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version 1.8, 2004/10/15 10:51:16

version 1.9, 2007/05/24 17:27:20

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<s id="id.000009">Sumptibus Hieronymi Tamburini.</s>

</section>

<s id="id.000010">ILLVSTRISSIMO <lb/>AC NOBILISSIMO <lb/>

<s id="id.000010">ILLVSTRISSIMO <lb/>AC NOBILISSIMO <lb/>PETRO FRANCISCO <lb/>MALASPINAE <lb/>

PETROFRANCISCO <lb/>MALASPINAE <lb/>

ÆDIFICIORVM MARCHIONI.</s>

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te rei, de qua agitur peritiorem, quemuè prudentiorem <lb/>

inuenire potuerim? </s>

<s id="id.000014">tu enim cùm Phy&longs;iologiæ, ac Mathe<lb/>

maticarum omnium Encyclopædiam mirum in modum<emph.end type="italics"/> <pb xlink:href="009/01/004.jpg" pagenum="4" /><emph type="italics"/>excolueris, adintima Mathematicarum penetralia ita <lb/>

maticarum omnium Encyclopædiam mirum in modum<emph.end type="italics"/> <pb pagenum="4" xlink:href="009/01/004.jpg"/><emph type="italics"/>excolueris, adintima Mathematicarum penetralia ita <lb/>

per&longs;ua&longs;i&longs;ti, vt Archimedis, & Apollonij admirandis, ac <lb/>

&longs;ubtilißimis Demon&longs;trationibus detinearis. </s>

<s id="id.000015">Quanta por<lb/>

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</s>

</section>

<s id="id.000023">Liber de &longs;e ip&longs;o.</s>

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<s id="id.000030">Fr. Hieronymus Onuphrius pro Reuerendi&longs;s. P. Inqui&longs;itore Bonon.</s>

</section>

<s id="id.000031">LECTORI.</s>

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tuti præ&longs;idijs, ne Græcorum quidem Interpretum explanationes, ne<lb/>

dum Ari&longs;t. ob&longs;curè dicta intelligunt.</s>

<s id="id.000038">Quarta. </s>

<s id="id.000039">Adde, quod etiam &longs;i quis leuiter &longs;it erudito illo Mathemati<lb/>

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<s id="id.000054">nego, ait; qui&longs;piam con&longs;equen

<pb xlink:href="009/01/008.jpg" pagenum="8" />tiam, non enim hoc e&longs;t argumentari à permutata ratione, deberet enim <lb/>

<pb pagenum="8" xlink:href="009/01/008.jpg"/>tiam, non enim hoc e&longs;t argumentari à permutata ratione, deberet enim <lb/>

inferre, &longs;ic, ergo ita &longs;e habebit voluntas noua ad antiquam, quemad<lb/>

modum effectus nouus ad antiquum. </s>

<s id="id.000055">quæ vitio&longs;a argumentatio quan<lb/>

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eò progre&longs;&longs;us e&longs;t, vt eas omnes omnino conuellere, atque ex albo &longs;cien

<pb xlink:href="009/01/009.jpg" pagenum="9" />tiarum, quamuis non Ari&longs;totele tantum, &longs;ed ip&longs;a etiam veritate repu<lb/>

<pb pagenum="9" xlink:href="009/01/009.jpg"/>tiarum, quamuis non Ari&longs;totele tantum, &longs;ed ip&longs;a etiam veritate repu<lb/>

gnante, expungere conati &longs;int; <expan abbr="idq;">idque</expan> ne&longs;cio an vlla alia de cau&longs;a egerint, <lb/>

quàm quod eas non &longs;atis calerent; non &longs;ecus <expan abbr="atq;">atque</expan> Ae&longs;opica illa Vulpes, <lb/>

quæ cum cauda mutilata e&longs;&longs;et, caudarum mutilationem reliquis vulpi<lb/>

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thematicis petenda e&longs;&longs;ent: reliqua autem me tantum attingere, quan<lb/>

tum harum rerum cum illis connexio po&longs;tulat.</s>

<s id="id.000078">His omnibus placuit appendices opportune nonnullas addere, qua<lb/>

rum prima de natura mathematicarum &longs;cientiarum: altera, qua omnes <lb/>

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</section>

<s id="id.000083">Pr&etail;cipua qu&etail;dam, aut noua, aut re&longs;taurata, <lb/>

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</row>

</table>

</section>

<s id="id.000084"><emph type="italics"/>PRIMVS INDEX LOCORVM ARIST.<emph.end type="italics"/></s>

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æquales duobus rectis: Aequalitas Geometrica, quæ.<emph.end type="italics"/></s>

<s id="id.000098"><emph type="italics"/>Cap. eodem, de exemplis, quibus vtuntuar Geometræ.<emph.end type="italics"/></s>

<s id="id.000098"><emph type="italics"/>Cap. eodem, de exemplis, quibus vtuntur Geometræ.<emph.end type="italics"/></s>

<s id="id.000099">In &longs;ecundo Priorum Re&longs;ol.<emph type="italics"/>Cap. 21. de lineis Paralellis, &longs;eu Coalternis.<emph.end type="italics"/></s>

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<s id="id.000129"><emph type="italics"/>T. 28. De Parallelis.<emph.end type="italics"/></s>

<s id="id.000130"><emph type="italics"/>T. 29. Cur in Mathematicis non &longs;it Paralogi&longs;mus. </s>

<s id="id.000131">Item quid multiplicata propor<lb/>

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<s id="id.000180"><emph type="italics"/>T. 28. Quid con&longs;onantia Diapa&longs;on.<emph.end type="italics"/></s>

<s id="id.000181"><emph type="italics"/>T. 68. Mathematicas Demon&longs;trationes babere cau&longs;am, quæ reducitur ad defini<lb/>

<s id="id.000181"><emph type="italics"/>T. 68. Mathematicas Demon&longs;trationes habere cau&longs;am, quæ reducitur ad defini<lb/>

tionem.<emph.end type="italics"/></s>

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<s id="id.000187"><emph type="italics"/>T. 71. De infinito Mathematica.<emph.end type="italics"/></s>

<s id="id.000188">Ex 4. Phy&longs;ic.</s>

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<s id="id.000222"><emph type="italics"/>T. eodem. </s>

<s id="id.000223">Num plures Pyramides locum replere valeant, vbi Ari&longs;totiles, & omnes <lb/>

<s id="id.000223">Num plures Pyramides locum replere valeant, vbi Ari&longs;toteles, & omnes <lb/>

expo&longs;itores erra&longs;&longs;e o&longs;tenduntur.<emph.end type="italics"/></s>

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<s id="id.000239"><emph type="italics"/>Cap. 6. Sententia Ari&longs;totelis de Glaxia, partim defenditur: vera, deinde <lb/>

aperitur.<emph.end type="italics"/></s>

<s id="id.000240"><emph type="italics"/>Summa 4. cap 1. De Monte Parna&longs;&longs;o, dubia. </s>

<s id="id.000241">Mare extraneum, quod. </s>

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maticas &longs;ugillaret. </s>

<s id="id.000296">Tetragoni&longs;mus est inuentio mediæ.<emph.end type="italics"/></s>

<s id="id.000297"><emph type="italics"/>Tex. 8. Geodæ&longs;ia quid.<emph.end type="italics"/></s>

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<s id="id.000352"><emph type="italics"/>Quæ&longs;t. 16. De ligni oblongi, ac breuis flexura.<emph.end type="italics"/></s>

<s id="id.000353"><emph type="italics"/>Quæ&longs;t. 17. De Cuneo.<emph.end type="italics"/></s>

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<s id="id.000408">De Ince&longs;&longs;u Animal.</s>

<s id="id.000409"><emph type="italics"/>Cap. 7. qua ratione in gre&longs;&longs;u fiat bypotenu&longs;a. </s>

<s id="id.000409"><emph type="italics"/>Cap. 7. qua ratione in gre&longs;&longs;u fiat hypotenu&longs;a. </s>

<s id="id.000410">& ea quid &longs;it.<emph.end type="italics"/></s>

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<s id="id.000413"><emph type="italics"/>Cap. 3. Automata.<emph.end type="italics"/></s>

<s id="id.000414">De Generatione Animal.</s>

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<s id="id.000462"><emph type="italics"/>Sectione 1. num. </s>

<s id="id.000463">3. De ortu &longs;yderum innerrantium: Succulæ, Hypades, Atlantides, <lb/>

<s id="id.000463">3. De ortu &longs;yderum inerrantium: Succulæ, Hypades, Atlantides, <lb/>

Virgiliæ, Pleiades. </s>

<s id="id.000465">17. De occa&longs;u affixarum &longs;tellarum.<emph.end type="italics"/></s>

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<s id="id.000469">2. Iterum Diametri ethymologia.<emph.end type="italics"/></s>

<s id="id.000471">3. Denarius numerus cur perfectus. </s>

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<s id="id.000490"><emph type="italics"/>13. Idem cum 4 &longs;uperiori. </s>

<s id="id.000491">reflexio radior&ubreve; pulchrè comparatur corpor&ubreve; re&longs;ultationi.<emph.end type="italics"/></s>

<s id="id.000491">reflexio radior&ubreve;m pulchrè comparatur corpor&ubreve;m re&longs;ultationi.<emph.end type="italics"/></s>

<s id="id.000492">Ex &longs;ectione 19. De Mu&longs;ica.</s>

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<s id="id.000526"><emph type="italics"/>30. De Harmonijs, &longs;eu Modis, &longs;eu Tonis pri&longs;corum.<emph.end type="italics"/></s>

<s id="id.000527"><emph type="italics"/>31. Vetustiores fui&longs;&longs;e magis Melopæos.<emph.end type="italics"/></s>

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<s id="id.000565"><emph type="italics"/>4. Pupillæ definitio.<emph.end type="italics"/></s>

<s id="id.000566"><emph type="italics"/>5. Cur mgra in omnibus hominibus.<emph.end type="italics"/></s>

<s id="id.000566"><emph type="italics"/>5. Cur nigra in omnibus hominibus.<emph.end type="italics"/></s>

<s id="id.000567"><emph type="italics"/>6. Cur in Sole euane&longs; cat.<emph.end type="italics"/></s>

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<s id="id.000569"><emph type="italics"/>8. Cur modo maior, modo minor videatur, & cui&longs;dam lepida deceptio.<emph.end type="italics"/></s>

<s id="id.000570">Additamentum de natura Mathematicarum di&longs;ciplinarum.</s>

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<s id="id.000579"><emph type="bold"/>Finis Primi Indicis.<emph.end type="bold"/></s>

</section>

<s id="id.000580"><emph type="italics"/>ALTER INDEX<emph.end type="italics"/></s>

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& cap. 7. &longs;ecundi Eudem. & cap. 12. &longs;ecundi Eudem. & problema 6. &longs;ectio

<pb xlink:href="009/01/023.jpg" pagenum="23" />nis 30. tot Ari&longs;totelis loca illu&longs;trat vnica hæc Euclidis Demon&longs;tratio.</s>

