE<emph.end/> ghegheuen een pilaer, ende twee punten inden as, t'een vast t'ander int langste deel verroerlick: Te vinden een rechthefwicht an tverroerlick, dat den pilaer in sijn ghegheuen standt houde </s>

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

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

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

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

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

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

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

<s> <emph type="other"/>NGHESIEN<emph.end/> den cloot des 3 veruolgs naect de lini AB, in t'punt G, als vastpunt, soo sal den as GH rechthouckich sijn op AB {}; Daerom laet ons weren den cloot, ende stellen in die plaets den pilaer D euewichtich met den cloot, alsoo dat den as GH (diens vastpunt G) rechthouckich sy op AB, ende de scheefheflini tusschen DF noch euewydich van AB, ende sniende de sijde des pilaers in I, Als hier neuens. </s><s> Ende is openbaer dat ghelijck AB tot BC, (dat is dobbel als vooren) also den pilaer D tottet t'ghewicht E. </s>

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<s> Maer ghelijck AB tot BC, alsoo den Pilaer tot t'ghewicht E door het 4 veruolg, daerom ghelijck LD tot DI, also den pilaer tot E. </s><s>Laet ons nu ande lini KD voughen t rechthefwicht M met den pilaer euestaltwichtig, t'selue ghewicht M sal met den pilaer euewichtich sijn door het voorstel: Daerom ghelijck LD tot DI, also M tot E.</s>

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

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

<s><emph type="other"/>LAET<emph.end/> ons trecken BN, sniende de voortghetrocken AC in N: Insghelijcx DO, sniende de voortghetrocken LI dat is de sijde des pilaers in O, ende also dat den houck IDO, euen sy anden houck CBN. </s><s>Laet ons oock voughen an DO t'scheefhefwicht P, dat den pilaer (de ghewichten M, E gheweert sijnde) in die standthaude. </s><s> Nu anghesien DL, des driehouckx DLI, lijckstandighe <arrow.to.target n="marg130"/> is met BA des driehouckx BAC, ende DI met BC, men besluyt daer uyt aldus: Ghelijck BA tot BC, also t'staltwicht van BA tottet staltwicht van BC (door het 2 vervolg) Ende oock ghelijck DL tot DI also t'staltwicht van DL tot t'staltwicht van DI, dat is alsoo M tot E. </s><s>Maer de lijckstandighe linien van dese ghelijcke driehoucken ABN, LDO, sijn BA met DL, ende BN met DO, Daerom segghen wy als vooren, Ghelijck BA tot BN, alsoo het staltwicht van BA tot het staltwicht van BN (door het I vervolgh) Ende oock ghelijck DL tot DO, also het staltwicht van DL tot het staltwicht van DO, dat is also M tot P. </s><s>Maer by aldien de lini BN, ghetrocken waer van B af ouer d'ander sijde van BC, so soude de lini DO, dan oock vallen van D ouer d'ander sijde van DI, dat is, daer DO nu valt onder DI, sy souder dan bouen vallen, ende t'voorgaende bewys soude oock dienen tot sulcke ghestalt, te weten, dat wy noch segghen souden, ghelijck BA tot BN, alsoo t'staltwicht van BA, tottet staltwicht van BN; Ende ghelijck DL tot DO, alsoo t'staltwicht van DL, tottet staltwicht van DO, dat is, also M tot P. </s><s>Inder voughen dat dese eueredenheydt <arrow.to.target n="marg131"/> niet alleen en bestaet inde voorbeelden, alwaer de heflini als DI rechthouckich is op den as, maer op allen houcken. </s>

<s>

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

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

<s> <emph type="other"/>AER<emph.end/> op dat nu blijcke dese eueredenheydt <arrow.to.target n="marg136"/> niet alleen also te bestaen inde pilaren alwaer de rechtheflini als DL, comt uyt t'middelpunt des pilaers, ende diens vastpunt is des assens uyterste, als hier vooren G int 6 vervolg; Soo laet ABC een driehouck sijn, wiens sijde AB dobbel is an BC, ende BC sy hanghende <arrow.to.target n="marg137"/> op AC: Ende laet DE een pilaer sijn diens as FG rechthouckich op AB, ende sniende AB in t'punt H, ende I sy eenich ander punt inden seluen as; </s>

