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version 1.96, 2003/09/10 11:37:38

version 1.102, 2003/09/11 00:56:13

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

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

<s> <emph type="other"/>T'GHEGHEVEN<emph.end/>. </s><s>Laet ABC een driehouck wesen, van t'welck yder sijde AB ende BC ghedeelt sy in drie euen deelen, met de punten D, E, F, G, ende tusschen de punten E, G, naest de derde sijde BC, sy ghetrocken de lini EG. </s><s><emph type="other"/>T'BEGHEERDE<emph.end/>. </s><s>Wy moeten bewysen dat EG duer des driehoucx ABC swaerheyts middelpunt streckt <emph type="other"/>T'BEREYTSEL<emph.end/>. </s><s>Laet ons trecken van A tot int middel van BC, de lini AH, sniende EG in I. </s><s><emph type="other"/>T'BEWYS<emph.end/>. </s><s>Ouermits <arrow.to.target n="marg193"/> AE sulcken reden heeft tot EB, als AG tot GC, soo is EG euewydighe met BC, ende veruolghens EI is euewydighe met BH, daerom ghelijck AE tot EB, alsoo AI tot IH, maer AE is dobbel tot EB door t'ghegheuen, daerom AI is dobbel tot IH, maer wesende AI dobbel tot IH, soo is I t'swaerheyts middelpunt des driehoucx ABC door het 4 voorstel, daerom EG streckt door des ghegheuen driehoucx swaerheyts middelpunt. </s><s><emph type="other"/>T'BESLVYT<emph.end/>. </s><s>Wesende dan 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, t'welck wy bewysen moesten. </s>

<s><emph type="other"/>T'BEREYTSEL<emph.end/>. </s><s>Laet ons trecken van A tot int middel van BC, de lini AH, sniende EG in I. </s><s><emph type="other"/>T'BEWYS<emph.end/>. </s><s>Ouermits <arrow.to.target n="marg193"/> AE sulcken reden heeft tot EB, als AG tot GC, soo is EG euewydighe met BC, ende veruolghens EI is euewydighe met BH, daerom ghelijck AE tot EB, alsoo AI tot IH, maer AE is dobbel tot EB door t'ghegheuen, daerom AI is dobbel tot IH, maer wesende AI dobbel tot IH, soo is I t'swaerheyts middelpunt des driehoucx ABC door het 4 voorstel, daerom EG streckt door des ghegheuen driehoucx swaerheyts middelpunt. </s><s><emph type="other"/>T'BESLVYT<emph.end/>. </s><s>Wesende dan 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, t'welck wy bewysen moesten. </s>

<s>

<margin.target id="marg193"/>2. v. 6. B. E.

</s>

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

Line 1644

Line 1643

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

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

<s> <emph type="other"/>T'GHEGHEVEN<emph.end/>. </s><s>Laet ABCD een ongheschict vierhouck wesen. </s><s><emph type="other"/>T'BEGHEERDE<emph.end/>. </s><s>Wy moeten sijn swaerheyts middelpunt vinden.</s>

Line 1659

Line 1658

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

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

<s> <emph type="other"/>T'GHEGHEVEN<emph.end/>. </s><s>Laet ABCDE een ongheschickt vijfhouck sijn. </s>

<s><emph type="other"/>T'BEGHEERDE<emph.end/>. </s><s>Wy moeten sijn swaerheyts middelpunt vinden. </s>

<s> <emph type="other"/>T'GHEGHEVEN<emph.end/>. </s><s>Laet ABCDE een ongheschickt vijfhouck sijn. </s><s><emph type="other"/>T'BEGHEERDE<emph.end/>. </s><s>Wy moeten sijn swaerheyts middelpunt vinden. </s><s><emph type="other"/>T'WERCK<emph.end/>. </s><s>Men sal trecken AC, ende vinden t'swaerheyts middelpunt des driehoucx ACB door het 3 voorstel, t'welck F sy, ende vanden vierhouck ACDE duer t'voorgaende I voorbeelt, t'welck G sy, ende de lini FG sal balck wesen, daer naer salmen maken twee euewydighe vierhoucken van een selfde hoochde, als HIKL euen anden vierhouck ACDE, ende HIMN euen anden driehouck ACB, deelende den balck GF in O, alsoo dat den erm OF, sulcken reden hebbe tot den erm OG, als IK tot IM; Ick seg dat O t'begheerde swaerheyts middelpunt is.</s>

