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version 1.16, 2002/08/09 22:48:45

version 1.17, 2002/08/15 00:15:54

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<s>Sed quia de Fide agitur S cripiurærum, propter illam cau&longs;am, quam non &longs;emel commemoravimus, Ne &longs;cilicet <lb/>qui&longs;quam eloquia divina non intelligens, cum de his rebus tale aliquid vel invenerit in Libris No&longs;tris, vel ex illis <lb/>audiverit, quod perceptis a&longs;&longs;ertionibus adver &longs;ari videatur, nullo modo eis, cetera utilia monentibus, vel narrantibus, <lb/>vel pranuntiantibus, credat: Breviter di&longs;cendum e&longs;t, de figura Cæli, hoc &longs;ci&longs;&longs;e Autores no&longs;tros, quod verit as ha<lb/>bet: Sed Spiritum Dei, qui per ip&longs;os loquebstur, nolui&longs;&longs;e i&longs;ta docere homines, nulli ad &longs;alutem profutura.<emph.end type="italics"/> D. <lb/>Augu&longs;t. </s>

<s>ad literam, Cap. </s>

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<s><margin.target id="marg877"></margin.target>* Cardan de re<lb/>rum variet. </s>

<s>Lib. 1. <lb/>Cap.

<s>1. <lb/>Cap.

1.</s>

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<s><margin.target id="marg918"></margin.target>* Delle Macchie <lb/>&longs;olarj.</s>

<s><margin.target id="marg919"></margin.target>* <emph type="italics"/>Vnius Corporis <lb/>fimplicis, unus e&longs;t <lb/>motus &longs;implex, et <lb/>huic duæ &longs;pecies, <lb/>Rectus & Circu<lb/>laris: Rectus du<lb/>plex à medio, & <lb/>ad medium; pri<lb/>mus levium, ut A<lb/>eris & Ignis: &longs;e<lb/>cundus gravium, <lb/>ut Aquæ & Ter<lb/>ræ: Circularis, <lb/>quie&longs;t circa medi<lb/>um competit C&oelig;lo, <lb/>quod neque e&longs;t <lb/>grave, neque leve.<emph.end type="italics"/><lb/>Ari&longs;t. <emph type="italics"/>de C&oelig;lo.<emph.end type="italics"/><lb/>Lib. </s>

<s>It is clear al&longs;o from the&longs;e Principles how fal&longs;e the&longs;e words of <lb/><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> are, that: <emph type="italics"/>Of one &longs;imple Body, there is one &longs;imple Motion<emph.end type="italics"/>; <lb/><emph type="italics"/>and this is of two kindes, Right and Circular: the Right is two<lb/>fold, from the medium, and to the medium; the fir&longs;t of Light Bo<lb/>dyes, as the Aire and Fire: the &longs;econd of Grave Bodyes, as the <lb/>Water and Earth: the Circular, which is about the medium, be<lb/>longeth to Heaven, which is neither Grave nor Light<emph.end type="italics"/>: For all this <lb/>Philo&longs;ophy is now for&longs;aken, and of it &longs;elf grown into di&longs;-e&longs;teem; <lb/>for though it be received for an unque&longs;tionable truth in this new <lb/>Opinion, that to a &longs;imple body appertains one only &longs;imple Moti<lb/><arrow.to.target n="marg920"></arrow.to.target><lb/>on, yet it granteth no Motion but what is Circular, by which alone <lb/>a&longs;imple body is con&longs;erved in its naturall Place, and &longs;ub&longs;i&longs;ts in its <lb/>Unity, and is properly &longs;aid to move <emph type="italics"/>in loco<emph.end type="italics"/> [<emph type="italics"/>in a place<emph.end type="italics"/>:] whereby <lb/><arrow.to.target n="marg921"></arrow.to.target><lb/>it comes to pa&longs;s that a Body for this rea&longs;on doth continue to move <lb/>in it &longs;elf, [<emph type="italics"/>or about its own axis<emph.end type="italics"/>;] and although it have a Motion, <pb pagenum="495"/>yet it abideth &longs;till in the &longs;ame place, as if it were perpetually im<lb/>moveable. </s>