<s>

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

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

<s> <emph type="other"/>LAET<emph.end/> ons nu an I des 7 veruolgs voughen trechthefwicht R euestaltwichtich met den pilaer, diens rechtheflini sy IS, sniende de sijde des pilaers in T, ende IQ snie de sijde des pilaers in V, ende laet an de lini PQ hanghen een ghewicht X, inde plaets vanden pilaer KL, t'welck euen sy anden helft van t'staltwicht des selfden pilaers KL, Laet ons oock weeren den driehouck ABC, ende den pilaer DE doen rusten op t'punt H als hier neuen. </s><s> Ende om de redenen als vooren, ghelijck TI tot IV, alsoo R tot X. </s><s>Ende dit niet alleen als IV rechthouckich is op den as FG, maer cromhouckich soot valt, waeraf men besondet bethooch soude mueghen doen, maer tis openbaer ghenouch door het 6 veruolgh.</s>

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

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

<s><emph type="other"/>WY<emph.end/> hebben int 8 vervolgh dese eueredenheut <arrow.to.target n="marg139"/> verclaert, alwaer t'roerende punt I, hoogher was dan t'vastpunt H, ende alwaer de scheefheflini IV helde naer de sijde des vastpunts H; Wy moeten nu <pb pagenum="48"/>bethooghen de selue eueredenheyt oock te bestaen in d'ander ghestalten, ende eerst alwaer troerende punt leegher sy dan t'vastpunt, ende alwaer de scheefheflini afwyct vande sijde des vastpunts in deser voughen: </s>

<s>

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<s> <emph type="other"/>LAET<emph.end/> ons stellen een form ghelijck an die des 9 veruolghs, alleen daer in verschillende dat dese FH wyct ouer d'ander sijde van FI, ende dat den houck HFC, euen sy anden houck RPO, waer duer G anden pilaer AM euen soo grooten ghewelt doet als Q, ende om de redenen des 9 veruolgs (die wy om cortheyt ouerslaen) G doet euen sulcken ghewelt anden pilaer AB, als Q anden pilaer LM; Nu ghelijck TP tot PR, alsoo S tot Q door het 9 vervolgh, maer IF is euen an TP, ende FH an PR, ende K an S, ende G an Q, daerom ghelijck IF tot FH, also K tot G.</s>

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

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

<s><emph type="other"/>LAET<emph.end/> ons stellen een form ghelijck an die des I0 veruolgs, alleen daer in verschillende dat dese PR wyckt ouer d'ander sijde van PT, ende dat PR euewydich sy met FH, waer duer Q anden pilaer AM, euen soo grooten ghewelt doet als G, ende om de redenen des 9 veruolghs, Q doet euen sulcken gheweldt anden pilaer LM, als G anden pilaer AB; Nu ghelijck IF tot FH, also K tot G door het 6 veruolgh: Maer TP is euen an IF, ende PR an FH, ende S an K, ende Q an G, daerom ghelijck TP tot PR, also S tot Q. </s><s>Ende inder seluer voughen salmen vanden anderen ghestalten door haer contrarien altijt dese eueredenheyt bewysen. </s>

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

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

<s><emph type="other"/>MAER<emph.end/> dat dese eueredenheydt <arrow.to.target n="marg142"/> oock bestaet inde ghestalt daer den as euewydich is vanden sichteinder <arrow.to.target n="marg143"/>, wort aldus bethoont: Laet AB een pilaer sijn, diens as CD euewydich <arrow.to.target n="marg144"/> sy vande sichteinder, ende t'vastpunt daer in E, ende t'roerlick punt F, ende G t'scheefhefwicht dat den pilaer in die ghestalt houdt, wiens scheefheflini FH, ende I trechthefwicht dat den pilaer oock in die ghestalt houdt, wiens rechtheflini FK; T'welck soo sijnde, Laet KF tot FH een ander reden hebben (soot mueghelick waer) dan I tot G, By voorbeelt KF sy tot FH, als I tot 2, maer I tot G, als 3 tot 7. </s>

<s>

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<s> <emph type="other"/>UYT<emph.end/> dese voorgaende bescrijuen wy een vertooch soodanich.</s>

<s><emph type="other"/>XII<emph.end/>. <emph type="other"/>VERTOOCH<emph.end/>. <emph type="other"/>XX<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s><emph type="other"/>XII. VERTOOCH. XX. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> inden as des pilaers een vastpunt, ende een roerlick, daer an hy door een rechthefwicht ende scheefhefwicht in seker standt ghehouden wort: Ghelijck rechtheflini tot scheefheflini, also rechthefwicht tot scheefhefwicht. </s>