<s><emph type="other"/>T'WERCK<emph.end/>. </s><s>Men sal trecken AC, ende vinden t'swaerheyts middelpunt des driehoucx ACB door het 3 voorstel, t'welck F sy, ende vanden vierhouck ACDE duer t'voorgaende I voorbeelt, t'welck G sy, ende de lini FG sal balck wesen, daer naer salmen maken twee euewydighe vierhoucken van een selfde hoochde, als HIKL euen anden vierhouck ACDE, ende HIMN euen anden driehouck ACB, deelende den balck GF in O, alsoo dat den erm OF, sulcken reden hebbe tot den erm OG, als IK tot IM; Ick seg dat O t'begheerde swaerheyts middelpunt is.</s>

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

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

<s> <emph type="other"/>T'GHEGHEVEN<emph.end/>. </s><s>Laet ABCDEF een ongheschickt seshouck sijn. </s><s><emph type="other"/>T'BEGHEERDE<emph.end/>. </s><s>Wy moeten sijn swaerheyts middelpunt vinden. </s><s><emph type="other"/>T'WERCK<emph.end/>. </s><s>Men sal trecken AC, ende vinden t'swaerheydts middelpunt des driehoucx ACB duer het 3 voorstel, t'welck G sy, ende vanden vijfhouck ACDEF, duer het voorgaende 2 voorbeelt, t'welck H sy, ende de lini GH sal balck wesen. </s><s>Daer naer salmen maken twee euewydighe vierhoucken van een selfde hoochde, als IKLM, euen anden vijfhouck ACDEF, ende IKNO <pb pagenum="72"/>euen anden driehouck ACB, deelende den balck HG in P, alsoo dat den erm PG, sulcken reden hebbe tot den erm PH, als de lini KM tot KN; Ick seg dat P t'begheerde swaerheyts middelpunt is. </s><s>Welcke maniere van wercking in allen anderen veelsijdeghe platten ghelijck sal sijn ande voorgaende.</s>

<s><emph type="other"/>T'WERCK<emph.end/>. </s><s>Men sal trecken AC, ende vinden t'swaerheydts middelpunt des driehoucx ACB duer het 3 voorstel, t'welck G sy, ende vanden vijfhouck ACDEF, duer het voorgaende 2 voorbeelt, t'welck H sy, ende de lini GH sal balck wesen. </s><s>Daer naer salmen maken twee euewydighe vierhoucken van een selfde hoochde, als IKLM, euen anden vijfhouck ACDEF, ende IKNO <pb pagenum="72"/>euen anden driehouck ACB, deelende den balck HG in P, alsoo dat den erm PG, sulcken reden hebbe tot den erm PH, als de lini KM tot KN; Ick seg dat P t'begheerde swaerheyts middelpunt is. </s><s>Welcke maniere van wercking in allen anderen veelsijdeghe platten ghelijck sal sijn ande voorgaende.</s>

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

<s> Wy heben hier bouen voorbeelden beschreuen alwaer t'ghegheuen plat verkeert wort in euenhooghe ende euewydighe vierhoucken, wy connen t'selfde oock doen sonder soodanighe verkeering, daer af wy verscheyden voorbeelden beschrijuen sullen als volght.</s>

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

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

<s> <emph type="other"/>T'GHEGHEVEN<emph.end/>. </s><s>Laet ABCD een ongheschickt vierhouck wesen. </s><s><emph type="other"/>T'BEGHEERDE<emph.end/>. </s><s>Wy moeten sijn swaerheydts middelpunt vinden. </s><s><emph type="other"/>T'WERCK<emph.end/>. </s><s>Men sal den vierhouck deelen in twee driehoucken, met de lini AC, ende vinden t'swaerheydts middelpunt van elcken driehouck door het 3 voorstel, dat van ACB sy E, ende vanden driehouck ACD sy F, de lini dan EF is balck. </s><s>Daer naer salmen trecken DG ende BH, beyde rechthouckich op AC, deylende den balck FE en I, alsoo dat den erm IE, sulcken reden hebbe tot den erm IF, als DG tot BH; Ick seg dat I t'begheerde swaerheyts middelpunt is.</s>