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<s><margin.target id="marg963"></margin.target><emph type="italics"/>(c)<emph.end type="italics"/> De Motu A<lb/>quarum. </s>

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<s>Fora&longs;<lb/>much therefore as N O is &longs;e&longs;quialter <lb/><arrow.to.target n="marg1191"></arrow.to.target><lb/>of R O, and M O of O H, <emph type="italics"/>(b)<emph.end type="italics"/> the <lb/>Remainder N M &longs;hall be &longs;e&longs;quialter <lb/>of the Remainder R H: Therefore <lb/>the Axis is greater than &longs;e&longs;quialter <lb/>of the Semi parameter by the quan<lb/>tity of the Line M O. </s>

<s>And let it be <lb/>&longs;uppo&longs;ed that the Portion hath not le&longs;&longs;e proportion in Gravity unto <lb/>the Liquid of equall Ma&longs;&longs;e, than the Square that is made of the <lb/>Exce&longs;&longs;e by which the Axis is greater than &longs;e&longs;quialter of the Semi<lb/>parameter hath to the Square made of the Axis: It is therefore ma<lb/>nife&longs;t that the Portion hath not le&longs;&longs;e proportion in Gravity to the <lb/>Liquid than the Square of the Line M O hath to the Square of N <lb/>O: But look what proportion the <emph type="italics"/>P<emph.end type="italics"/>ortion hath to the Liquid in <lb/>Gravity, the &longs;ame hath the <emph type="italics"/>P<emph.end type="italics"/>ortion &longs;ubmerged to the whole Solid: <lb/>for this hath been demon&longs;trated <emph type="italics"/>(c)<emph.end type="italics"/> above: ^{*}And look what pro<lb/><arrow.to.target n="marg1192"></arrow.to.target><lb/>portion the &longs;ubmerged Portion hath to the whole <emph type="italics"/>P<emph.end type="italics"/>ortion, the <lb/><arrow.to.target n="marg1193"></arrow.to.target><lb/>&longs;ame hath the Square of <emph type="italics"/>P<emph.end type="italics"/> F unto the Square of N O: For it hath <lb/>been demon&longs;trated in <emph type="italics"/>(d) Lib. de Conoidibus,<emph.end type="italics"/> that if from a Right<lb/><arrow.to.target n="marg1194"></arrow.to.target><lb/>angled Conoid two <emph type="italics"/>P<emph.end type="italics"/>ortions be cut by Planes in any fa&longs;hion pro<lb/>duced, the&longs;e <emph type="italics"/>P<emph.end type="italics"/>ortions &longs;hall have the &longs;ame Proportion to each <lb/>other as the Squares of their Axes: The Square of P F, therefore, <lb/>hath not le&longs;&longs;e proportion to the Square of N O than the Square of <lb/>M O hath to the Square of N O: ^{*}Wherefore P F is not le&longs;&longs;e than <lb/><arrow.to.target n="marg1195"></arrow.to.target><lb/>M O, ^{*}nor B P than H O. ^{*}If therefore, a Right Line be drawn <lb/><arrow.to.target n="marg1196"></arrow.to.target><lb/>from H at Right Angles unto N O, it &longs;hall meet with B <emph type="italics"/>P,<emph.end type="italics"/> and &longs;hall <lb/><arrow.to.target n="marg1197"></arrow.to.target><lb/>fall betwixt B and P; let it fall in T: <emph type="italics"/>(e)<emph.end type="italics"/> And becau&longs;e <emph type="italics"/>P<emph.end type="italics"/> F is <lb/><arrow.to.target n="marg1198"></arrow.to.target><lb/>parallel to the Diameter, and H T is perpendicular unto the &longs;ame <lb/>Diameter, and R H equall to the Semi-parameter; a Line drawn <lb/>from R to T and prolonged, maketh Right Angles with the Line <pb pagenum="360"/>contingent unto the Section in the Point P: Wherefore it al&longs;o <lb/>maketh Right Angles with the Surface of the Liquid: and that <lb/>part of the Conoidall Solid which is within the Liquid &longs;hall move <lb/>upwards according to the Perpendicular drawn thorow B parallel <lb/>to R T; and that part which is above the Liquid &longs;hall move down<lb/>wards according to that drawn thorow G, parallel to the &longs;aid R T: <lb/>And thus it &longs;hall continue to do &longs;o long untill that the Conoid be <lb/>re&longs;tored to uprightne&longs;&longs;e, or to &longs;tand according to the Perpendicular.</s>