<s><emph type="other"/>XII<emph.end/>. <emph type="other"/>VERTOOCH<emph.end/>. <emph type="other"/>XX<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s><emph type="other"/>XII. VERTOOCH. XX. VOORSTEL<emph.end/>.</s>

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<s> T' <emph type="other"/>BESLVYT<emph.end/>. </s><s>Wesende dan inden as des pilaers een vastpunt, &c. </s><s><emph type="other"/>MERCKT<emph.end/>. </s><s>Soo eenighe der linien als IF, FK, de sijde des pilaers niet en sneen, men sal die sijde voorder trecken tot dat sy ghesneen wort, als inde voorgaende laetste form. </s>

<s><emph type="other"/>XIII<emph.end/>. <emph type="other"/>VERTOOCH<emph.end/>. <emph type="other"/>XXI<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s><emph type="other"/>XIII. VERTOOCH. XXI. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> inden as des pilaers een vastpunt, ende een roerlick, daer an hy door een rechtdaelwicht ende scheefdaelwicht in seker standt gehouden wort: Ghelijck rechtdaellini tot scheefdaellini, also rechtdaelwicht tot scheefdaelwicht. </s>

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<s> T' <emph type="other"/>BESLVYT<emph.end/>. </s><s>Wesende dan inden as des pilaers een vastpunt ende een roerlick, &c.</s>

<s><emph type="other"/>IX<emph.end/>. <emph type="other"/>EYSCH<emph.end/>. <emph type="other"/>XXII<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s><emph type="other"/>IX. EYSCH. XXII. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> ghegheuen een bekenden pilaer, met een vastpunt inden as, ende een roerlick punt, an t'welck eenich onbekent treckwicht den pilaer in ghegheuen ghestalt houdt: Dat treckwicht bekent te maken. </s>

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

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

<s> <emph type="other"/>ALS<emph.end/> des ghewichts trecklini rechthouckich op den as is; Soo doedet anden pilaer ghegeuener ghestalt de grootste ghewelt. </s>

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<s> <emph type="other"/>HET<emph.end/> blijft dat hoe de houcken der trecklinien vande ghewichten, op den as den rechthouck naerder sijn, hoe de ghewichten meerder ghewelt doen; Ende ter contrarie hoe sy vanden rechthouck meer verschillen, hoe de ghewichten minder ghewelt doen. </s>

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

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

<s> <emph type="other"/>TWEE<emph.end/> oneuewydighe linien daer een pilaer an hangt beyde oneindelick voortghetrocken, snien malcanderen inde swaerheydts middellini des pilaers. </s>

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

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

<s> T' <emph type="other"/>GHEGHEVEN<emph.end/>. </s><s>Laet AB een pilaer sijn welcke in die standt ghehouden wort door de scheefdaellini CD, ende scheefheflini EF, de selue sijn voortghetrocken tot G, H, sniende malcanderen in I. </s><s>T' <emph type="other"/>BEGHEERDE<emph.end/>. </s><s>Wy moeten bewysen dat I inde swaerheydts mid<pb pagenum="59"/>dellini is des pilaers AB. </s><s>T' <emph type="other"/>BEWYS<emph.end/>. </s><s>Laet ons GC ansien voor styl, ofte stijue lini ende nemen dat de macht die an D int neertrecken was, nu neerstekende sy in yder punt tusschen C en G daermen haer stelt, ende den pilaer AB, sal alsoo op allen punten diemen tusschen C, G ende E, H voor uytersten neemt, sijn ghegheuen standt houden. </s><s>Laet ons nemen I ghemeen uyterste van d'een en d'ander lini, den pilaer dan houdt daer an sijn ghegheuen standt; maer hanghende den pilaer an t'punt I, de hanghende door I is des pilaers swaerheyts middellini, inde welcke I is. </s>

<s><emph type="other"/>IIII<emph.end/>. <emph type="other"/>VOORBEELT<emph.end/>.</s>

<s><emph type="other"/>IIII. VOORBEELT<emph.end/>.</s>

<s> T' <emph type="other"/>GHEGHEVEN<emph.end/>. </s><s>Laet AB een pilaer sijn, welcke in die standt ghehouden wort door de scheefdaellini CD, ende de scheefheflini EF, de selue sijn voortghetrocken tot <emph type="other"/>GH<emph.end/>, sniende malcanderen in I. </s><s>T' <emph type="other"/>BEGHEERDE<emph.end/>. </s><s>Wy moeten bewysen dat I inde swaerheyts middellini is des pilaers AB. </s>