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

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

<s> <emph type="other"/>T'GHEGHEVEN<emph.end/>. </s><s>Laet ABCDE een ongheschickt vijfhouck sijn. </s><s><emph type="other"/>T'BEGHEERDE<emph.end/>. </s><s>Wy moeten sijn swaerheyts middelpunt vinden. </s><s><emph type="other"/>T'WERCK<emph.end/>. </s><s>Men sal den vijfhouck deelen in drie driehoucken, met eenighe linien als AD, AC, vindende daer naer het swaerheyts middelpunt des vierhoucx ACDE duer het 4 voorbeelt, t'welck F sy, ende des driehoucx ACB duer het 3 voorstel, t'welck G sy, ende de lini FG, is balck, Daer naer ghetrocken BH rechthouckich op AC; Ende CI met EK rechthouckich op AD, men sal der drie linien AD, AC, HB, vinden de vierde euerednighe <arrow.to.target n="marg197"/>, welcke sy LM, deelende den balck <arrow.to.target n="marg198"/> FG in N, alsoo dat den erm NG sulcken reden hebbe tot den erm NF, ghelijck CI met EK, tot LM; Ick seg dat N het begheerde swaerheydts middelpunt is.</s>

<s>

<margin.target id="marg197"/>Proportionalis.

<margin.target id="marg198"/>Door het I2. v. 6. B. E.

</s>

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

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

<s> <emph type="other"/>T'GHEGHEVEN<emph.end/>. Laet ABCDEF een ongheschickt seshouck sijn. <emph type="other"/>T'BEGHEERDE<emph.end/>. Wy moeten sijn swaerheydts middelpunt vinden.</s>

<s> <emph type="other"/>T'WERCK<emph.end/>.</s><s> Men sal den seshouck deelen in vier driehoucken, met eenighe linien als AC, AD, FD, vindende daer naer het swaerheyts middelpunt des vierhoucx ADCB door het 4. voorbeelt, t'welck G sy, ende des vierhoucx ADEF, t'welck H sy, ende de lini HG is balck. </s><s>Daernaer ghetrocken BI ende DK rechthouckich op AC, insghelijcx AL ende EM beyde rechthouckich op FD, men sal der drie linien welcker eerste FD, de tweede AC, de derde BI met KD, vinden de vierde euerednighe, welcke NO sy, deelende den balck HG in P, also dat den erm PG, sulcken reden hebbe tot den erm PH, ghelijck AL met EM, tot NO; Ick seg dat P het begheerde swaerheyts middelpunt is.

</s><s>Ende soo salmen voort mueghen varen met ander veelhouckeghe platten.

</s>

<s>

<s> <emph type="other"/>T'BEWYS<emph.end/>. </s><s>Ghelijck int eerste voorbeelt HI tot HL, alsoo den erm NE tot den erm NF, maer <arrow.to.target n="marg199"/> ghelijck HI tot HL, alsoo den vierhouck GHIK, tot den vierhouck GHLM, ghelijck dan GHIK tot GHLM, also NE tot NF, maer GHIK is euen an den driehouck ACD, ende GHLM anden driehouck ACB door t'werck, ghelijck dan den driehouck ACD tot ACB, alsoo den erm NE tot NF. </s><s> Het punt dan N is (door het voorstel des I boucx) des vierhoucx swaerheyts middelpunt. </s><s>Sghelijcx sal oock bewijs sijn des 2 ende 3 voorbeelts. </s><s> T'vierde voorbeelt is openbaer als wy bewesen hebben dat ghelijck DG, tot HB, alsoo den driehouck ACD, tot ACB in deser voughen: Nemende AC voor hoochde, ende DG ende HB voor gronden, soo heeft den rechthouck begrepen onder AC ende DG, sulcken reden tot den rechthouck onder AC ende HB, ghelijck DG tot HB <arrow.to.target n="marg200"/>; Maer ghelijck dien rechthouck tot desen, alsoo den driehouck ACD tot ACB, want elck driehouck is sijn rechthoucx helft <arrow.to.target n="marg201"/>, ghelijck dan DG tot HB, alsoo den driehouck ACD tot ACB. </s><s>Des 5 voorbeelts bewys sal oock claer sijn als wy bewesen hebben, dat ghelijck EK met IC tot LM, alsoo den vierhouck ACDE tot den driehouck ACB, aldus: Anghesien LM vierde euerednighe is der drie AD, AC, HB, de rechthouck begrepen onder AD ende LM, sal euen sijn <arrow.to.target n="marg202"/> an den rechthouck begrepen onder AC ende HB, Laet ons nu EK, IC, LM, ansien voor gronden, wiens ghemeene hoochde AD; </s>

<s>

<margin.target id="marg199"/>I. v. 6. B. E.