<pb pagenum="23" xlink:href="009/01/023.jpg"/>nis 30. tot Ari&longs;totelis loca illu&longs;trat vnica hæc Euclidis Demon&longs;tratio.</s>

<s id="id.000606">Ad &longs;cholion præcedentis 32. primi, vide tex. 39. primi Po&longs;ter. loco 3. Item <lb/>

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<s id="id.000645">9. vide problem. </s>

<s id="id.000646">3. &longs;ectionis 15. loco 4.</s>

<s id="id.000647"><emph type="italics"/>In decimo.<emph.end type="italics"/></s>

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<s id="id.000660">vide initio Priorum, in verbum (Re&longs;olutio)</s>

<s id="id.000661">Atqne hæc &longs;unt, quæ ex Elementorum opere Ari&longs;toteles pa&longs;&longs;im v&longs;urpauit, <lb/>

<s id="id.000661">Atque hæc &longs;unt, quæ ex Elementorum opere Ari&longs;toteles pa&longs;&longs;im v&longs;urpauit, <lb/>

quæque nos infra explicabimus.</s>

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&longs;um cum libuerit, &longs;ecerni.</s>

</section>

<s id="id.000664"><emph type="italics"/>TERTIVS INDEX ALPHABETICVS,<emph.end type="italics"/></s>

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</row>

<row>

<cell><emph type="italics"/>Antipbonæ voces.<emph.end type="italics"/> 358. 363. 370. 371.</cell>

<cell><emph type="italics"/>Antiphonæ voces.<emph.end type="italics"/> 358. 363. 370. 371.</cell>

</row>

<row>

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<cell><emph type="italics"/>Conus, & cylindrus, cur variè mouentur.<emph.end type="italics"/></cell>

</row>

<row>

<cell><emph type="italics"/>Cubus numerus. duo cubi cubus, quid &longs;ignificet.<emph.end type="italics"/></cell>

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</row>

<row>

<cell><emph type="italics"/>Diapa&longs;on quid. 90. 350. omnium con&longs;onantiarum pulcberrima.<emph.end type="italics"/></cell>

<cell><emph type="italics"/>Diapa&longs;on quid. 90. 350. omnium con&longs;onantiarum pulcherrima.<emph.end type="italics"/></cell>

</row>

<row>

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</row>

<row>

<cell><emph type="italics"/>Figurarum &longs;olidarum, quænam totum locum repleant: vbi Ari&longs;t. & omnium expo&longs;i-torum rratum aperitur.<emph.end type="italics"/></cell>

<cell><emph type="italics"/>Figurarum &longs;olidarum, quænam totum locum repleant: vbi Ari&longs;t. & omnium expo&longs;i-torum ratum aperitur.<emph.end type="italics"/></cell>

</row>

<row>

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</row>

<row>

<cell><emph type="italics"/>Figurationes pro demonftrationibus Mathem.<emph.end type="italics"/></cell>

<cell><emph type="italics"/>Figurationes pro demon&longs;trationibus Mathem.<emph.end type="italics"/></cell>

</row>

<row>

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<cell><emph type="italics"/>Geographiæ veteris plura errata,<emph.end type="italics"/> 145. 146. 147. 148.</cell>

</row>

<row>

<cell><emph type="italics"/>Gnomon, quid. 3. &<emph.end type="italics"/></cell>

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<cell/>

</row>

<row>

<cell><emph type="italics"/>Halonis demonfiratio.<emph.end type="italics"/></cell>

<cell><emph type="italics"/>Halonis demon&longs;tratio.<emph.end type="italics"/></cell>

</row>

<row>

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<cell><emph type="italics"/>Mathematicæ o&longs;tendunt per cau&longs;am materialem, & formalem. 205. earum vtilitas. ibidem. De earum natura. in proprio tractatu.<emph.end type="italics"/></cell>

<cell/>

</row>

<row>

<cell><emph type="italics"/>Mathematicæ maximè tractant de Bono, & Pulcro, qua ratione.<emph.end type="italics"/></cell>

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<cell><emph type="italics"/>Principia Mathematicorum.<emph.end type="italics"/> 2.</cell>

</row>

<row>

<cell><emph type="italics"/>Principia &longs;cientiarum duplicia. Ex quibus, & circa quod.<emph.end type="italics"/></cell>

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</row>

<row>

<cell><emph type="italics"/>Quantitas an conctet ex indiui&longs;ibili. toto libello de lineis in&longs;ecabilibus argumentis mathematicis.<emph.end type="italics"/></cell>

<cell><emph type="italics"/>Quantitas an con&longs;tet ex indiui&longs;ibili. toto libello de lineis in&longs;ecabilibus argumentis mathematicis.<emph.end type="italics"/></cell>

<cell/>

</row>

<row>

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</row>

<row>

<cell><emph type="italics"/>Securis problema, vbi de antiquæ &longs;euris figura, & angulo pulchra demon&longs;tran-tur.<emph.end type="italics"/></cell>

<cell><emph type="italics"/>Securis problema, vbi de antiquæ &longs;ecuris figura, & angulo pulchra demon&longs;tran-tur.<emph.end type="italics"/></cell>

</row>

<row>

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<cell><emph type="italics"/>Tetragoni&longs;mus. vide Quadratura.<emph.end type="italics"/></cell>

<cell/>

</row>

<row>

<cell><emph type="italics"/>Teretizare, quid.<emph.end type="italics"/></cell>

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<s id="id.000666">Finis Tertij Indicis.</s>

</section>

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</row>

<row>

<cell><emph type="italics"/>Cometas in &longs;uprema aeris regione collocat; cuius contrarium ibi line ari demonctratione ostenditur.<emph.end type="italics"/></cell>

<cell><emph type="italics"/>Cometas in &longs;uprema aeris regione collocat; cuius contrarium ibi line ari demon&longs;tratione ostenditur.<emph.end type="italics"/></cell>

</row>

<row>

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</front>

<body>

<chap>

<s id="id.000668">LOCA <lb/>MATHEMATICA <lb/>EX LIBRO <lb/>

<s id="id.000668">LOCA <lb/>MATHEMATICA <lb/>EX LIBRO <lb/>PRÆDICAMENTORVM <lb/>

PRÆDICAMENTORVM<lb/>

Per ordinem declarata.</s>

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nus repertam e&longs;&longs;e, &longs;i nimirum de problemate loquantur, theorema Archi

<pb xlink:href="009/01/034.jpg" pagenum="34" />medis e&longs;t propo&longs;itio prima acuti&longs;&longs;imi libelli de Dimen&longs;ione circuli; e&longs;t au<lb/>

<pb pagenum="34" xlink:href="009/01/034.jpg"/>medis e&longs;t propo&longs;itio prima acuti&longs;&longs;imi libelli de Dimen&longs;ione circuli; e&longs;t au<lb/>

tem huiu&longs;modi. </s>

<s id="id.000679">Quilibet circulus æqualis e&longs;t triangulo rectangulo, cuius <lb/>

quidem &longs;emidiameter vni laterum, quæ circa rectum angulum &longs;unt, ambi<lb/>

tus verò ba&longs;i eius e&longs;t æqualis.</s>

<s id="id.000680">Sit, v.g. datus circulus, cuius &longs;emidiameter A B; & fit triangulum rectangu<lb/>

lum A B C, cuius angulus B, &longs;it rectus, & latus B A, <expan abbr="con&longs;titu&etilde;s">con&longs;tituens</expan> angulum re<lb/>

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pocratem quadra&longs;&longs;e lunulam, vt &longs;uo loco dicemus, & Archimedem in libel

<pb xlink:href="009/01/035.jpg" pagenum="35" />lo de quadratura Paraboles, quadra&longs;&longs;e ip&longs;am Parabolem, quæ tamen duæ fi<lb/>

<pb pagenum="35" xlink:href="009/01/035.jpg"/>lo de quadratura Paraboles, quadra&longs;&longs;e ip&longs;am Parabolem, quæ tamen duæ fi<lb/>

guræ, lunula &longs;cilicet, & parabola &longs;unt curuilineæ.</s>

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<s id="id.000698">quæ non &longs;unt in antiqua tran<lb/>

&longs;latione de&longs;ump&longs;imus ex ca&longs;tigati&longs;&longs;imo græco codice editionis Francfor<lb/>

dien&longs;is, propterea quod totum hunc locum declarant; &longs;unt autem i&longs;ta, <lb/>

<foreign lang="greek">ai/gar arxai/ pro/terai tw_n qewrhma/twn th ta/xei.</foreign> per &longs;cientias autem demon&longs;tra<lb/>

<foreign lang="greek">ai/ gar arxai/ pro/terai tw=n qewrhma/twn th| ta/ch. </foreign> per &longs;cientias autem demon&longs;tra<lb/>

tiuas intelligendas e&longs;&longs;e hoc loco ip&longs;as Mathematicas ex eo patet, quod illis <lb/>

a&longs;&longs;ignet Ari&longs;t. De&longs;criptiones; nam hoc verbo, De&longs;criptiones, &longs;eu figuratio<lb/>

nes, &longs;olet ip&longs;e Mathematicas Demon&longs;trationes innuere, quod in ip&longs;is figu<lb/>

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<s id="id.000702">Ex cap. de motu <emph type="italics"/>(Quadratum augetur Gnomone circumpo&longs;ito)<emph.end type="italics"/> Gnomon vox <lb/>

græca inter alia &longs;ignificat in&longs;trumentum illud, quod Latini tum amu&longs;&longs;im, <lb/>

tum normam appellant, Itali verò, Squadra, ad <lb/>

cuius &longs;imilitudinem Geometræ denominarunt fi<lb/>

guram quandam, &longs;eu portionem cuiu&longs;uis paralle<lb/>

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verò nominabant di&longs;cur&longs;um <expan abbr="ill&utilde;">illum</expan>, quo ex vero illo per re&longs;olutionem inuento,

<pb xlink:href="009/01/036.jpg" pagenum="36" />o&longs;tendebant conclu&longs;ionem. </s>

<pb pagenum="36" xlink:href="009/01/036.jpg"/>o&longs;tendebant conclu&longs;ionem. </s>

<s id="id.000715">Porrò Diogenes Laert. huius re&longs;olutionis in<lb/>

uentorem facit Platonem: à quo eam Leodamas Tha&longs;ius didicit, cuius be<lb/>

neficio, pluries deinde Geometricas demon&longs;trationes adinuenit. </s>

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docet primis duobus analyticis; &longs;ecundò penes materiam, quam tradit duo

<pb xlink:href="009/01/037.jpg" pagenum="37" />bus vltimis, non prætereundum. </s>

<pb pagenum="37" xlink:href="009/01/037.jpg"/>bus vltimis, non prætereundum. </s>

<s id="id.000733">reliquas duas logicæ partes, Topicam &longs;ci<lb/>

licet, & Elenchos, quæ &longs;yllogi&longs;mos probabilem, & apparentem docent, no<lb/>

luit appellare re&longs;olutorios, quamuis inuentionem mediorum doceant, quia <lb/>