<s> T' <emph type="other"/>BEWYS<emph.end/>. </s><s>Laet ons HE ansien voor stijl, ofte stiue lini, ende nemen dat de macht die an E int opheffen was, nu opstekende sy in yder punt tusschen E en H, daermen haer stelt, ende den pilaer AB sal also op allen punten diemen tusschen <emph type="other"/>CG<emph.end/> ende <emph type="other"/>EH<emph.end/> voor uytersten neemt, sijn ghegheuen standt houden. </s><s>Laet ons nu nemen I ghemeen uyterste punt van d'een en dander lini, den pilaer dan houdt daer op sijn ghegheuen standt, maer rustende den pilaer op t'punt I, soo is de hanghende door I des pilaers swaerheydts middellini, inde welcke I is. </s><s>T' <emph type="other"/>BESLVYT<emph.end/>. </s><s>Twee oneuewydighe linien dan, daer een pilaer an hangt beyde oneyndelick voortghetrocken, snien malcanderen inde swaerheydts middellini des pilaers, t'welck wy bewysen moesten.</s>

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

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

<s> <emph type="other"/>SOO<emph.end/> d'eene der twee linien daer een pilaer an hangt rechthouckich op den sichteinder <arrow.to.target n="marg160"/> is, d'ander salder oock rechthouckich op sijn: Ende sooder d'een scheefhouckich op is, dander salder oock scheefhouckich op wesen: Ende soo dese naer die neigt, die sal naer dese neighen: Maer so dese van die wyckt, die sal oock van dese wycken. </s>

<s>

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<s> <emph type="other"/>VOORDER<emph.end/> , anghesien EF neigt naer de sijde van A, soo sal de lini die den pilaer in die ghestalt houdt moeten neighen naer EF. </s><s>Want laetse (soot mueghelick waer) daer van wycken, als CK, sniende de voortghetrocken EI in K, inder voughen dat de hanghende lini door K, sal om de redenen als bouen swaerheydts middellini wesen des pilaers, t'welck noch ongheschicter is dan doen wy die seyden door I te vallen: D'ander lini dan die den pilaer in de ghestalt can houden, en wyckt van EF niet, sy en is met haer oock gheen euewydighe als bouen bethoont is, ende ter sijden uyt te wijcken is openbaer onmueghelick, sy neigt dan nootsaecklick naer EF. </s><s>Ende soo EF ouer d'ander sijde neigde, men sal insghelijcx bethoonen dat d'ander lini van haer wycken sal. </s><s> T' <emph type="other"/>BESLVYT<emph.end/>. </s><s>Soo d'eene dan der twee linien, &c.</s>

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

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

<s> <emph type="other"/>HANGHENDE<emph.end/> een pilaer euestaltwichtich teghen twee scheefhefwichten: Ghelijck scheefheflini tot rechtheflini, alsoo elck scheefhefwicht tot sijn rechthefwicht. </s>

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

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

<s> <emph type="other"/>ALLE<emph.end/> de eueredenheden <arrow.to.target n="marg162"/> , welcke hier vooren beschreuen sijn vanden pilaer tot de ghewichten an hem hanghende, ende dier ghewichten linien: De selue te wesen van yder lichaem tot de ghewichten an hem alsoo hanghende, ende dier ghewichten linien. </s>

<s>

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<s> T' <emph type="other"/>GHEGHEVEN<emph.end/>. </s><s>Laet ABCD een gheschickt ofte inschriuelick vijfhouck wesen, diens formens middelpunt F sy. </s><s>T' <emph type="other"/>BEGHEERDE<emph.end/>. </s><s>Wy moeten bewysen dat F oock het swaerheyts middelpunt is. </s><s>T' <emph type="other"/>BEREYTSEL<emph.end/>. </s><s>Laet ghetrocken worden van A tot int middel van DC, de lini AG; sghelijcx van B tot int middel van ED, de lini BH. </s><s>T' <emph type="other"/>BEWYS<emph.end/>. </s><s>Wesende den vijfhouck opghehanghen byde lini AG, het deel AGDE sal euewichtich hanghen teghen het deel AGCB, want sy sijn euegroot, ghelijck, ende van ghelijcker ghestalt: AG dan is swaerheyts middellini des vijfhoucx, ende om de selue reden sal BH oock des selfden vijfhoucx swaerehyts middellini wesen; maer dese doorsnien malcanderen in des formens middelpunt F, ende elck dier linien heeft in haer het swaerheyts middelpunt, tis dan F. </s><s> Sghelijcx sal oock t'bewys sijn in allen anderen hebbende een formens middelpunt als Seshoucken, Ronden, Scheefronden, &c. </s><s>T' <emph type="other"/>BESLVYT<emph.end/>. </s><s>Yder plats middelpunt der form dan, is oock sijn swaerheyts middelpunt, t'welck wy bewysen moesten.</s>