<s>de Conoidibus,<emph.end type="italics"/> that if from a Right<lb/><arrow.to.target n="marg1194"></arrow.to.target><lb/>angled Conoid two <emph type="italics"/>P<emph.end type="italics"/>ortions be cut by Planes in any fa&longs;hion pro<lb/>duced, the&longs;e <emph type="italics"/>P<emph.end type="italics"/>ortions &longs;hall have the &longs;ame Proportion to each <lb/>other as the Squares of their Axes: The Square of P F, therefore, <lb/>hath not le&longs;&longs;e proportion to the Square of N O than the Square of <lb/>M O hath to the Square of N O: ^{*}Wherefore P F is not le&longs;&longs;e than <lb/><arrow.to.target n="marg1195"></arrow.to.target><lb/>M O, ^{*}nor B P than H O. ^{*}If therefore, a Right Line be drawn <lb/><arrow.to.target n="marg1196"></arrow.to.target><lb/>from H at Right Angles unto N O, it &longs;hall meet with B <emph type="italics"/>P,<emph.end type="italics"/> and &longs;hall <lb/><arrow.to.target n="marg1197"></arrow.to.target><lb/>fall betwixt B and P; let it fall in T: <emph type="italics"/>(e)<emph.end type="italics"/> And becau&longs;e <emph type="italics"/>P<emph.end type="italics"/> F is <lb/><arrow.to.target n="marg1198"></arrow.to.target><lb/>parallel to the Diameter, and H T is perpendicular unto the &longs;ame <lb/>Diameter, and R H equall to the Semi-parameter; a Line drawn <lb/>from R to T and prolonged, maketh Right Angles with the Line <pb pagenum="360"/>contingent unto the Section in the Point P: Wherefore it al&longs;o <lb/>maketh Right Angles with the Surface of the Liquid: and that <lb/>part of the Conoidall Solid which is within the Liquid &longs;hall move <lb/>upwards according to the Perpendicular drawn thorow B parallel <lb/>to R T; and that part which is above the Liquid &longs;hall move down<lb/>wards according to that drawn thorow G, parallel to the &longs;aid R T: <lb/>And thus it &longs;hall continue to do &longs;o long untill that the Conoid be <lb/>re&longs;tored to uprightne&longs;&longs;e, or to &longs;tand according to the Perpendicular.</s>

<s><margin.target id="marg1188"></margin.target>(a) <emph type="italics"/>By 10. of the <lb/>fifth.<emph.end type="italics"/></s>

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<s><margin.target id="marg1321"></margin.target>(b) <emph type="italics"/>By 19 of the <lb/>fifth.<emph.end type="italics"/></s>

<s><emph type="italics"/>A<emph.end type="italics"/>nd let them be like to the <emph type="italics"/>P<emph.end type="italics"/>ortion <emph type="italics"/>A B L.<emph.end type="italics"/>] Apollonius <emph type="italics"/>thus defineth<emph.end type="italics"/><lb/><arrow.to.target n="marg1322"></arrow.to.target><lb/><emph type="italics"/>like Portions of the Sections of a Cone, in<emph.end type="italics"/> Lib. 6. Conicornm, <emph type="italics"/>as<emph.end type="italics"/> Eutocius <emph type="italics"/>writeth<emph.end type="italics"/> ^{*}; <lb/><arrow.to.target n="marg1323"></arrow.to.target><lb/><foreign lang="greek">o)/n oi(_s a)x deisw_n o)/n e(xa/sw| warallh/lwn th_ <35>a\sei, i(/swn to\ plh_o<34>, ai( para/llhlos, kai\ a(i <35>a/seis wro\s ta/s apotrm<gap/><lb/>nome/nas a)po\ <gap/> diame/tswn tw_s korufai_s e)n toi_s a)ntoi_s lo/gois ei)si, kai\ ai( a)potemno/menai wro\s ta\s a) temnomi/nas<gap/></foreign><lb/><emph type="italics"/>that is,<emph.end type="italics"/> In both of which an equall number of Lines being drawn parallel to the <lb/>Ba&longs;e; the parallel and the Ba&longs;es have to the parts of the Diameters, cut off from <lb/>the Vertex, the &longs;ameproportion: as al&longs;o, the parts cut off, to the parts cut off. <lb/><emph type="italics"/>Now the Lines parallel to the Ba&longs;es are drawn, as I &longs;uppo&longs;e, by making a Rectilineall Figure (cal-<emph.end type="italics"/><lb/><arrow.to.target n="marg1324"></arrow.to.target><lb/><emph type="italics"/>led)<emph.end type="italics"/> Signally in&longs;cribed [<foreign lang="greek">xh_ma giwri/mws e)gn\<36>ro/menon</foreign>] <emph type="italics"/>in both portions, having an equall num<lb/>ber of Sides in both. </s>