</s>

<s> T'vierde voorbeelt is openbaer als wy bewesen hebben dat ghelijck DG, tot HB, alsoo den driehouck ACD, tot ACB in deser voughen: Nemende AC voor hoochde, ende DG ende HB voor gronden, soo heeft den rechthouck begrepen onder AC ende DG, sulcken reden tot den rechthouck onder AC ende HB, ghelijck DG tot HB <arrow.to.target n="marg200"/>; Maer ghelijck dien rechthouck tot desen, alsoo den driehouck ACD tot ACB, want elck driehouck is sijn rechthoucx helft <arrow.to.target n="marg201"/>, ghelijck dan DG tot HB, alsoo den driehouck ACD tot ACB. </s>

<s>

<margin.target id="marg200"/>I. v. 6. B. E.

<margin.target id="marg201"/>4I. v. I. B. E.

<margin.target id="marg202"/>I6. v. 6. B. E.

</s>

<s>Des 5. voorbeelts bewys sal oock claer sijn als wy bewesen hebben, dat ghelijck EK met IC tot LM, alsoo den vierhouck ACDE tot den driehouck ACB, aldus: Anghesien LM vierde euerednighe is der drie AD, AC, HB, de rechthouck begrepen onder AD ende LM, sal euen sijn <arrow.to.target n="marg202"/> an den rechthouck begrepen onder AC ende HB, Laet ons nu EK, IC, LM, ansien voor gronden, wiens ghemeene hoochde AD; </s><s> Maer <arrow.to.target n="marg203"/> ghelijck die gronden <pb pagenum="74"/>tot malcanderen, alsoo de rechthoucken begrepen onder haer ende hare ghemeene hoochde, daerom oock ghelijck de twee gronden EK, IC, tot den grondt LM, alsoo dier gronden rechthoucken tot deses grondts rechthouck; maer die twee rechthoucken sijn elck het dobbel haers driehoucx; Ghelijck dan EK met IC tot LM, also het dobbel vanden vierhouck ACDE tot den rechthouck begrepen onder AD ende LM: Maer desen is euen an den rechthouck begrepen onder AC ende HB als vooren betoocht is, ende de selue rechthouck begrepen onder AC ende HB is het dobbel des driehoucx ACB, daerom ghelijck EK met IC tot LM, alsoo het dobbel des vierhoucx ACDE tot het dobbel des driehoucx ACB, ende veruolghens ghelijck EK met IC tot LM, alsoo den vierhouck ACDE tot den driehouck ACB, waer uyt de reste openbaer is. </s><s>T'bewys van het 6 voorbeelt is duer dit oock kennelick ghenouch. </s><s><emph type="other"/>T'BESLVYT<emph.end/>. </s><s>Wesende dan ghegheuen een rechthouckich plat: Wy hebben sijn swaerheydts middelpunt gheuonden naer den eysch.</s>

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

<s> <emph type="other"/>T'GHEGHEVEN<emph.end/>. </s><s>Laet ABCDEF een ongheschickt seshouck sijn. </s><s><emph type="other"/>T'BEGHEERDE<emph.end/>. </s><s>Wy moeten sijn swaerheydts middelpunt vinden. </s><s><emph type="other"/>T'WERCK<emph.end/>. </s><s>Men sal den seshouck deelen in vier driehoucken, met eenighe linien als AC, AD, FD, vindende daer naer het swaerheyts middelpunt des vierhoucx ADCB door het 4 voorbeelt, t'welck G sy, ende des vierhoucx ADEF, t'welck H sy, ende de lini HG is balck. </s><s>Daernaer ghetrocken BI ende DK rechthouckich op AC, insghelijcx AL ende EM beyde rechthouckich op FD, men sal der drie linien welcker eerste FD, de tweede AC, de derde BI met KD, vinden de vierde euerednighe, welcke NO sy, deelende den balck HG in P, also dat den erm PG, sulcken reden hebbe tot den erm PH, ghelijck AL met EM, tot NO; Ick seg dat P het begheerde swaerheyts middelpunt is. </s><s> Ende soo salmen voort mueghen varen met ander veelhouckeghe platten. </s>