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

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

<s> <emph type="other"/>YDER<emph.end/> driehoucx swaerheydts middelpunt, is inde lini ghetrocken vanden houck tot int middel der sijde. </s>

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<s>I. <emph type="other"/>EYSCH<emph.end/>. <emph type="other"/>III<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s>I. <emph type="other"/>EYSCH. III. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> ghegheuen een driehouck: Sijn swaerheyts middelpunt te vinden. </s>

<s> T' <emph type="other"/>GHEGHEVEN<emph.end/>. </s><s>Laet ABC een driehouck wesen. </s><s>T' <emph type="other"/>BEGHEERDE<emph.end/>. </s><s>Wy moeten sijn swaerheytds middelpunt vinden. </s><s> T' <emph type="other"/>WERCK<emph.end/>. </s><s>Men sal van A tot int middel van BC, trecken de lini AD, sghelijcx van C tot int middel van AB, de lini CE, sniende AD in F: Ick seg dat F t'begheerde swaerheydts middelpunt is. </s><s>T' <emph type="other"/>BEWYS<emph.end/>. </s><s>T'swaerheyts middelpunt des driehoucx ABC, is inde lini AD, ende oock in CE, duer het 2 voorstel, tis dan F, t'welck wy bewysen moesten. </s><s>T' <emph type="other"/>BESLVYT<emph.end/>. </s><s>Wesende dan ghegheuen een driehouck: Wy hebben sijn swaerheydts middelpunt gheuonden naer den eysch.</s>

<s><emph type="other"/>III<emph.end/>. <emph type="other"/>VERTOOCH<emph.end/>. <emph type="other"/>IIII<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s><emph type="other"/>III. VERTOOCH. IIII. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>HET<emph.end/> swaerheydts middelpunt eens driehoucx deelt de lini vanden houck tot int middel der sijde alsoo, dattet stick naer den houck, dobbel is an t'ander. </s>

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<s><emph type="other"/>IIII<emph.end/>. <emph type="other"/>VERTOOCH<emph.end/>. V. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s><emph type="other"/>IIII. VERTOOCH<emph.end/>. V. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> twee sijden eens driehoucx elck ghedeelt in drie euen deelen: De lini tusschen de twee punten der deeling naest de derde sijde, streckt door des driehoucx swaerheyts middelpunt. </s>

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<s><emph type="other"/>II<emph.end/>. <emph type="other"/>EYSCH<emph.end/>. <emph type="other"/>VI<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s><emph type="other"/>II. EYSCH. VI. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> ghegheuen een rechtlinich plat <arrow.to.target n="marg194"/>: Sijn swaerheyts middelpunt te vinden. </s>

<s>

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

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

<s> <emph type="other"/>HET<emph.end/> swaerheyts middelpunt des vierhoucx met twee euewydighe <arrow.to.target n="marg206"/> sijden, is inde lini tusschen dier sijden middelpunten. </s>

<s>

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<s> Maer den driehouck GEB, is oock euestaltwichtich teghen den driehouck GEA, daerom van euestaltwychtighe ghetrocken euestaltwichtighe, de resten als de vierhoucken EFDA, EFCB, sullen noch euestaltwichtich blijuen, ende haer swaerheyts middelpunt noch inde lini GF, maer niet uyt de form in EG; Nootsaecklick dan in EF. </s><s>T' <emph type="other"/>BESLVYT<emph.end/>. </s><s>Het swaerheydts middelpunt dan des vierhoucx met twee euewydighe sijden, is inde lini tusschen dier sijden middelpunten, t'welck wy bewysen moesten.</s>

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

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

<s> <emph type="other"/>HET<emph.end/> swaerheyts middelpunt des vierhoucx met twee euewydighe sijden, deelt de lini tusschen dier euewydighens middelpunten also, dat het stick naer de minste sijde, tot het ander, sulcken reden heeft, als tweemaal de meeste sijde met eenmael de minste, tot tweemael de minste met eenmael de meeste. </s>