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<s id="id.000739">& quæ incommen&longs;. </s>

<s id="id.000740">&longs;ic; commen&longs;. </s>

<s id="id.000741">magnitudines dicuntur, quas <lb/>

eadem men&longs;ura metitur, vt &longs;i fuerint duæ magnitu<lb/>

dines, A, & B, quas eadem men&longs;ura C, ide&longs;t quan<lb/>

titas C, metiatur, ide&longs;t <expan abbr="quãtitas">quantitas</expan> C, applicata quan<lb/>

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neam A, replicata eam præcisè, & perfectè omninò <lb/>

adæquaret: & eadem linea C, applicata lineæ B, & &longs;uper illam ter, v.g. re<lb/>

petita ip&longs;am con&longs;umeret, diceretur <expan abbr="vtranq;">vtranque</expan> metiri, & proinde duas lineas <lb/>

A, & B, e&longs;&longs;e comm. definit po&longs;tea <expan abbr="incomm&etilde;&longs;">incommen&longs;</expan> hoc modo, incomm. autem, qua<lb/>

A, & B, e&longs;&longs;e comm. definit po&longs;tea <expan abbr="incomm&etilde;&longs;">incommen&longs;.</expan> hoc modo, incomm. autem, qua<lb/>

rum nullam contingit communem men&longs;uram reperiri; vt &longs;i duarum linea<lb/>

rum, A, B, nunquam po&longs;&longs;et reperiri aliqua men&longs;u<lb/>

ra, quæ <expan abbr="vtranq;">vtranque</expan> adæquatè metiretur, v. g. &longs;i linea <lb/>

C, men&longs;uraret A, quater &longs;umpta, ter autem &longs;umpta <lb/>

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<s id="id.000746">inter lineas incommen&longs;. </s>

<s id="id.000747">&longs;unt diameter, & latus eiu&longs;<lb/>

dem quadrati, quia nulla pote&longs;t reperiri men&longs;ura quantumuis exigua, vti <lb/>

e&longs;t lineola E, in præ&longs;enti quadrato, etiam&longs;i illam in <lb/>

infinitum &longs;ubdiuidas, quæ <expan abbr="vtranq;">vtranque</expan> lineam, diame<lb/>

trum &longs;cilicet A C, & latus quoduis ex quatuor, v. g. <lb/>

latus B C, præcisè omnino metiatur. </s>

<s id="id.000748">theorema <lb/>

i&longs;tud demon&longs;tratur in vltima 10. Elem. eodem me<lb/>

dio, quod ab Ari&longs;totele hic innuitur; Euclides ex <lb/>&longs;uppo&longs;itione alterius partis contradictionis ip&longs;ius <pb xlink:href="009/01/038.jpg" pagenum="38" />propo&longs;itionis, quæ fal&longs;a e&longs;t, nimirum &longs;uppo&longs;ito prædictas lineas e&longs;&longs;e comm. <lb/>

dio, quod ab Ari&longs;totele hic innuitur; Euclides ex <lb/>&longs;uppo&longs;itione alterius partis contradictionis ip&longs;ius <pb pagenum="38" xlink:href="009/01/038.jpg"/>propo&longs;itionis, quæ fal&longs;a e&longs;t, nimirum &longs;uppo&longs;ito prædictas lineas e&longs;&longs;e comm. <lb/>

deducit ad impo&longs;&longs;ibile, &longs;iue, vt ait hic Ari&longs;t. fal&longs;um ratiocinatur, quod &longs;ci<lb/>

licet idem numerus e&longs;&longs;et par, & impar, quod Ari&longs;t. &longs;ignificat, quando ait, <lb/>

imparia æqualia paribus fiunt. </s>

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tem figura in omnibus textibus deprauata, quam &longs;ic puto <expan abbr="rè&longs;t&imacr;tuendam">rè&longs;tituendam</expan> e&longs;&longs;e <lb/>

ex quodam græco codice, qui characteres hoc modo appo&longs;uerat. </s>

<s id="id.000761">&longs;it I&longs;o&longs;ce<lb/>

les C A B, cuius ba&longs;is C B, Dico angulos &longs;upra ba&longs;im, <lb/>

in quibus literæ E F, e&longs;&longs;e inuicem æquales. </s>

<s id="id.000762">facto centro <lb/>

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<s id="id.000769">Ex cap. 2. &longs;ecti 2. lib. 1. <emph type="italics"/>(Secundum veritatem quidem ex ijs, quæ &longs;ecundum <lb/>

veritatem de&longs;cribuntur ine&longs;&longs;e, ad dialecticos autem &longs;yllogi&longs;mos ex propo&longs;itionibus <lb/>

&longs;ecundum opinionem)<emph.end type="italics"/> verba illa; ex ijs, quæ <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> veritatem de&longs;cribuntur <pb xlink:href="009/01/039.jpg" pagenum="39" />ine&longs;&longs;e; &longs;ic græcè, <foreign lang="greek">e/a tw_n xata\ aleiq/ei/an diagegramme/non,</foreign> vbi manife&longs;tè vtitur <lb/>

&longs;ecundum opinionem)<emph.end type="italics"/> verba illa; ex ijs, quæ <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> veritatem de&longs;cribuntur <pb pagenum="39" xlink:href="009/01/039.jpg"/>ine&longs;&longs;e; &longs;ic græcè, <foreign lang="greek">e/k tw=n kata\ alhqei/an diagegramme/non </foreign> vbi manife&longs;tè vtitur <lb/>

verbo, De&longs;cribere, per quod &longs;uperius annotauimus apud Ari&longs;t. &longs;ignificari <lb/>

Geometricas demon&longs;trationes, nam eas opponit dialecticis &longs;yllogi&longs;mis, &longs;e<lb/>

quentibus verbis, cum dixit (ad dialecticos autem &longs;yllogi&longs;mos ex propo&longs;i<lb/>

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<s id="id.000772">Ex eodem loco paulo po&longs;t <emph type="italics"/>(Quare principia quidem, quæ &longs;ecundum <expan abbr="vnum-quodq;">vnum<lb/>

quodque</expan> &longs;unt experimenti est tradere: dico autem, vt a&longs;trologicam experientiam <lb/>

a&longs;trologicæ &longs;cientiæ: acceptis enim apparentibus <expan abbr="&longs;uffici&etilde;ter">&longs;ufficienter</expan>, ita inuentæ &longs;unt a&longs;tro<lb/>

logicæ demonstrationes)<emph.end type="italics"/> Cum rationem tradat inueniendorum mediorum ad <lb/>quodlibet problema demon&longs;trandum; nunc docet, non omnia in &longs;cientijs <lb/>

logicæ demonstrationes)<emph.end type="italics"/> Cum rationem tradat inueniendorum mediorum ad <lb/>quodlibet problema demon&longs;trandum; nunc docet, non omnia in &longs;cientijs <lb/>po&longs;&longs;e probari, aut demoν&longs;trari: principia enim &longs;cientiarum <expan abbr="nõ">non</expan> demon&longs;tran<lb/>

po&longs;&longs;e probari, aut demou&longs;trari: principia enim &longs;cientiarum <expan abbr="nõ">non</expan> demon&longs;tran<lb/>

tur, &longs;ed &longs;ola experientia manife&longs;ta &longs;unt; vt patet in A&longs;tronomia, quæ ab ex<lb/>

perientia &longs;ua &longs;olet &longs;tabilire principia: principijs autem <expan abbr="experim&etilde;to">experimento</expan> con&longs;ti<lb/>

tutis ex ip&longs;is reliqua problemata <expan abbr="demon&longs;trãtur">demon&longs;trantur</expan>. </s>

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nem illam, quam duæ lineæ non in directum po&longs;itæ faciunt: &longs;iue etiam (vt <lb/>

melius percipiamus) angulum e&longs;&longs;e acumen illud, &longs;iue mucronem <expan abbr="ill&utilde;">illum</expan>, quem <lb/>

duæ lineæ non in directum con&longs;titutæ faciunt, vt duarum linearum A B, A C, <lb/>

inclinatio in puncto A, &longs;iue acumen illud, &longs;iue mucro, <lb/>

e&longs;t ratio anguli. </s>

<s id="id.000783">&longs;olum igitur duo anguli erunt æqua<lb/>

les, <expan abbr="quãdo">quando</expan> vnius acumen æquale erit acumini alterius; <lb/>

etiam &longs;i lineæ con&longs;tituentes vnum angulum &longs;int lon<lb/>

giores lineis alterum angulum con&longs;tituentibus, quia <lb/>quantitas anguli non attenditur penes longitudinem <pb xlink:href="009/01/040.jpg" pagenum="40" /><expan abbr="linear&utilde;">linearum</expan>, &longs;ed penes inclinationem, & mucronem, quem faciunt: vnde etiam&longs;i <lb/>

giores lineis alterum angulum con&longs;tituentibus, quia <lb/>quantitas anguli non attenditur penes longitudinem <pb pagenum="40" xlink:href="009/01/040.jpg"/><expan abbr="linear&utilde;">linearum</expan>, &longs;ed penes inclinationem, & mucronem, quem faciunt: vnde etiam&longs;i <lb/>

duæ lineæ prædictæ A B, A C, productæ, &longs;iue etiam decurtatæ fuerint, dum<lb/>

modo &longs;itus, &longs;iue po&longs;itio ip&longs;arum, quam ad inuicem habent, non varietur, <lb/>

erit &longs;emper eadem quantitas anguli A. </s>

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<s id="id.000786">Porrò quemadmodum vnus angulus vni angulo æqualis e&longs;t, ita <lb/>

<expan abbr="aliquãdo">aliquando</expan> duo anguli &longs;unt vni angulo æquales, vt patet, &longs;i vnus angulus, v.g. <lb/>

angulus B A C, diuidatur in duos angulos à linea A D. tunc enim duo angu<lb/>

li partiales B A D, D A C, erunt æquales totali angulo <lb/>

B A C, cum partes omnes &longs;imul &longs;umptæ &longs;int &longs;uo toti æqua<lb/>

les. </s>

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li &longs;imul ad vnum punctum con&longs;tituti <expan abbr="adæquar&etilde;tur">adæquarentur</expan> mucro<lb/>

ni illi, quem con&longs;tituerent alij duo anguli, quibus illi tres <lb/>

&longs;unt pares, v.g. &longs;int tres anguli trianguli A B C, <expan abbr="&longs;int&qacute;">&longs;intque</expan>; alij duo anguli recti, <lb/>

quos linea perpendicularis D E, facit cum li<lb/>

nea F G; &longs;it <expan abbr="inquã">inquam</expan> anguli recti D E F, D E G, <lb/>

tunc tres anguli illius <expan abbr="triãguli">trianguli</expan> <expan abbr="dic&etilde;tur">dicentur</expan> æqua<lb/>

les duobus hi&longs;ce rectis, &longs;i tres illi mucrones <lb/>

trianguli &longs;imul &longs;umpti, & vniti ad punctum <lb/>

E, ad quod duo <expan abbr="quoq;">quoque</expan> mucrones angulorum <lb/>

rectorum coeunt, congruent omnino duobus <lb/>

prædictis angulis rectis, &longs;iue duobus illis mu<lb/>

cronibus angulorum rectorum, &longs;iue con&longs;ti<lb/>

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angulum F E H, & &longs;i ibi iuxta ip&longs;um apponeretur mucro A, faceret angulum <lb/>