<s>6. Conicornm, <emph type="italics"/>as<emph.end type="italics"/> Eutocius <emph type="italics"/>writeth<emph.end type="italics"/> ^{*}; <lb/><arrow.to.target n="marg1323"></arrow.to.target><lb/><foreign lang="greek">o)/n oi(_s a)x deisw_n o)/n e(xa/sw| warallh/lwn th_ <35>a\sei, i(/swn to\ plh_o<34>, ai( para/llhlos, kai\ a(i <35>a/seis wro\s ta/s apotrm<gap/><lb/>nome/nas a)po\ <gap/> diame/tswn tw_s korufai_s e)n toi_s a)ntoi_s lo/gois ei)si, kai\ ai( a)potemno/menai wro\s ta\s a) temnomi/nas<gap/></foreign><lb/><emph type="italics"/>that is,<emph.end type="italics"/> In both of which an equall number of Lines being drawn parallel to the <lb/>Ba&longs;e; the parallel and the Ba&longs;es have to the parts of the Diameters, cut off from <lb/>the Vertex, the &longs;ameproportion: as al&longs;o, the parts cut off, to the parts cut off. <lb/><emph type="italics"/>Now the Lines parallel to the Ba&longs;es are drawn, as I &longs;uppo&longs;e, by making a Rectilineall Figure (cal-<emph.end type="italics"/><lb/><arrow.to.target n="marg1324"></arrow.to.target><lb/><emph type="italics"/>led)<emph.end type="italics"/> Signally in&longs;cribed [<foreign lang="greek">xh_ma giwri/mws e)gn\<36>ro/menon</foreign>] <emph type="italics"/>in both portions, having an equall num<lb/>ber of Sides in both. </s>

<s>Therefore, like Portions are cut off from like Sections of a Cone; and <lb/>their Diameters, whether they be perpendicular to their Ba&longs;es, or making equall Angles with their <lb/>Ba&longs;es, have the &longs;ame proportion unto their Ba&longs;es.<emph.end type="italics"/><lb/><arrow.to.target n="marg1325"></arrow.to.target></s>

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<s><margin.target id="marg1422"></margin.target><emph type="italics"/>Of Natation<emph.end type="italics"/></s>

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<s>But, becau&longs;e that this Doctrine of <emph type="italics"/>Archimedes,<emph.end type="italics"/> peru&longs;ed, tran&longs;cri<lb/><arrow.to.target n="marg1426"></arrow.to.target><lb/>bed and examined by <emph type="italics"/>Signor France&longs;co Buonamico,<emph.end type="italics"/> in his <emph type="italics"/>fifth Book <lb/>of Motion, Chap.<emph.end type="italics"/> 29, and afterwards by him confuted, might by the <lb/>Authority of &longs;o renowned, and famous a Philo&longs;opher, be rendered <lb/>dubious, and &longs;u&longs;pected of fal&longs;ity; I have judged it nece&longs;&longs;ary to de<lb/>fend it, if I am able &longs;o to do, and to clear <emph type="italics"/>Archimedes,<emph.end type="italics"/> from tho&longs;e <lb/>cen&longs;ures, with which he appeareth to be charged. <emph type="italics"/>Buonamico<emph.end type="italics"/> re<lb/><arrow.to.target n="marg1427"></arrow.to.target><lb/>jecteth the Doctrine of <emph type="italics"/>Archimedes,<emph.end type="italics"/> fir&longs;t, as not con&longs;entaneous with <lb/>the Opinion of <emph type="italics"/>Aristotle,<emph.end type="italics"/> adding, that it was a &longs;trange thing to him, <lb/><arrow.to.target n="marg1428"></arrow.to.target><lb/>that the Water &longs;hould exceed the Earth in Gravity, &longs;eeing on the <lb/>contrary, that the Gravity of water, increa&longs;eth, by means of the parti<lb/><arrow.to.target n="marg1429"></arrow.to.target><lb/>cipation of Earth. </s>