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<s><emph type="other"/>III<emph.end/>. <emph type="other"/>EYSCH<emph.end/>. <emph type="other"/>IX<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>. </s>

<s><emph type="other"/>III. EYSCH. IX. VOORSTEL<emph.end/>. </s>

<s> <emph type="other"/>WESENDE<emph.end/> ghegheuen t'swaerheyts middelpunt eens plats ende sijns deels, wiens reden an t'ander deel kennelick is: Het swaerheyts middelpunt van t'ander deel te vinden. </s>

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<s> Latet nu wesen <pb pagenum="77"/>(soot mueghelick waer) tusschen de punten <emph type="other"/>EG<emph.end/> als I; Maer den langsten erm EF sal dan meerder reden hebben tot den cortsten EI, dan de swaerste swaerheyt BDC tot de lichtste BDA, twelck teghen het voorstel des I boucx waer. </s><s>Ten is dan tusschen <emph type="other"/>EG<emph.end/> niet: Sghelijcx salmen oock bethoonen dattet bouen G niet en is. </s><s>Tis dan nootsaecklick G, t'welck wy bewysen moesten.</s>

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

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

<s> T' <emph type="other"/>GHEGHEVEN<emph.end/>. </s><s>Laet ABCD een rondt wesen, diens halfmiddellini <arrow.to.target n="marg210"/> EA, ende swaerheyts middelpunt E sy, ende trondt AFGH, deel des rondts ABCD, ende sijn swaerheyts middelpunt I, ende middellini <arrow.to.target n="marg211"/> AG. </s><s>T' <emph type="other"/>BEGHEERDE<emph.end/>. </s><s>Wy moeten het swaerheyts middelpunt vinden des ander deels, dat is der maen ABCDHGF. </s><s> T' <emph type="other"/>WERCK<emph.end/>. </s><s>Men sal IE voorttrecken tot in K, also dat IE sulcken reden hebbe tot EK, als de maen ABCDHGF tot het rondt AFGH, ende K sal t'begheerde swaerheydts middelpunt wesen. </s><s>Daer af t'bewys ghelijck sal sijn an tvoorgaende. </s><s>Maer om de reden dier maen tot dat rondt te vinden, men sal trecken CL euen met AG, daernaer AL, vindende <arrow.to.target n="marg212"/> de derde everednighe welcker eerste AL, de tweede LC, ende de derde sy M, Ende AL tot M, sal de reden sijn der maen tot het rondt AFGH. </s><s> Want ouermits ALC rechthouck is (reden dat sy int half rondt staet <arrow.to.target n="marg213"/>) het ront diens middellini AL, sal euen sijn ande maen, ende AL tot M is de ghedobbelde reden <arrow.to.target n="marg214"/> van AL tot LC, dat is van AL tot AG, daerom &c.</s>

<s>

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<s> Sghelijcx soudemen voortvaren dat int rondt ABCD meer ronden ghebraken; by voorbeelt het rondt NO, wiens middelpunt P. </s><s>Want <pb pagenum="78"/>PK voortghetrocken tot in Q, alsoo dat PK sulcken reden hadde tot KQ, als het restende tot het rondt NO, so soude Q t'begheerde swaerheyts middelpunt sijn. </s><s>Ende alsoo met allen anderen formen welcker deelen reden kennelick is. </s><s>T' <emph type="other"/>BESLVYT<emph.end/>. </s><s>Wesende dan ghegheuen de swaerheyts middelpunten eens plats ende sijns deels, wiens reden an t'ander deel kennelick is: wy hebben het swaerheyts middelpunt gheuonden des ander deels naer den eysch.</s>

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

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

<s> <emph type="other"/>YDER<emph.end/> brantsnees <arrow.to.target n="marg215"/> swaerheyts middelpunt is in haer middellini. </s>

<s>

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

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

<s> <emph type="other"/>ALLER<emph.end/> brantsneens middellinien worden van het swaerheyts middelpunt eueredelick <arrow.to.target n="marg219"/> ghedeelt. </s>

<s>

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</s>

<s><emph type="other"/>IIII<emph.end/>. <emph type="other"/>EYSCH<emph.end/>. <emph type="other"/>XII<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>. </s>

<s><emph type="other"/>IIII. EYSCH. XII. VOORSTEL<emph.end/>. </s>

<s> <emph type="other"/>WESENDE<emph.end/> ghegheuen een brantsne <arrow.to.target n="marg242"/>: Huer swaerheyts middelpunt te vinden </s>

