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Colored diff for /texts/archimedes/xml/Attic/stevi_weegc_01_nl_1586.xml between version 1.38 and 1.41

version 1.38, 2003/09/08 13:38:51

version 1.41, 2003/09/08 14:30:28

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

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

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

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

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

<s> <emph type="other"/>TGHEGHEVEN<emph.end/>. </s><s>Laet A des balcx BC vastpunt, ende AB met AC twee euen ermen sijn, ende an B hanghe het rechtreckwicht D, ende an C sy het rechthefwicht E, euewichtich an D, ende sijn balck sy FG, diens vastpunt H, ende euen ermen HF, HG, ende den houck ABI, sy euen anden houck ACF. </s><s><emph type="other"/>TBEGHEERDE<emph.end/>. </s><s>Wy moeten bewysen dat het rechtdaelwicht D, ende trechthefwicht E, ande euen ermen AB, AC, euen ghewelden doen. </s><s><emph type="other"/>TBEREYTSEL<emph.end/>. </s><s>Laet an C een ghewicht K <pb pagenum="33"/>hanghen, euen an D. </s><s><emph type="other"/>TBEWYS<emph.end/>. </s><s>Laet ons weeren E, ende is blijckelijck dat de macht van D is de ermen AB, AC, in die ghegheuen ghestalt te houden, want D is euen an K, ende AB an AC. </s><s>Laet nu D weeren, ende E wederom anhanghen, ende de macht van E is oock de ermen AB, AC, in die ghegheuen ghestalt te houden, want K is euen an E, ende HF an HG, daerom E ende D doen an,euen ermen AB,AC, euen ghewelden. </s>

<s> <emph type="other"/>TGHEGHEVEN<emph.end/>. </s><s>Laet A des balcx BC vastpunt, ende AB met AC twee euen ermen sijn, ende an B hanghe het rechtreckwicht D, ende an C sy het rechthefwicht E, euewichtich an D, ende sijn balck sy FG, diens vastpunt H, ende euen ermen HF, HG, ende den houck ABI, sy euen anden houck ACF. </s><s><emph type="other"/>TBEGHEERDE<emph.end/>. </s><s>Wy moeten bewysen dat het rechtdaelwicht D, ende trechthefwicht E, ande euen ermen AB, AC, euen ghewelden doen. </s><s><emph type="other"/>TBEREYTSEL<emph.end/>. </s><s>Laet an C een ghewicht K hanghen, euen an D. </s><s><emph type="other"/>TBEWYS<emph.end/>. </s><s>Laet ons weeren E, ende is blijckelijck dat de macht van D is de ermen AB, AC, in die ghegheuen ghestalt te houden, want D is euen an K, ende AB an AC. </s><s>Laet nu D weeren, ende E wederom anhanghen, ende de macht van E is oock de ermen AB, AC, in die ghegheuen ghestalt te houden, want K is euen an E, ende HF an HG, daerom E ende D doen an,euen ermen AB,AC, euen ghewelden. </s>

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

<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 tscheefdaelwicht D, diens scheefdaellini BE, ende an C sy tscheefhefwicht F, euen an D, ende sijn scheefheflini sy CG, ende den houck ABE, sy euen anden houck ACG. </s><s><emph type="other"/>TBEGHEERDE<emph.end/>. </s><s>Wy moeten bewysen dat het scheefdaelwicht D, ende tscheefhefwicht 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 scheefheflini CI, euewydich <arrow.to.target n="marg115"/> sy van BE, ende CB sy wat voortghetrocken tot in K. </s>

<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 tscheefdaelwicht D, diens scheefdaellini BE, ende an C sy tscheefhefwicht F, euen an D, ende sijn scheefheflini sy CG, ende den houck ABE, sy euen anden houck ACG. </s><s><emph type="other"/>TBEGHEERDE<emph.end/>. </s><s>Wy moeten bewysen dat het scheefdaelwicht D, ende tscheefhefwicht 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 <pb pagenum="33"/>hanghen euen an D, diens scheefheflini CI, euewydich <arrow.to.target n="marg115"/> sy van BE, ende CB sy wat voortghetrocken tot in K. </s>

<s>

<margin.target id="marg115"/>Parallela.

</s>

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<s> <emph type="other"/>NGHESIEN<emph.end/> den heelen pilaer door tghestelde 6 lb weeght, waer af Æ de 4 lb verheft, so volgt nootsaeckelick datter opt punt R, dat is op tsop des keghels &OElig;, 2 lb rusten. </s>

<s> <emph type="other"/>OFTE<emph.end/> soomen an R een rechthefwicht vougde, inde plaets des keghels &OElig;, als hier neuen, dat sal weghen 2 lb. </s><s> <emph type="other"/>OFTE<emph.end/> soomen an V een keghel vougde, inde plaets des rechthefwichts Æ, als hier neuen, dat op den keghel &OElig; rusten sal 2 lb, ende op den keghel 4 lb. </s><s> <emph type="other"/>OFTE<emph.end/> soomen den pilaer ophinghe an twee euewidighe <arrow.to.target n="marg117"/> linien &OElig;R, ende V, als hier neuen, dat ande lini &OElig;R hanghen sal 2 lb, ende ande lini V 4 lb.</s>

<s> <emph type="other"/>OFTE<emph.end/> soomen den pilaer ophinghe an twee euewidighe <arrow.to.target n="marg117"/> linien &OElig;R, ende ΦV, als hier neuen, dat ande lini &OElig;R hanghen sal 2 lb, ende ande lini ΦV 4 lb.</s>

<s>

<margin.target id="marg117"/>Parallelæs.

</s>

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

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

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

<s>

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

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

</s>

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

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

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

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