H E I. quem &longs;i deinceps &longs;ub&longs;equetur reliquus angulus C, con&longs;titueret <expan abbr="reli-qu&utilde;">reli<lb/>

quum</expan> angulum I E G. iam, vt vides, illi tres anguli ad E, tran&longs;lati, &longs;unt æqua<lb/>

les duobus rectis ad E, pariter con&longs;titutis, cum illi tres fiant partes duorum <lb/>

les duobus rectis ad E, pariter con&longs;titutis, cum illi tres fiant partes duorum <lb/>rectorúm, vel quia occupant idem &longs;patium, vel eandem lineam rectam F E G, <lb/>

rectorú, vel quia occupant idem &longs;patium, vel eandem lineam rectam F E G, <lb/>

con&longs;tituant. </s>

<s id="id.000788">habet igitur omne triangulum &longs;iue &etail;quilaterum, &longs;iue &longs;calenum, <lb/>

&longs;iue I&longs;o&longs;celes mirabilem hanc proprietatem, vt tres anguli, cuiu&longs;uis trian<lb/>

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des deinde ibidem aliter, quam Pythagorici idem demon&longs;trauit. </s>

<s id="id.000790">Quod &longs;i <lb/>

quis huius rei <expan abbr="experi&etilde;tiam">experientiam</expan> aliquam velit; etiam&longs;i non exactam (cum æqua<lb/>

litas mathematica non cadat &longs;ub &longs;en&longs;um, &longs;ed &longs;ola intelligentia percipiatur, <lb/>quippe quæ in materia intelligibili, non autem &longs;en&longs;ibili ver&longs;atur, & cuius <pb xlink:href="009/01/041.jpg" pagenum="41" />æqualitas nullum di&longs;crimen, quantumuis minimum admittat, quod &longs;en&longs;ui <lb/>

litas mathematica non cadat &longs;ub &longs;en&longs;um, &longs;ed &longs;ola intelligentia percipiatur, <lb/>quippe quæ in materia intelligibili, non autem &longs;en&longs;ibili ver&longs;atur, & cuius <pb pagenum="41" xlink:href="009/01/041.jpg"/>æqualitas nullum di&longs;crimen, quantumuis minimum admittat, quod &longs;en&longs;ui <lb/>

vitare ob &longs;ui imperfectionem non licet: vnde inter eæ, quæ mathematicè <lb/>

&longs;unt æqualia, nullus intellectus aliquam valeat reperire differentiam) &longs;umat <lb/>

inquam triangulum quodpiam materiale, vt ex charta, quantum fieri po<lb/>te&longs;t perfectum, deinde ducat lineam vnam perpendicularem &longs;uper aliam, <lb/>

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&longs;cribunt, vt per ea, de verè mathematicis di&longs;currant.</s>

</chap>

<chap>

<s id="id.000808"><emph type="italics"/>Ex Libro &longs;ecundo Priorum.<emph.end type="italics"/></s>

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enim græca <foreign lang="greek">parallhlos,</foreign> idem &longs;ignificat, ac mutuus, & coalternus. </s>

<s id="id.000813">quoad <lb/>

exempli explicationem vtor figura textibus apponi &longs;olita, quæ e&longs;t præ&longs;ens. <lb/>

probat Euclides in 28. primi Elem. quod &longs;i <lb/>

linea recta quædam, vti E F, cadens &longs;uper <lb/>

duas rectas, vti &longs;unt A B, C D, fecerit angu<lb/>

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<s id="id.000818">Ex cap. 22. lib. 2. Priorum <emph type="italics"/>(Vt &longs;i volens mon&longs;trare, quod diameter e&longs;t incom<lb/>

men&longs;. argueret Zenonis rationem, quod non e&longs;t moueri)<emph.end type="italics"/> &longs;uperius &longs;ecto 3. lib. 1. <lb/>

fusè explicauimus hanc a&longs;ymmetriam, quam &longs;i quis vellet demon&longs;trare ea<lb/>

dem illa ratione, qua Zeno motum impugnabat, quia &longs;cilicet <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan> com<lb/>

dem illa ratione, qua Zeno motum impugnabat, quia &longs;cilicet <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan> com<lb/>munis, quæ debet vtramque, quantitatem men&longs;urare, debet in men&longs;urando <lb/>infinitas partes pertran&longs;ire, nimirum medietates medietatum in infinitum, <lb/>

munis, quæ debet vtramq, quantitatem men&longs;urare, debet in men&longs;urando <lb/>infinitas partes pertran&longs;ire, nimirum medietates medietatum in infinitum, <lb/>

e&longs;t autem impo&longs;&longs;ibile pertran&longs;ire infinitas huiu&longs;modi partes, & propterea <lb/>

non poterit metiri, <expan abbr="neq;">neque</expan> vnam, <expan abbr="neq;">neque</expan> alteram ex <expan abbr="quãtitatibus">quantitatibus</expan>, quæ putaban<lb/>

tur commen&longs;urabiles, afferret hic, inquit Ari&longs;t. non cau&longs;am pro cau&longs;a.</s>

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angulo videlicet G H D. &longs;i ergo inquit Ari&longs;t &longs;upponamus i&longs;tud fal&longs;um, an<lb/>

gulum &longs;cilicet E G B, externum e&longs;&longs;e maiorem angulo interno G H D, &longs;equi<lb/>

tur etiam fal&longs;um, videlicet lineas <expan abbr="æquidi&longs;tãtes">æquidi&longs;tantes</expan> A B, C D, concurrere. </s>

<s id="id.000825">& pro<lb/>batur con&longs;equentia hoc modo, quia &longs;i angulus E G B, maior e&longs;t angulo <pb xlink:href="009/01/043.jpg" pagenum="43" />G H D, appo&longs;ito <expan abbr="vtiq;">vtique</expan> communi angulo B G H, erant primum, duo anguli <lb/>

<s id="id.000825">& pro<lb/>batur con&longs;equentia hoc modo, quia &longs;i angulus E G B, maior e&longs;t angulo <pb pagenum="43" xlink:href="009/01/043.jpg"/>G H D, appo&longs;ito <expan abbr="vtiq;">vtique</expan> communi angulo B G H, erant primum, duo anguli <lb/>

E G B, B G H, maiores, quam &longs;int duo B G H, G H D, quia &longs;i inæqualibus <lb/>

æqualia addantur, tota erunt inæqualia, vt prius per 4, axioma: hoc loco <lb/>

communis angulus additur &longs;emel maiori angulo, & &longs;emel minori; & ideo <lb/>

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<s id="id.000830">Præterea &longs;i &longs;upponamus aliam fal&longs;itatem, &longs;cilicet triangulum habere tres <lb/>

angulos maiores duobus rectis, &longs;equetur eadem iterum fal&longs;itas, &longs;cilicet pa<lb/>

rallelas coincidere, & probatur &longs;ic; &longs;int enim <lb/>

<expan abbr="triãguli">trianguli</expan> A B C, tres anguli maiores, quam duo <lb/>

recti anguli, & per punctum C, ducta &longs;it recta <lb/>

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<s id="id.000844">Notandum hic cum eruditi&longs;&longs;imo Burana, Abductionem hanc, de qua in hoc <lb/>

cap. agitur e&longs;&longs;e vocem mathematicam, <expan abbr="cam&qacute;">camque</expan>; Ari&longs;t. quemadmodum multa <lb/>

cap. agitur e&longs;&longs;e vocem mathematicam, <expan abbr="cam&qacute;">eamque</expan>; Ari&longs;t. quemadmodum multa <lb/>

alia à Mathematicis mutuatum ad omnes alias &longs;cientias tran&longs;tuli&longs;&longs;e. </s>

<s id="id.000845">e&longs;&longs;e <pb xlink:href="009/01/044.jpg" pagenum="44" />autem terminum mathematicum colligitur manife&longs;tè ex Proelo, qui lib. 3. <lb/>

<s id="id.000845">e&longs;&longs;e <pb pagenum="44" xlink:href="009/01/044.jpg"/>autem terminum mathematicum colligitur manife&longs;tè ex Proelo, qui lib. 3. <lb/>

in comm. Elem. Euclidis ad primam propo&longs;itionem primi Elementi, pag. <lb/>

</s>

<s id="id.000846">121. &longs;ic ait, Abductio verò e&longs;t tran&longs;itus à propo&longs;ito problemate, vel theo<lb/>

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quod patet ducta &longs;emidiametro H G, perpendiculari ex B C, quæ &longs;uo extre<lb/>

mo puncto G, &longs;ecat bifariam, & <expan abbr="diametr&utilde;">diametrum</expan> B D, & circumferentiam B G C. <lb/>

facto ergo centro G, de&longs;cribatur alter circulus per puncta B C D F, <expan abbr="conne-ctatur&qacute;">conne<lb/>

ctaturque</expan>; recta G C. in triangulo orthogonio B C D, latus B D, &longs;ubtenditur <pb xlink:href="009/01/045.jpg" pagenum="45" /><figure id="id.009.01.045.1.jpg" xlink:href="009/01/045/1.jpg" place="text"/><lb/>

ctaturque</expan>; recta G C. in triangulo orthogonio B C D, latus B D, &longs;ubtenditur <pb pagenum="45" xlink:href="009/01/045.jpg"/><figure id="id.009.01.045.1.jpg" place="text" xlink:href="009/01/045/1.jpg"/><lb/>

angulo recto C, ergo quadratum eius ex corol<lb/>

lario 47. primi, duplum erit quadrati B C, quare <lb/>

etiam circulus B C D F, duplus erit circuli A B<lb/>

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<s id="id.000859">&longs;ed vt reliquum circu<lb/>

li quadret, &longs;ic pergit, ponatur recta L M, dupla <lb/>

ip&longs;ius B C, &longs;upra quam &longs;emicirculus de&longs;cribatur <lb/>

L O M, cui in&longs;cribatur hexagoni <lb/>

æquilateri dimidium L Q S M, & &longs;u<lb/>

per tribus hexagoni lateribus, &longs;int <lb/>

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re valuit. </s>

<s id="id.000865">Hæc pluribus, vt &longs;equentibus etiam textibus, in quibus huius te<lb/>

tragoni&longs;mi fit mentio &longs;atisfacere po&longs;&longs;imus. </s>

<s id="id.000866">Hippocrates i&longs;te Chius e&longs;t alter <pb xlink:href="009/01/046.jpg" pagenum="46" />ab illo Hippocrate Coo medicorum Magi&longs;tro, vt colligitur ex Alexandre <lb/>