<s>[ Figuren ingevoegd: ]</s>

<s> Maer <arrow.to.target n="marg203"/> ghelijck die gronden <pb pagenum="74"/>tot malcanderen, alsoo de rechthoucken begrepen onder haer ende hare ghemeene hoochde, daerom oock ghelijck de twee gronden EK, IC, tot den grondt LM, alsoo dier gronden rechthoucken tot deses grondts rechthouck; maer die twee rechthoucken sijn elck het dobbel haers driehoucx; Ghelijck dan EK met IC tot LM, also het dobbel vanden vierhouck ACDE tot den rechthouck begrepen onder AD ende LM: Maer desen is euen an den rechthouck begrepen onder AC ende HB als vooren betoocht is, ende de selue rechthouck begrepen onder AC ende HB is het dobbel des driehoucx ACB, daerom ghelijck EK met IC tot LM, alsoo het dobbel des vierhoucx ACDE tot het dobbel des driehoucx ACB, ende veruolghens ghelijck EK met IC tot LM, alsoo den vierhouck ACDE tot den driehouck ACB, waer uyt de reste openbaer is. </s><s>T'bewys van het 6 voorbeelt is duer dit oock kennelick ghenouch. </s><s><emph type="other"/>T'BESLVYT<emph.end/>. </s><s>Wesende dan ghegheuen een rechthouckich plat: Wy hebben sijn swaerheydts middelpunt gheuonden naer den eysch.</s>

<s>

<margin.target id="marg202"/>I6. v. 6. B. E.

<margin.target id="marg203"/>I. v. 6. B. E.

</s>

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

<s> <emph type="other"/>MY<emph.end/> <arrow.to.target n="marg204"/>{Commentarius in quadraturam paraboles.} <arrow.to.target n="marg205"/></s>

<s> <emph type="other"/>MY<emph.end/> is onder het drucken ter handt ghecomen, Fredric Commandins <arrow.to.target n="marg205"/>verclaring ouer de viercanting der Brantsne van Archimedes, alwaer hy onder het 6 voorstel de manier beschrijft, om t'swaerheyts middelpunt te vinden van yder rechtlinich plat, ende dat op een ander wijse als de twee voorgaende. So ymant tottet ouersien der selue begheerich waer, salse daer vinden.

</s>

<s>

<margin.target id="marg204"/>is onder het drucken ter handt ghecomen, Fredric Commandins verclaring ouer de viercanting der Brantsne van Archimedes

<margin.target id="marg205"/>Commentarius in quadraturam paraboles.

<margin.target id="marg205"/>, alwaer hy onder het 6 voorstel de manier beschrijft, om t'swaerheyts middelpunt te vinden van yder rechtlinich plat, ende dat op een ander wijse als de twee voorgaende. So ymant tottet ouersien der selue begheerich waer, salse daer vinden.

</s>

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

Line 1753

Line 1732

</s>

<s> <emph type="other"/>T'GHEGHEVEN<emph.end/>. </s><s>Laet ABCD een vierhouck sijn, diens twee euewydighe sijden AB ende DC, ende de lini uyt E middel van AB, tot F middel van DC, sy EF. </s><s><emph type="other"/>T'BEGHEERDE<emph.end/>. </s><s>Wy moeten bewysen dat t'swaerheyts middelpunt des vierhoucx ABCD inde lini EF is. </s><s><emph type="other"/>T'BEREYTSEL<emph.end/>. </s><s>Laet de drie linien DA, FE, CB, voortghetrocken worden, welcke om de eueredenheyt <arrow.to.target n="marg207"/> der linien AE, EB, DF, FC, vergaren sullen in een selfde punt t'welck G sy. </s><s><emph type="other"/>T'BEWYS<emph.end/>. </s><s>Laet ons den driehouck GDC ophanghen byde lini GF, ende het deel GFC sal euestaltwichtich sijn, teghen GFD door het voorstel, waer deur oock t'swaerheyts mid<pb pagenum="75"/>delpunt des driehoucx GDC inde lini GF is.</s><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><emph type="other"/>T'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>

<margin.target id="marg207"/>Proportionem.