<s>

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<s>V. <emph type="other"/>EYSCH<emph.end/>. <emph type="other"/>XIII<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>. </s>

<s>V. <emph type="other"/>EYSCH. XIII. VOORSTEL<emph.end/>. </s>

<s> <emph type="other"/>WESENDE<emph.end/> ghegheuen een ghecorte brantsne: Huer swaerheyts middelpunt te vinden </s>

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

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

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

<s> <emph type="other"/>YDER<emph.end/> lichaems formens middelpunt, is oock sijn swaerheyts middelpunt. </s>

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<s> Sghelijcx sal oock t'bewys sijn van allen lichamen hebbende middelpunten der form, soo wel vermeerde ende ghecorte gheschicte lichamen, als gheschicte, want soomense ophangt byde middellinien deur eenighen lichamelicken houck, ofte duer het middelpunt haerder gronden ende des formens middelpunt, soo hebben al de naelden (wiens ghemeene sop het formens middelpunt, ende gronden de platten des lichaems sijn) tot allen sijden ghelijcke ghestalt, daerom oock duer ghemeene wetenschap, ende duer de begheerte des I boucx, alles hangt an die lini euewichtich, ende veruolghens de sne sulcker twee swaerheyts middellinien malcander sniende in des formens middelpunt, is ock het sawerheyts middelpunt. </s><s>T' <emph type="other"/>BESLVYT<emph.end/>. </s><s>Yder lichaems formens middelpunt dan, is oock sijn swaerheyts middelpunt.</s>

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

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

<s> <emph type="other"/>YDER<emph.end/> pilaers swaerheyts middelpunt is int middel vanden as. </s>

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<s> T' <emph type="other"/>GHEGHEVEN<emph.end/>. </s><s>Laet AB een vierhouckich pilaer wesen, diens grondt ACDE. </s><s>T' <emph type="other"/>BEGHEERDE<emph.end/>. </s><s>Wy moeten bewysen dat sijn swaerheyts middelpunt int middel vanden as is. </s><s>T' <emph type="other"/>BERYTSEL<emph.end/>. </s><s>Laet ons trecken een plat duer AD, ende haer lijckstandighe int decksel, deelende also den ghegheuen pilaer in twee driehouckighe pilaren, welcker yder het swaerheyts middelpunt int middel vanden as heeft duer het I voorbeelt, daerom ghetrocken den balck tusschen die twee punten, ende den seluen ghedeelt in sijn ermen, het onderscheydt der ermen sal het swaerheyts middelpunt sijn des ghegheuen pilaers, welck punt valt in t'swaerheyts middelpunt des plats euewydich vanden grondt den pilaer in twee euen stucken deelende, ende t'selue int middel der lini tusschen de swaerheyts middelpunten des gronts ende decksels, dat is int middel vanden as; T'selue salmen oock alsoo bethoonen in yder pilaer. </s><s>T' <emph type="other"/>BESLVYT<emph.end/>. </s><s>Yder pilaers swaerheyts middelpunt dan, is int middel vanden as, t'welck wy bewysen moesten.</s>

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

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

<s> <emph type="other"/>YDER<emph.end/> naeldens <arrow.to.target n="marg253"/> swaerheyts middelpunt is inden as. </s>

<s>

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<s><emph type="other"/>VI<emph.end/>. <emph type="other"/>EYSCH<emph.end/>. <emph type="other"/>XVII<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s><emph type="other"/>VI. EYSCH. XVII. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> ghegheuen een naelde: Huer swaerheyts middelpunt te vinden. </s>

<s> T' <emph type="other"/>GHEGHEVEN<emph.end/>. </s><s>Laet ABCD een naelde wesen, diens grondt sy den driehouck BCD. </s><s>T' <emph type="other"/>BEGHEERDE<emph.end/>. </s><s>Wy moeten haer swaerheyts middelpunt vinden. </s><s>T' <emph type="other"/>WERCK<emph.end/>. </s><s>Men sal de swaerheyts middelpunten vinden van eenighe twee driehoucken, als E van BCD, ende F van ADC, treckende de linien AE, BF; welcker sne G, ick seg te wesen het begheerde swaerheyts middelpunt. </s><s>T' <emph type="other"/>BEWYS<emph.end/>. </s><s>Des naldens ABCD swaerheyts middelpunt is in AE, ende oock in BF, duer het I6 voorstel, het is dan nootsaeclick G. </s><s> T' <emph type="other"/>BESLVYT<emph.end/>. </s><s>Wesende dan ghegheuen een naelde: Wy hebben huer swaerheyts middelpunt gheuonden naer den eysch.</s>