<s id="id.000866">Hippocrates i&longs;te Chius e&longs;t alter <pb pagenum="46" xlink:href="009/01/046.jpg"/>ab illo Hippocrate Coo medicorum Magi&longs;tro, vt colligitur ex Alexandre <lb/>

Aphrod. in Primum Meteororum de Cometis.</s>

</chap>

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<s id="id.000880">alludit ad demon&longs;trationem quandam, quam ip&longs;e infe<lb/>

rius in exemplum adducet, & quæ e&longs;t in 3. Elem. Euclidis 31. in qua talis fi<lb/>

gura proponitur qualis e&longs;t præ&longs;ens, in qua vides triangulum A B C. in &longs;e<lb/>

micirculo. </s>

<s id="id.000881">tunc autem dicitur triangulum in <lb/>

&longs;emicirculo, quando ba&longs;is ip&longs;ius e&longs;t diameter <lb/>

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ceptis &longs;ic <expan abbr="loc&utilde;">locum</expan> hunc explicare po&longs;&longs;umus, cum diameter quadrati &longs;it incom

<pb xlink:href="009/01/047.jpg" pagenum="47" />men&longs;urabilis lateri &longs;ui quadrati, fal&longs;um erit dicere diametrum e&longs;&longs;e com<lb/>

<pb pagenum="47" xlink:href="009/01/047.jpg"/>men&longs;urabilis lateri &longs;ui quadrati, fal&longs;um erit dicere diametrum e&longs;&longs;e com<lb/>

men&longs;urabilem prædicto lateri, quod autem fal&longs;um e&longs;t, illud non e&longs;t; igitur <lb/>

impo&longs;sibile e&longs;t &longs;cire diametrum e&longs;&longs;e commen&longs;urabile.</s>

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<s id="id.000902">Eodem tex. 9. <emph type="italics"/>(Et <expan abbr="quibu&longs;cunq;">quibu&longs;cunque</expan> inexi&longs;tentium ip&longs;is, ip&longs;æ &longs;unt in oratione, quid<emph.end type="italics"/> <pb xlink:href="009/01/048.jpg" pagenum="48" /><emph type="italics"/>est declarante, quemadmodum rectum ine&longs;t lineæ, & circulare: & impar, & par<lb/>

<s id="id.000902">Eodem tex. 9. <emph type="italics"/>(Et <expan abbr="quibu&longs;cunq;">quibu&longs;cunque</expan> inexi&longs;tentium ip&longs;is, ip&longs;æ &longs;unt in oratione, quid<emph.end type="italics"/> <pb pagenum="48" xlink:href="009/01/048.jpg"/><emph type="italics"/>est declarante, quemadmodum rectum ine&longs;t lineæ, & circulare: & impar, & par <lb/>

numero, & primum, & compo&longs;itum, & æquilaterum, & altera parte longius. </s>

<expan abbr="o&itilde;bus">oimbus</expan> bis in&longs;unt in oratione, quid e&longs;t <expan abbr="declarãte">declarante</expan>, ibi quidem linea, hic vero numerus)<emph.end type="italics"/><lb/>

<expan abbr="o&itilde;bus">omnibus</expan> bis in&longs;unt in oratione, quid e&longs;t <expan abbr="declarãte">declarante</expan>, ibi quidem linea, hic vero numerus)<emph.end type="italics"/><lb/>

quia locus hic benè exponitur à Toleto, & melius etiam à Conymbr. </s>

<s id="id.000904">addam <lb/>

tantummodo quædam, quæ ad perfectam eius intelligentiam de&longs;iderantur. <lb/>

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<s id="id.000912">Per æquilaterum, intelligit quadratum, quadratus autem numerus defi<lb/>

nitione 18. &longs;eptimi &longs;ic explicatur: Quadratus numerus e&longs;t, qui &longs;ub duobus <lb/>

æqualibus numeris continetur, ide&longs;t, qui fit ex ductu vnius numeri in &longs;e ip<lb/>

&longs;um, vt &longs;i ducantur 3. in 3. fient 9. qui continetur &longs;ub duobus <lb/>

ternarijs; omnes autem ternarij &longs;unt æquales. </s>

<s id="id.000913">is autem nu<lb/>

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<s id="id.000916">Per altera parte longius, intelligit numerum, qui producitur à duobus <lb/>

numeris inæqualibus inuicem multiplicatis, qualis e&longs;t <lb/>

duodenarius, qui ex ductu trium in quatuor produci<lb/>

tur, & refert figuram altera parte longiorem, &longs;iue, vt <lb/>

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<s id="id.000920">Tex. 11. <emph type="italics"/>(Per &longs;e autem, & &longs;ecundum quod ip&longs;um, idem, vt per &longs;e lineæ inest<emph.end type="italics"/> <pb xlink:href="009/01/049.jpg" pagenum="49" /><emph type="italics"/>punctum, & rectum; etenim &longs;ecundum quod linea, & triangulo, &longs;ecundum quod <lb/>

<s id="id.000920">Tex. 11. <emph type="italics"/>(Per &longs;e autem, & &longs;ecundum quod ip&longs;um, idem, vt per &longs;e lineæ inest<emph.end type="italics"/> <pb pagenum="49" xlink:href="009/01/049.jpg"/><emph type="italics"/>punctum, & rectum; etenim &longs;ecundum quod linea, & triangulo, &longs;ecundum quod <lb/>

triangulum duo recti: etenim per &longs;e triangulum duobus rectis æquale. </s>

<s id="id.000921">Vniuer&longs;ale <lb/>

autem e&longs;t tunc, quando in quolibet, & primo mon&longs;tratur, vt duos rectos habere, <lb/>

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<s id="id.000931">Tex. 13. <emph type="italics"/>(Si quis igitur mon&longs;trauerit, quod rectæ <expan abbr="nõ">non</expan> coincidunt, videbitur <expan abbr="vtiq;">vtique</expan> <lb/>

<s id="id.000931">Tex. 13. <emph type="italics"/>(Si quis igitur mon&longs;trauerit, quod rectæ <expan abbr="nõ">non</expan> coincidunt, videbitur <expan abbr="vtiq;">vtique</expan> <lb/>huius e&longs;&longs;e demonstratio, eo quod in omnibus e&longs;t rectis; non e&longs;t autem: &longs;i quidem <lb/>

buius e&longs;&longs;e demonstratio, eo quod in omnibus e&longs;t rectis; non e&longs;t autem: &longs;i quidem <lb/>

non quoniam &longs;ic æquales, fit hoc, &longs;ed &longs;ecundum quod <expan abbr="quomodocunq;">quomodocunque</expan> æquales)<emph.end type="italics"/> pro<lb/>

ponit tres errores, qui circa demon&longs;trationem de vniuer&longs;ali contingunt, <lb/>

quos omnes Geometricis exemplis illu&longs;trat; affert autem primo pro tertio <lb/>

errore duo exempla, quorum primum in præmi&longs;&longs;is verbis continetur, <expan abbr="atq;">atque</expan> <lb/>

ex 28. primi Elem. de&longs;umitur, quam propterea primo loco exponendam <lb/>

cen&longs;ui. </s>

<s id="id.000932">Quando igitur duæ rectæ con&longs;titu<lb/>

tæ fuerint, vt A B, C D, in quas alia recta, <lb/>

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quia linea E F, pote&longs;t facere aliquando prædictos angulos non <expan abbr="tant&utilde;">tantum</expan> æqua<lb/>

les duobus rectis, verum etiam rectos, quo etiam modo <expan abbr="probar&etilde;tur">probarentur</expan> cædem <lb/>

lineæ e&longs;&longs;e parallelæ, vt in &longs;equenti figura, cum &longs;int anguli A G I, C I G, re<lb/>

cti, probabitur de rectis A B, C D, æquidi&longs;tan<lb/>

tia. </s>

<s id="id.000934">Ex his facile textum in hunc modum expo<lb/>

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videbitur <expan abbr="vtiq;">vtique</expan> huius e&longs;&longs;e demon&longs;tratio de vniuer&longs;ali per &longs;e, & de primo &longs;u

<pb xlink:href="009/01/050.jpg" pagenum="50" />biecto, vel &longs;ecundum quod ip&longs;um, eò quod probatur vniuer&longs;aliter de lineis <lb/>

<pb pagenum="50" xlink:href="009/01/050.jpg"/>biecto, vel &longs;ecundum quod ip&longs;um, eò quod probatur vniuer&longs;aliter de lineis <lb/>

omnibus habentibus prædictos angulos rectos. </s>

<s id="id.000935">non autem de omni, &longs;ecun<lb/>

dum quod ip&longs;um, &longs;i quidem non competit affectio hæc, e&longs;&longs;e parallelas, li<lb/>

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modum & mon&longs;trabatur aliquando &longs;eor&longs;um, contingens <expan abbr="vtiq;">vtique</expan> de omnibus vnica <lb/>demon&longs;tratione mon&longs;trari; &longs;ed quia non &longs;unt nominatum quidam omnia hæc vnum, <lb/>

numeri, longitudines, tempora &longs;olida, & &longs;pecie differunt à &longs;einuicem &longs;eor&longs;um <expan abbr="ac-cipiebãtur">ac<lb/>

cipiebantur</expan>. </s>

<s id="id.000949">nunc autem vniuer &longs;aliter mon&longs;tratur, <expan abbr="neq;">neque</expan> enim &longs;ecundum quod lineæ, <lb/>

<s id="id.000949">nunc autem vniuer aliter mon&longs;tratur, <expan abbr="neq;">neque</expan> enim &longs;ecundum quod lineæ, <lb/>aut &longs;ecundum quod numeri, inerat; &longs;ed &longs;ecundum quod hoc, quod vniuer&longs;ale &longs;up<lb/>

aut &longs;ecundum quod numeri, inerat; &longs;ed &longs;ecundum quod boc, quod vniuer &longs;ale &longs;up<lb/>

ponunt e&longs;&longs;e)<emph.end type="italics"/> affert exemplum &longs;ecundi erroris, qui accidit, quando vniuer&longs;a<lb/>

le exi&longs;tit quidem, &longs;ed tamen e&longs;t innominatum, pro cuius explicatione &longs;cien

<pb xlink:href="009/01/051.jpg" pagenum="51" />dum quid &longs;it alterna proportio. </s>

<pb pagenum="51" xlink:href="009/01/051.jpg"/>dum quid &longs;it alterna proportio. </s>

<s id="id.000950">Alternam igitur proportionem definit Eu<lb/>

clides definitione 12. quinti, &longs;ic, e&longs;t &longs;umptio antecedentis ad <expan abbr="anteced&etilde;tem">antecedentem</expan>, <lb/>