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<s><margin.target id="marg1436"></margin.target>The Authors <lb/>an&longs;wer to the <lb/>fourth Object<lb/>ion.</s>

<s><margin.target id="marg1437"></margin.target>Of Natation, <lb/>Lib. </s>

<s><margin.target id="marg1437"></margin.target>Of Natation, <lb/>Lib. 1. Prop. </s>

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<s><margin.target id="marg1498"></margin.target>Water con&longs;i&longs;ts <lb/>not of continu<lb/>all, but only <lb/>of contiguous <lb/>parts.</s>

<s><margin.target id="marg1499"></margin.target><emph type="italics"/>Set what &longs;atis<lb/>faction he hath <lb/>given, as to this <lb/>point, in Lib. </s>

<s><margin.target id="marg1499"></margin.target><emph type="italics"/>Set what &longs;atis<lb/>faction he hath <lb/>given, as to this <lb/>point, in Lib. de <lb/>Motu. </s>

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<s>And briefly in generall.</s>

<s><margin.target id="marg1508"></margin.target>Of Natation <lb/>Lib. </s>

<s><margin.target id="marg1508"></margin.target>Of Natation <lb/>Lib. 1. Prop. </s>

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<s><margin.target id="marg1528"></margin.target><emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> opi<lb/>nion touching <lb/>the Operation <lb/>of Figure ex<lb/>amined.</s>

<s><margin.target id="marg1529"></margin.target><emph type="italics"/>Ari&longs;tot de Cælo,<emph.end type="italics"/><lb/>Lib. </s>

<s><margin.target id="marg1529"></margin.target><emph type="italics"/>Ari&longs;tot de Cælo,<emph.end type="italics"/><lb/>Lib. 4. Cap.

<s>4. Cap.

66.</s>

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<s>Now the mird of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> being &longs;uch, and ap<lb/>pearing by con&longs;equence, rather contrary at the fir&longs;t &longs;ight, then fa<lb/>vourable to the a&longs;&longs;ertion of the Oponents, it is nece&longs;&longs;ary, that their <lb/>Interpretation be not exactly the &longs;ame with that, but &longs;uch, as being <lb/>in part under&longs;tood by &longs;ome of them, and in part by others, was &longs;et <lb/>down: and it may ea&longs;ily be indeed &longs;o, being an Interpretation <lb/>con&longs;onent to the &longs;ence of the more famous Interpretors, which is, <lb/>that the Adverbe <emph type="italics"/>Simply<emph.end type="italics"/> or <emph type="italics"/>Ab&longs;olutely,<emph.end type="italics"/> put in the Text, orght not to <lb/>be joyned to the Verbe to <emph type="italics"/>Move,<emph.end type="italics"/> but with the Noun <emph type="italics"/>Cau&longs;es<emph.end type="italics"/>: &longs;o that <lb/>the purport of <emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> words, is to affirm, That Figures are not the <lb/>Cau&longs;es ab&longs;olutely of moving or not moving, but yet are Cau&longs;es <emph type="italics"/>Se<lb/>cundum quid, viz<emph.end type="italics"/> in &longs;ome &longs;ort; by which means, they are called <lb/>Auxiliary and Concomitant Cau&longs;es: and this Propo&longs;ition is received <lb/>and a&longs;&longs;erted as true by <emph type="italics"/>Signor Buonamico Lib.<emph.end type="italics"/> 5. <emph type="italics"/>Cap.<emph.end type="italics"/> 28. where he <lb/>thus writes. <emph type="italics"/>There are other Cau&longs;es concomitant, by which &longs;ome <lb/>things float, and others &longs;ink, among which the Figures of Bodies hath <lb/>the fir&longs;t place,<emph.end type="italics"/> &c.</s>

<s><margin.target id="marg1531"></margin.target>Lib. 4. Cap.