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

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

<s> <emph type="other"/>HET<emph.end/> swaerheyts middelpunt van yder naelde deelt den as alsoo, dat het stick naer den houck drievoudich is an t'ander. </s>

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<s><emph type="other"/>VIIEYSCH<emph.end/>. <emph type="other"/>XIXVOORSTEL<emph.end/>.</s>

<s><emph type="other"/>VIIEYSCH. XIXVOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> ghegheuen t'swaerheyts middelpunt eens lichaems ende sijns deels, wiens reden an t'ander deel kennelick is: Het swaerheyts middelpunt des ander deels te vinden. </s>

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<s> T' <emph type="other"/>GHEGHEVEN<emph.end/>. </s><s>Laet ABCDEF een ghecorte naelde sijn, diens decksel ABC, ende grondt DEF. </s><s>T' <emph type="other"/>BEGHEERDE<emph.end/>. </s><s>Wy moeten huer swaerheyts middelpunt vinden. </s><s>T' <emph type="other"/>WERCK<emph.end/>. </s><s>Men sal de ghecorte naelde volmaken, daer an stellende het ghebrekende ABCG, vindende H swaerheyts middelpunt des driehoucx DEF, treckende den as GH, wiens punt inden driehouck ABC, sy I, daernaer salmen teeckenen K, alsoo dat GK drievoudich sy an KI: Insghelijcx L, also dat GL drievoudich sy an LH, teeckenende M, alsoo dat KL sulcken reden hebbe tot LM, ghelijck de ghecorte naelde ABCDEF, tot de naelde ABCG, Ick seg dat M t'begheerde swaerheyts middelpunt is. </s><s>T' <emph type="other"/>BEWYS<emph.end/>. </s><s>L is swaerheyts middelpunt des heels, ende K des deels, ende ghelijck t'onderste deel tottet bouenste, also KL tot LM, Daerom M, door het voorstel des I boucx is t'begheerde swaerheyts middelpunt, t'welck wy bewysen moesten. </s><s>Sghelijcx sal oock den voortganck sijn in allen anderen ghecorte naelden. </s><s>T' <emph type="other"/>BESLVYT<emph.end/>. </s><s>Wesende dan ghegheuen een ghecorte naelde: Wy hebben huer swaerheyts middelpunt gheuonden, naer den eysch.</s>

<s><emph type="other"/>IX<emph.end/>. <emph type="other"/>EYSCH<emph.end/>. <emph type="other"/>XXI<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s><emph type="other"/>IX. EYSCH. XXI. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> ghegheuen een platgrondich lichaem soodanigher form alst valt: Sijn swaerheyts middelpunt te vinden. </s>

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<s><emph type="other"/>XIII<emph.end/>. <emph type="other"/>VERTOOCH<emph.end/>. <emph type="other"/>XXII<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s><emph type="other"/>XIII. VERTOOCH. XXII. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>YDER<emph.end/> branders <arrow.to.target n="marg269"/> swaerheyts middelpunt is inden as. </s>

<s>

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<s>X. <emph type="other"/>EYSCH<emph.end/>. <emph type="other"/>XXIII<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s>X. <emph type="other"/>EYSCH. XXIII. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> ghegheuen een brander: Huer swaerheyts middelpunt te vinden. </s>

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<s> <emph type="other"/>ANGHESIEN<emph.end/> des driehoucx lini vanden houck tot int middel der sijde, van t'swaerheyts middelpunt in sulcken reden ghedeelt wordt, als desen as des branders duer het voorstel, soo volgt dat inden driehouck der ghelijcke ghedaenten sullen beuonden worden duer omschreuen ende binneschreuen vierhoucken, ghelijck hier vooren gheschiet is met omschreuen ende binneschreuen pilaren.</s>

<s><emph type="other"/>XI<emph.end/>. <emph type="other"/>EYSCH<emph.end/>. <emph type="other"/>XXIIII<emph.end/>. <emph type="other"/>VOORSTEL<emph.end/>.</s>

<s><emph type="other"/>XI. EYSCH. XXIIII. VOORSTEL<emph.end/>.</s>

<s> <emph type="other"/>WESENDE<emph.end/> ghegheuen een ghecorten brander: Huer swaerheyts middelpunt te vinden. </s>

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