& con&longs;equentis ad con&longs;equentem. </s>

<s id="id.000951">Explico, exponantur qua<lb/>

tuor quantitates proportionales, v.g. vt 6. ad 3. ita &longs;int 4. ad <lb/>

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hunc interpretaberis; Propter hoc, quod præcedenti textu dictum e&longs;t; no<lb/>

tandum in primo errore vniuer&longs;ale, tanquam &longs;i non e&longs;&longs;et vniuer&longs;ale o&longs;ten<lb/>

ditur de &longs;ingulari, &longs;i quis igitur mon&longs;trauerit &longs;ingillatim de <expan abbr="vnoquoq;">vnoquoque</expan> trian<lb/>

gulo in &longs;ingulari, &longs;cilicet de vno æquilatero, tantum, & de vno Scaleno, & <lb/>de vno I&longs;o&longs;cele, &longs;eparatim, vtens aut eadem demon&longs;tratione dum de <expan abbr="vno&qacute;">vnoque</expan>; <pb xlink:href="009/01/052.jpg" pagenum="52" />&longs;epatatim o&longs;tendit, aut vtens diuer&longs;is demon&longs;trationibus, vna pro æquila<lb/>

gulo in &longs;ingulari, &longs;cilicet de vno æquilatero, tantum, & de vno Scaleno, & <lb/>de vno I&longs;o&longs;cele, &longs;eparatim, vtens aut eadem demon&longs;tratione dum de <expan abbr="vno&qacute;">vnoque</expan>; <pb pagenum="52" xlink:href="009/01/052.jpg"/>&longs;eparatim o&longs;tendit, aut vtens diuer&longs;is demon&longs;trationibus, vna pro æquila<lb/>

tero, altera pro I&longs;o&longs;cele, tertia pro Scaleno, o&longs;tendens, quod <expan abbr="vnumquodq;">vnumquodque</expan> <lb/>

illorum habet tres angules æquales duobus rectis angulis; i&longs;te nondum no<lb/>

uit triangulum omne habere talem affectionem, ni&longs;i modo &longs;ophi&longs;tico, quia <lb/>

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lis e&longs;t. </s>

<s id="id.000979">8. qui e&longs;t ad in&longs;tar cubi geometrici, & continetur &longs;ub tribus binarijs <lb/>

multiplicatis inuicem, quæ multiplicatio &longs;ic in&longs;tituitur, exponuntur tres bi<lb/>

narij, 2, 2, 2, primus ducitur in &longs;ecundum, & producitur. <lb/>

</s>

<s id="id.000980">4. qui e&longs;t numerus quadratus huius figuræ, <figure id="id.009.01.052.2.jpg" xlink:href="009/01/052/2.jpg" place="text"/>, deinde <lb/>

<s id="id.000980">4. qui e&longs;t numerus quadratus huius figuræ, <figure id="id.009.01.052.2.jpg" place="text" xlink:href="009/01/052/2.jpg"/>, deinde <lb/>

tertius binarius ducitur in prædictum quadratum 4. & pro<lb/>

ducitur 8. qui dicitur cubus, quia &longs;i intelligantur duo qua<lb/>

ternarij, vnus &longs;upra alterum, vt in præ&longs;enti figura refe<lb/>

runt cubicam figuram, cuius tam longitudo, quam latitudo,

<pb xlink:href="009/01/053.jpg" pagenum="53" />& altitudo, e&longs;t 2. Similiter cubus numerus e&longs;t 27. quia &longs;it ex tribus terna<lb/>

<pb pagenum="53" xlink:href="009/01/053.jpg"/>& altitudo, e&longs;t 2. Similiter cubus numerus e&longs;t 27. quia &longs;it ex tribus terna<lb/>

rijs inuicem modo prædicto multiplicatis, 3. 3. 3. nam 3. in 3. ductis &longs;it 9. <lb/>

qui e&longs;t quadratus. </s>

<s id="id.000981">quo deinde ducto in tertium ter<lb/>

narium, producitur 27. qui e&longs;t cubus, & refert figu<lb/>

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dentur eminus videri minora, quam quæ videntur cominus, quia illa viden<lb/>

tur &longs;ub angulo minori, hæc verò &longs;ub angulo maiori, quod verò remotiora <lb/>

videantur &longs;ub angulo minori, quam propinquiora cæteris paribus probat <lb/>

per 21. primi Elem. &longs;it enim ma<lb/>

gnitudo vi&longs;a A B, remotior ab o<lb/>

culo in C, po&longs;ito, & vi&longs;a propin<lb/>

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optica. </s>

<s id="id.000990">Exemplum &longs;ubalternationis Mu&longs;icæ &longs;it, <expan abbr="con&longs;onãtia">con&longs;onantia</expan> Diapa&longs;on, quam <lb/>

vulgò octauam appellant in data chorda collocare, hoc e&longs;t, vocem grauio<lb/>

rem facere duplam vocis acutioris &longs;umatur chorda A B, & diuidatur bifa<lb/>riam, &longs;ine in æqualia in C; tota igitur chorda A B, ad dimidium A C, haber <pb xlink:href="009/01/054.jpg" pagenum="54" /><figure id="id.009.01.054.1.jpg" xlink:href="009/01/054/1.jpg" place="text"/><lb/>

rem facere duplam vocis acutioris &longs;umatur chorda A B, & diuidatur bifa<lb/>riam, &longs;ine in æqualia in C; tota igitur chorda A B, ad dimidium A C, habet <pb pagenum="54" xlink:href="009/01/054.jpg"/><figure id="id.009.01.054.1.jpg" place="text" xlink:href="009/01/054/1.jpg"/><lb/>

proportionem, quam 2. ad 1. <lb/>

&longs;iue duplam, ergo etiam &longs;o<lb/>

nus totius chordæ A B, ad <expan abbr="&longs;o-n&utilde;">&longs;o<lb/>

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<s id="id.000999">&longs;it qua<lb/>drandus circulus A B C D, cui circum&longs;cribatur quadratum E F G H. per <lb/>

7 quarti, & alterum quadratum I L M N, eidem in&longs;cribatur per 6. quarti, <lb/>

quid autem &longs;it circum&longs;cribere, & in&longs;cribere figuram circulo, ex definitione <lb/>

3. & 4. eiu&longs;dem libri petatur, quamuis <lb/>

ex in&longs;pectione figuræ <expan abbr="pr&etail;s&etilde;tis">pr&etail;sentis</expan> &longs;atis per<lb/>

cipi po&longs;&longs;it; deinde aliud <expan abbr="quadrat&utilde;">quadratum</expan> me<lb/>

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<s id="id.001006">In codem textu <emph type="italics"/>(<expan abbr="Vnumquodq;">Vnumquodque</expan> autem &longs;cimus, non &longs;ecundum accidens, quando <lb/>

&longs;ecundum illud cogno&longs;camus, &longs;ecundum quod ine&longs;t ex principijs illius, &longs;ecundam <lb/>

quod illud; vt duobus rectis æquales, habere, cui ine&longs;t per &longs;e, quod dictum e&longs;t ex<emph.end type="italics"/> <pb xlink:href="009/01/055.jpg" pagenum="55" /><emph type="italics"/>principijs huius)<emph.end type="italics"/> affert nunc exemplum alterius demon&longs;trationis, quæ non <lb/>

quod illud; vt duobus rectis æquales, habere, cui ine&longs;t per &longs;e, quod dictum e&longs;t ex<emph.end type="italics"/> <pb pagenum="55" xlink:href="009/01/055.jpg"/><emph type="italics"/>principijs huius)<emph.end type="italics"/> affert nunc exemplum alterius demon&longs;trationis, quæ non <lb/>

ex communibus, vt præcedens Bry&longs;onis, &longs;ed ex proprijs principijs o&longs;tendit <lb/>

affectionem de &longs;ubiecto proprio. </s>

<s id="id.001007">E&longs;t autem illud exemplum toties decan<lb/>

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circo operæpretium e&longs;&longs;e puto explicare demon&longs;trationem, 32. primi Eucli<lb/>

dis, quæ i&longs;tud ex proprijs principijs demon&longs;trat, & quam hoc loco Ari&longs;to<lb/>

teles innuit, hoc enim modo ip&longs;ius Ari&longs;t. mentem probè penetrare poteri<lb/>

mus. </s>

<s id="id.001008">&longs;it ergo <expan abbr="triãgulum">triangulum</expan> A B C. </s>

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tionibus geometricis con&longs;truuntur, nunquam &longs;unt media propria demon<lb/>

&longs;trationum, &longs;ed tantummodo a&longs;&longs;umuntur ad probandum medium iam ex<lb/>

cogitatum e&longs;&longs;e veram cau&longs;am conclu&longs;ionis. </s>

<s id="id.001019">Hinc etiam manife&longs;tè colligas <pb xlink:href="009/01/056.jpg" pagenum="56" />Mathematicas facultates habere demon&longs;trationes perfecti&longs;&longs;imas, quod <lb/>

<s id="id.001019">Hinc etiam manife&longs;tè colligas <pb pagenum="56" xlink:href="009/01/056.jpg"/>Mathematicas facultates habere demon&longs;trationes perfecti&longs;&longs;imas, quod <lb/>

ageometreti negare &longs;olent, &longs;ed audacter aiunt exempla Ari&longs;t. non e&longs;&longs;e vera: <lb/>

<expan abbr="neq;">neque</expan> requiri veritatem exemplorum; in <expan abbr="quor&utilde;">quorum</expan> <expan abbr="vtroq;">vtroque</expan> peccant, nam dictum <lb/>

illud v&longs;urpari &longs;olet, & debet de exemplis moralibus. </s>

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<s id="id.001021">Verum i&longs;ti confundunt conformitatem cum veritate. </s>

<s id="id.001022">Veritas exemplo tunc <lb/>

ine&longs;t, quando illud, quod in exemplo narratur, verè extitit, vt &longs;i quis in <lb/>

exemplum pudicitiæ afferret hi&longs;toriam Io&longs;ephi, <expan abbr="ver&utilde;">verum</expan> i&longs;tuà e&longs;&longs;et exemplum. <lb/>

exemplum pudicitiæ afferret hi&longs;toriam Io&longs;ephi, <expan abbr="ver&utilde;">verum</expan> i&longs;tud e&longs;&longs;et exemplum. <lb/>

</s>

<s id="id.001023">quæ veritas in exemplis moralibus non &longs;emper e&longs;t nece&longs;&longs;aria, talia exempla <lb/>

&longs;unt &longs;æpè parabolæ, & fabulæ, quæ nunquam extiterunt, v. g. narratur ab <lb/>

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<s id="id.001035">Ibidem <emph type="italics"/>(Sed quemadmod&ubreve; harmonica per Arithmeticam)<emph.end type="italics"/> vide &longs;upra tex. 20.</s>

<s id="id.001035">Ibidem <emph type="italics"/>(Sed quemadmod&ubreve;m harmonica per Arithmeticam)<emph.end type="italics"/> vide &longs;upra tex. 20.</s>

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quouis &longs;ecat oppo&longs;itum latus bifariam, crit in linea A D, <expan abbr="centr&utilde;">centrum</expan> grauitatis.