<s>4. Cap.

61 <lb/>Text. </s>

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<s>The other <lb/>occa&longs;ion is, that he did believe, that like as there is a po&longs;itive and in<lb/>trin&longs;ecall Quality, whereby Elementary Bodies have a propen&longs;ion <lb/>of moving towards the Centre of the Earth, &longs;o there is another like<pb pagenum="470"/>wi&longs;e intrin&longs;ecall, whereby &longs;ome of tho&longs;e Bodies have an <emph type="italics"/>Impetus<emph.end type="italics"/> of <lb/><arrow.to.target n="marg1538"></arrow.to.target><lb/>flying the Centre, and moving upwards: by Vertue of which in<lb/>trin&longs;e call Principle, called by him Levity, the Moveables which have <lb/>that &longs;ame Motion more ea&longs;ily penetrate the more &longs;ubtle <emph type="italics"/>Medium,<emph.end type="italics"/><lb/>than the more den&longs;e: but &longs;uch a Propo&longs;ition appears likewi&longs;e un<lb/>certain, as I have above hinted in part, and as with Rea&longs;ons and <lb/>Experiments, I could demon&longs;trate, did not the pre&longs;ent Argument im<lb/>portune me, or could I di&longs;patch it in few words.</s>

<s><margin.target id="marg1538"></margin.target>Lib. 4. Cap.

<s>4. Cap.

5.</s>

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<s>And this <lb/>is the only true proper and ab&longs;olute Cau&longs;e of Natation and Sub<lb/>mer&longs;ion, &longs;o that nothing el&longs;e hath part therein: and the Board of the <lb/>Adver&longs;aries &longs;wimmeth, when it is conjoyned with as much Air, <lb/>as, together with it, doth form a Body le&longs;s grave than &longs;o much water <lb/>as would fill the place that the &longs;aid Compound occupyes in the <lb/>water; but when they &longs;hall demit the &longs;imple Ebony into <lb/>the water, according to the Tenour of our Que<lb/>&longs;tion, it &longs;hall alwayes go to the bottom, <lb/>though it were as thin as a <lb/>Paper.</s>

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<s>Before I come to declare the promi&longs;ed way <lb/>to recover any laden or empty Ship when <lb/>it is &longs;unke; I thinke it convenient (<emph type="italics"/>Mo&longs;t <lb/>Serene and Illu&longs;trious Prince,<emph.end type="italics"/>) fir&longs;t to de<lb/>clare the reall cau&longs;e of its &longs;inking.<pb pagenum="484"/><arrow.to.target n="marg1552"></arrow.to.target></s>

<s><margin.target id="marg1552"></margin.target><emph type="italics"/>Archimed.<emph.end type="italics"/> of <lb/>Natation, Lib. </s>

<s><margin.target id="marg1552"></margin.target><emph type="italics"/>Archimed.<emph.end type="italics"/> of <lb/>Natation, Lib. 2. <lb/>Prop. </s>

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<s><margin.target id="marg1553"></margin.target><emph type="italics"/>Archimed.<emph.end type="italics"/> of <lb/>Natation, Lib. </s>

<s><margin.target id="marg1553"></margin.target><emph type="italics"/>Archimed.<emph.end type="italics"/> of <lb/>Natation, Lib. 1. <lb/>Prop. </s>

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<s><margin.target id="marg1554"></margin.target><emph type="italics"/>A chimed.<emph.end type="italics"/> of <lb/>Natation, Lib. </s>

<s><margin.target id="marg1554"></margin.target><emph type="italics"/>A chimed.<emph.end type="italics"/> of <lb/>Natation, Lib. 1. <lb/>Prop. </s>

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