</s>

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

<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><emph type="other"/>T'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. 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>

<s> <emph type="other"/>T'GHEGHEVEN<emph.end/>. </s><s>Laet ABCD een vierhouck wesen met twee euewydighe sijden AB, DC, ende de lini tusschen haer middelpunten sy EF, ende t'swaerheydts middelpunt sy G. </s><s><emph type="other"/>T'BEGHEERDE<emph.end/>. </s><s>Wy moeten bewysen dat ghelijck tweemael DC met eenmael AB, tot tweemael AB met eenmael DC. </s><s>also GE tot GF. </s><s><emph type="other"/>T'BEREYTSEL<emph.end/>. </s><s>Laet ghetrocken worden DB, ende ghedeelt in drie euen deelen met de punten H, I, ende door de selue ghetrocken worden KL, ende MN, euewydich van DC, sniende EF in O en P. </s><s>Daer naer de lini DE, sniende MI in Q, Ende BF sniende KL in R, Ende ten laetsten RQ. </s><s><emph type="other"/>T'BEWYS<emph.end/>. </s><s>Anghesien het swaerheydts middelpunt des driehoucx BDC, is in BF, duer het voorstel, ende oock in HL duer het voorstel, soo is R, sijn swaerheyts middelpunt, ende om de selue reden is Q swaerheyts middelpunt des driehoucx ABD, ende QR is dier driehoucken balck, inden welcken haer beyder, dat is des vierhoucx ABCD, swaerheyts <pb pagenum="76"/>middelpunt is, t'selue is oock in EF duer het voorstel, daerom G is t'swaerheyts middelpunt des vierhoucx ABCD. </s><s>Maer want de twee driehoucken CDB ende ABD sijn tusschen twee euewydighe AB ende DC, so sijn sy inde reden van haer gronden <arrow.to.target n="marg208"/>, dat is ghelijck den driehouck CDB tot ABD, alsoo DC tot AB: Maer ghelijck den driehouck CDB tot ADB, also den erm GQ tot GR duer het voorstel des I boucx, ghelijck dan DC tot AB, alsoo GQ tot GR; maer ghelijck GQ tot GR, alsoo PG tot GO (want sy tusschen de euewydeghe MN, KL sijn) ghelijck dan DC tot AB, alsoo GP tot PO [GO], daerom oock ghelijck tweemael DC met eenmael AB, tot tweemael AB met eenmael DC, also tweemael GP met eenmael GO, tot tweemael GO met eenmael GP. </s><s> Maer GE is euen an tweemael GP met eenmael GO, ende GF is euen an tweemael GO met eenmael GP, daerom ghelijck tweemael DC met eenmael AB, tot tweemael AB met eenmael DC, alsoo GE tot GF. </s><s><emph type="other"/>T'BESLVYT<emph.end/>. </s><s>Het swaerheyts middelpunt dan des vierhoucx met twee, &c.</s>

<s><emph type="other"/>T'BEWYS<emph.end/>. </s><s>Anghesien het swaerheydts middelpunt des driehoucx BDC, is in BF, duer het voorstel, ende oock in HL duer het voorstel, soo is R, sijn swaerheyts middelpunt, ende om de selue reden is Q swaerheyts middelpunt des driehoucx ABD, ende QR is dier driehoucken balck, inden welcken haer beyder, dat is des vierhoucx ABCD, swaerheyts <pb pagenum="76"/>middelpunt is, t'selue is oock in EF duer het voorstel, daerom G is t'swaerheyts middelpunt des vierhoucx ABCD. </s><s>Maer want de twee driehoucken CDB ende ABD sijn tusschen twee euewydighe AB ende DC, so sijn sy inde reden van haer gronden <arrow.to.target n="marg208"/>, dat is ghelijck den driehouck CDB tot ABD, alsoo DC tot AB: Maer ghelijck den driehouck CDB tot ADB, also den erm GQ tot GR duer het voorstel des I boucx, ghelijck dan DC tot AB, alsoo GQ tot GR; maer ghelijck GQ tot GR, alsoo PG tot GO (want sy tusschen de euewydeghe MN, KL sijn) ghelijck dan DC tot AB, alsoo GP tot PO [GO], daerom oock ghelijck tweemael DC met eenmael AB, tot tweemael AB met eenmael DC, also tweemael GP met eenmael GO, tot tweemael GO met eenmael GP. </s><s> Maer GE is euen an tweemael GP met eenmael GO, ende GF is euen an tweemael GO met eenmael GP, daerom ghelijck tweemael DC met eenmael AB, tot tweemael AB met eenmael DC, alsoo GE tot GF. </s><s><emph type="other"/>T'BESLVYT<emph.end/>. </s><s>Het swaerheyts middelpunt dan des vierhoucx met twee, &c.</s>

<s>

<margin.target id="marg208"/>I. v. 6. B. E.

</s>

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