&longs;ed eadem ratione erit etiam in linea B E, er<lb/>

go non ni&longs;i in puncto F, quod <expan abbr="&longs;ol&utilde;">&longs;olum</expan> e&longs;t in vtra<lb/>

que, quod erat demon&longs;trandum. </s>

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<s id="id.001049">Ibidem <emph type="italics"/>(Geometrica verò quid irrationale, aut refrangi, aut concurrere)<emph.end type="italics"/> per <lb/>

verbum, irrationale, non videtur Ari&longs;t. intellexi&longs;&longs;e proprietatem illam duo<lb/>

rum linearum incommen&longs;urabilium longitudine, & potentia, quia v&longs;us fui&longs;<lb/>

&longs;et verbo, <foreign lang="greek">a/rrpton.</foreign> quod apud Geometras v&longs;urpari &longs;olet in illa &longs;ignificatio<lb/>

&longs;et verbo, <foreign lang="greek">a/orhton.</foreign> quod apud Geometras v&longs;urpari &longs;olet in illa &longs;ignificatio<lb/>

ne, &longs;ed v&longs;us e&longs;t verbo, <foreign lang="greek">a\logon,</foreign> quod latinè redditur improportionale.</s>

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aduerte, quod quamuis nonnulli codices habeant pro, in mathematicis, in

<pb xlink:href="009/01/058.jpg" pagenum="58" />di&longs;ciplinis, idem tamen apud græcos <foreign lang="greek">maqhmata</foreign> &longs;unt, ac apud latinos di&longs;ci<lb/>

<pb pagenum="58" xlink:href="009/01/058.jpg"/>di&longs;ciplinis, idem tamen apud græcos <foreign lang="greek">maqhmata</foreign> &longs;unt, ac apud latinos di&longs;ci<lb/>

plinæ; verbum autem <foreign lang="greek">maqhmata</foreign> v&longs;urpat hoc loco Ari&longs;toteles. </s>

<s id="id.001066">Porrò non <lb/>

e&longs;t in mathematicis, &longs;icut in alijs paralogi&longs;mus, quia in omni demon&longs;tra<lb/>

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plici proportione: etenim ignis celeriter gignitur, vt ait: & hæc est proportio. </s>

<s id="id.001072">&longs;ic <lb/>autem non e&longs;t &longs;yllogi&longs;mus, ni&longs;i celerrimam proportio &longs;equatur multiplex: & ignem <lb/>

celerrima in motu proportio)<emph.end type="italics"/> verba illa (in multiplici proportione) græcè &longs;ic <lb/>

&longs;e habent, <foreign lang="greek">en th pollaplasioni analogia,</foreign> quod melius redditur latinè in mul<lb/>

&longs;e habent, <foreign lang="greek">en th| pollaplasioni analogia|,</foreign> quod melius redditur latinè in mul<lb/>

tiplici proportione, quemadmodum fecimus, quam in multiplicata, quem<lb/>

admodum in vulgata editione. </s>

<s id="id.001073">porrò quid inter multiplicem, & multipli<lb/>

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præ&longs;tantia elucet, quia &longs;cilicet mathematicæ pro medijs vtuntur definitio

<pb xlink:href="009/01/059.jpg" pagenum="59" />nibus &longs;ubiecti, aut pa&longs;&longs;ionis, quæ nullo modo &longs;unt accidentalia conclu&longs;ioni, <lb/>

<pb pagenum="59" xlink:href="009/01/059.jpg"/>nibus &longs;ubiecti, aut pa&longs;&longs;ionis, quæ nullo modo &longs;unt accidentalia conclu&longs;ioni, <lb/>

v. g. in prima Euclidis demon&longs;tratione per definitionem &longs;ubiecti probantur <lb/>

tres lineæ e&longs;&longs;e æquales, quia nimirum &longs;int &longs;emidiametri circulorum æqua<lb/>

lium, quæ e&longs;t ip&longs;arum definitio. </s>

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<s id="id.001097">Tex. 30. (<emph type="italics"/>Rur&longs;us quemadmodum mon&longs;trant Lunam, quod &longs;phærica &longs;it per aug<lb/>

<s id="id.001097">Tex. 30. (<emph type="italics"/>Rur&longs;us quemadmodum mon&longs;trant Lunam, quod &longs;phærica &longs;it per aug<lb/>menta: &longs;i enim quod ita augetur, e&longs;t &longs;phæricum; augetur autem Luna; plan&ubreve;m quod <lb/>

menta: &longs;i enim quod ita augetur, e&longs;t &longs;phæricum; augetur autem Luna; plan&ubreve; quod <lb/>

&longs;phærica<emph.end type="italics"/>) Illius demon&longs;trationis, quæ ab effectu procedit, affert exemplum <lb/>

ex a&longs;tronomia; A&longs;tronomi enim demon&longs;trant Lunam e&longs;&longs;e &longs;phæricam ab ef<lb/>

fectu ip&longs;ius &longs;phæricitatis, qui e&longs;t illuminatio &longs;phærica: &longs;ic enim ratiocinan<lb/>

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<s id="id.001102">perge ad

<pb xlink:href="009/01/060.jpg" pagenum="60" />huc te ip&longs;um conuertere, & videbis paulatim lumen oculo tuo decre&longs;cere <lb/>

<pb pagenum="60" xlink:href="009/01/060.jpg"/>huc te ip&longs;um conuertere, & videbis paulatim lumen oculo tuo decre&longs;cere <lb/>

non aliter ac in Luna &longs;ene&longs;cente. </s>

<s id="id.001103"><expan abbr="atq;">atque</expan> hoc e&longs;t &longs;phæricè illuminari, fierique <lb/>

&longs;phærica illuminationis augmenta. </s>

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di&longs;tinctam à Geometria, ni&longs;i &longs;icuti partem à toto: nam cum Geometria <lb/>

con&longs;ideret quantitatem, &longs;ecundum tres dimen&longs;iones, longitudinem, latitu<lb/>dinem, & profunditatem, oritur triplex illius diui&longs;io, de lineis, de &longs;uperfi<lb/>

ciebus, de &longs;olidis. </s>

<s id="id.001109">pars igitur, quæ de &longs;olidis tractat, <expan abbr="pattim&qacute;">pattimque</expan>; continetur <lb/>

<s id="id.001109">pars igitur, quæ de &longs;olidis tractat, <expan abbr="pattim&qacute;">paρtimque</expan>; continetur <lb/>

11. 12. 13. 14. & 15. Euclidis, partim aliorum Geometrarum libris, vt li<lb/>

bro Archim. de Sphæra, & Cyl. & &longs;imilibus, dicitur Stereometria à græco <lb/>

<foreign lang="greek">steoeov,</foreign> ide&longs;t &longs;olidum. </s>

<foreign lang="greek">stereon,</foreign> ide&longs;t &longs;olidum. </s>

<s id="id.001110">Porrò cur malit Ari&longs;t. Mechanicam &longs;ubalternari Ste<lb/>

reometriæ, quam toti Geometriæ, qua tamen, vt videre e&longs;t apud Archime<lb/>

dem, innititur, fortè ea ratio e&longs;t, quia Mechanica præcipuè con&longs;iderat ma<lb/>

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habere tres angulos æquales duobus rectis angulis &longs;ecundum aliquod com

<pb xlink:href="009/01/061.jpg" pagenum="61" />mune, quia illis competit, quatenus ambo &longs;unt figura quædam, ide&longs;t, qua<lb/>

<pb pagenum="61" xlink:href="009/01/061.jpg"/>mune, quia illis competit, quatenus ambo &longs;unt figura quædam, ide&longs;t, qua<lb/>

tenus <expan abbr="vtrumq;">vtrumque</expan> illorum triangulum e&longs;t; triangulo <expan abbr="namq;">namque</expan> omni primo com<lb/>

petit habere tres angulos æquales duobus rectis.</s>

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Ari&longs;t. con&longs;idera&longs;&longs;e, Minam re&longs;pectu Talenti, re&longs;pectu enim illius dici pote&longs;t <lb/>

principium, cum &longs;ex millia minarum in Attico talento continerentur.</s>

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conuenit, e&longs;t <expan abbr="&qacute;">que</expan>; huiu&longs;modi: Omnis figuræ rectili<lb/>neæ anguli externi omnes &longs;imul &longs;umpti, &longs;unt æqu<lb/>

les quatuor rectis angulis, quæ affectio demon<lb/>

&longs;tratur in &longs;cholio 32. primi Elem. dicuntur autem <lb/>

anguli externi, qui productis lateribus fiunt, vt in <lb/>triangulo præ&longs;enti anguli externi &longs;unt, B D C,<pb xlink:href="009/01/062.jpg" pagenum="62" />D F E, F B A, ita vt quælibet figura tot angulos externos &longs;ortiatur, quot <lb/>

anguli externi, qui productis lateribus fiunt, vt in <lb/>triangulo præ&longs;enti anguli externi &longs;unt, B D C,<pb pagenum="62" xlink:href="009/01/062.jpg"/>D F E, F B A, ita vt quælibet figura tot angulos externos &longs;ortiatur, quot <lb/>

habet latera; cum exproductis lateribus oriantur. </s>

<s id="id.001151">Vt autem propo&longs;itio ve<lb/>

rificetur, &longs;ingula latera ordinatim &longs;unt producenda, hoc e&longs;t, ver&longs;us eandem <lb/>

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<s id="id.001170">Et paulo po&longs;t <emph type="italics"/>(Quemadmod&ubreve; &longs;i vi<lb/>

<s id="id.001170">Et paulo po&longs;t <emph type="italics"/>(Quemadmod&ubreve;m &longs;i vi<lb/>

trum perforatum videremus, & lumen <lb/>

permeans, planum vtique e&longs;&longs;et propter <lb/>

quid comburit)<emph.end type="italics"/> Ioquitur de ea com<lb/>

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manentes, &longs;phæram vitream perua

<pb xlink:href="009/01/063.jpg" pagenum="63" />dunt, <expan abbr="atq;">atque</expan> in exitu ita refraguntur, vt ad A, punctum coaceruati, ibi po&longs;<lb/>

<pb pagenum="63" xlink:href="009/01/063.jpg"/>dunt, <expan abbr="atq;">atque</expan> in exitu ita refraguntur, vt ad A, punctum coaceruati, ibi po&longs;<lb/>

&longs;int, &longs;i quid combu&longs;tibile occurrat, comburere. </s>

<s id="id.001174">Si igitur, inquit Ari&longs;t. vide<lb/>

remus illos radios &longs;ic permeare, & refrangi, planum <expan abbr="vtiq;">vtique</expan> nobis e&longs;&longs;et pro<lb/>

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tia e&longs;t compo&longs;itio &longs;oni grauis, & acuti, quæ &longs;uauiter auribus accidit; & quo<lb/>

rum &longs;onorum proportio ad inuicem &longs;it &longs;icuti proportio numerorum, qui <lb/>

quaternario includuntur: vt e&longs;t proportio 2. ad 1. vel 3. ad 1. vel 4. ad 1. <lb/>

vel 3. ad 2. vel 4. ad 3. <expan abbr="Quotie&longs;eunq;">Quotie&longs; cunque</expan> igitur duo &longs;oni habuerin quam piam<pb xlink:href="009/01/064.jpg" pagenum="64" />ex <expan abbr="quinq;">quinque</expan> prædictis proportionibus, &longs;i &longs;imul coaluerint, ita vt ex eis vnue <lb/>

vel 3. ad 2. vel 4. ad 3. <expan abbr="Quotie&longs;eunq;">Quotie&longs;cunque</expan> igitur duo &longs;oni habuerin quampiam <pb pagenum="64" xlink:href="009/01/064.jpg"/>ex <expan abbr="quinq;">quinque</expan> prædictis proportionibus, &longs;i &longs;imul coaluerint, ita vt ex eis vnus <lb/>

tantum &longs;onus efficiatur; &longs;onus ille erit concordans, & auribus gratus. </s>

<s id="id.001197"><expan abbr="atq;">atque</expan> <lb/>

hæc e&longs;t &longs;ententia pri&longs;corum præ&longs;ertim Pythagoreorum, qui propterea di<lb/>

cebant non licere Mu&longs;ico vltra quaternarium pertran&longs;ire, eò quod &longs;olæ pro<lb/>

portiones, vt diximus, numerorum quaternario contentorum, concordem, <lb/>

ac con&longs;onantem concentum efficere poterant: quod vt adhuc melius per<lb/>

cipiamus, accipe exemplum. </s>

<s id="id.001198">Sint duæ chordæ <lb/>

A, & B, æqualis cra&longs;&longs;itici, & æquè ten&longs;æ. </s>

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nere triangulum in communi, cum inter definitiones ip&longs;ius contineatur,

<pb xlink:href="009/01/065.jpg" pagenum="65" />quod tamen non ob&longs;tat, quominus probare po&longs;&longs;it, aliquando po&longs;&longs;e <expan abbr="cõ&longs;trni">con&longs;trui</expan>, <lb/>

<pb pagenum="65" xlink:href="009/01/065.jpg"/>quod tamen non ob&longs;tat, quominus probare po&longs;&longs;it, aliquando po&longs;&longs;e <expan abbr="cõ&longs;trni">con&longs;trui</expan>, <lb/>

& e&longs;&longs;e aliquod particulare triangulum, vt fit in prædicta demon&longs;tratione, <lb/>

Euclidis.</s>

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tamen nos mox aperiemus. </s>

<s id="id.001227">per angulum in &longs;emicirculo intelligas eum, qui <lb/>

fit à lineis ductis ab extremitatibus diametri, & &longs;imul in quoduis punctum <lb/>

circumferentiæ coeuntibus, vt in figura <lb/>

præ&longs;enti vides lineas A C, B C, ad C, pun<lb/>

ctum conuenire, <expan abbr="ibi&qacute;">ibique</expan>; facere angulum, <lb/>

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totius, etiam ex &longs;ententia ip&longs;ius Ari&longs;t. ex hac præterea materia conflatur <lb/>

definitio minoris extremi, vel &longs;ubiecti; dum dicitur, angulus in &longs;emicircu<lb/>

lo e&longs;t dimidium duorum rectorum. </s>

<s id="id.001234">&longs;yllogi&longs;mus enim reducitur tandem ad <pb xlink:href="009/01/066.jpg" pagenum="66" />hanc formam, dimidium duorum rectorum e&longs;t rectus, angulus in &longs;emicir<lb/>

<s id="id.001234">&longs;yllogi&longs;mus enim reducitur tandem ad <pb pagenum="66" xlink:href="009/01/066.jpg"/>hanc formam, dimidium duorum rectorum e&longs;t rectus, angulus in &longs;emicir<lb/>

culo e&longs;t dimidium duorum <expan abbr="rector&utilde;">rectorum</expan>, ergo angulus in &longs;emicirculo e&longs;t rectus. <lb/>

</s>

<s id="id.001235">vides in minori propo&longs;itione contineri definitionem &longs;ubiecti materialem? <lb/>

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les figuræ rectilíneæ &longs;unt; quæ & angulos &longs;ingulos, &longs;ingulis angulis æquales <lb/>

habent, <expan abbr="atq;">atque</expan> etiam latera, quæ circa angulos æquales &longs;unt proportionalia. <lb/>

</s>

<s id="id.001261">vt &longs;i duo triangula appo&longs;ita habeant angulos æquales, <expan abbr="angul&utilde;">angulum</expan> A, angulo D: <lb/>angulum B, angulo E. angulum C, angulo F. & præterea latera, quæ &longs;unt <pb xlink:href="009/01/067.jpg" pagenum="67" /><figure id="id.009.01.067.1.jpg" xlink:href="009/01/067/1.jpg" place="text"/><lb/>

<s id="id.001261">vt &longs;i duo triangula appo&longs;ita habeant angulos æquales, <expan abbr="angul&utilde;">angulum</expan> A, angulo D: <lb/>angulum B, angulo E. angulum C, angulo F. & præterea latera, quæ &longs;unt <pb pagenum="67" xlink:href="009/01/067.jpg"/><figure id="id.009.01.067.1.jpg" place="text" xlink:href="009/01/067/1.jpg"/><lb/>

circa angulos æquales, v. g. circa an<lb/>

gulos A, & D, habeant proportiona<lb/>

lia, hoc e&longs;t, vt latus A B, ad latus A C; <lb/>

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quia nimirum habet angulum acutum &longs;uperficialem, ide&longs;t, quem duæ &longs;uper<lb/>

ficies &longs;imul in acie gladij concurrentes efficiunt.</s>

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<s id="id.001300">Notandum po&longs;tea cum Alexandro (quod & &longs;uperius alias commo<lb/>nui in cap. de Priori, & alibi) per verbum (De&longs;cribi) &longs;ignificari hoc loco <lb/>

geometricè demon&longs;trare, quoniam Geometræ <expan abbr="nõ">non</expan> ni&longs;i adhibitis de&longs;criptio<lb/>nibus, &longs;eu figuris demon&longs;trant. </s>

<s id="id.001301">Vult autem Ari&longs;t. exemplo mathematico <lb/>

o&longs;tendere, difficile e&longs;&longs;e di&longs;putare, aut <expan abbr="argum&etilde;tari">argumentari</expan>, ni&longs;i prius rectè a&longs;&longs;ignetur <pb xlink:href="009/01/069.jpg" pagenum="69" />definitio illius rei, de qua di&longs;&longs;eritur. </s>

o&longs;tendere, difficile e&longs;&longs;e di&longs;putare, aut <expan abbr="argum&etilde;tari">argumentari</expan>, ni&longs;i prius rectè a&longs;&longs;ignetur <pb pagenum="69" xlink:href="009/01/069.jpg"/>definitio illius rei, de qua di&longs;&longs;eritur. </s>

<s id="id.001302">Porrò exemplum mathematicum hic <lb/>

allatum &longs;ic videtur explicandum: Conetur aliquis demon&longs;trare hanc pro<lb/>

po&longs;itionem; &longs;i linea ducta fuerit æquidi&longs;tans lateri vnius plani trianguli, &longs;e<lb/>cabit & latera, & locum, ide&longs;t &longs;uperficiem illam triangularem &longs;imiliter, ide&longs;t <lb/>

in eadem proportione, vt in triangulo A B C, <lb/>

linea D E, parallela ba&longs;i B C, &longs;ecat latera A B, <lb/>

& A C, in punctis D, & E, in eadem ratione, <lb/>

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</chap>

<chap>

<s id="id.001316"><emph type="italics"/>Ex Primo Elenchorum.<emph.end type="italics"/></s>

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<s id="id.001335">Ad finem cap. <emph type="italics"/>(Aut vt Antiphon quadra<lb/>

uit)<emph.end type="italics"/> &longs;imile peccatum pecca&longs;&longs;e Antiphon<lb/>

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cius. </s>

<s id="id.001337">circulo quadrando in&longs;cribebat pri<lb/>

mò quadratum A B C D. deinde in &longs;ingu<lb/>

lis quatuor &longs;egmentis in&longs;cribebat totidem <lb/>trigona æquilatera, vt patet in ad&longs;cripta <pb xlink:href="009/01/071.jpg" pagenum="71" />figura. </s>

lis quatuor &longs;egmentis in&longs;cribebat totidem <lb/>trigona æquilatera, vt patet in ad&longs;cripta <pb pagenum="71" xlink:href="009/01/071.jpg"/>figura. </s>

<s id="id.001338">po&longs;tea &longs;uper &longs;ingula latera horum triangulorum in reliquis &longs;egmen<lb/>

tis in&longs;cribebat adhuc triangula &longs;imilia triangulo A I E. alia in&longs;uper trigona <lb/>

&longs;uper latera i&longs;torum con&longs;tituebat, donec ambitus figuræ illius multilateræ <lb/>in circulo delineatæ, circumferentiæ circuli aptaretur. </s>

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<s id="id.001342"><emph type="italics"/>Logicorum locorum finis.<emph.end type="italics"/></s>

</chap>

<chap>

<s id="id.001343">EX PRIMO LIBRO <lb/>

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<s id="id.001358">2.1. continetur: quibus per&longs;pectis facilis erit phy&longs;ico totius <lb/>

loci intelligentia.</s>

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<s id="id.001368">pro medio autem <lb/>

huius pa&longs;&longs;ionis accipit lineam perpendicularem, quam innuit verbis illis <lb/>

<emph type="italics"/>(quoniam enim hoc rectum e&longs;t<emph.end type="italics"/>) vt in figura &longs;it triangulum A B C, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; vt latus <lb/>

A C, &longs;it perpendiculare <expan abbr="c&utilde;">cum</expan> latere B C, & pro<lb/>

ducatur B C, in D; tunc triangulum A B C, <lb/>

habere tres angulos, A, B, & A C B, æquales <lb/>

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ctum crit <expan abbr="perp&etilde;diculare">perpendiculare</expan>, quia fal&longs;um <lb/>non, ni&longs;i ex fal&longs;o &longs;equitur.</s>

</chap>

<chap>

<s id="id.001370"><emph type="italics"/>Ex Tertio Phy&longs;icorum.<emph.end type="italics"/></s>

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<s id="id.001375">Pythagorici enim (à quibus i&longs;ta mutuatus <lb/>

e&longs;t Ari&longs;t. numeros impares &longs;olos appellabant Gnomones, eò quod in for<lb/>

mam normæ æquilateræ, &longs;iue Gnomonis con&longs;titui po&longs;&longs;int, vt patet in his <lb/>

nimirum in ternario, quinario, &longs;eptenario, & &longs;ic de <lb/>

reliquis imparibus. </s>

<s id="id.001376">pares autem numeri, quia ne<lb/>

queunt in figuram normæ æquilateræ di&longs;poni, cum <lb/>

non habeant vnitatem pro angulo, & paria po&longs;tea la<lb/>

tera, vt oportet, non merentur appellari Gnomones, vt quaternarius, &longs;i di<lb/>

&longs;ponatur &longs;ic <figure id="id.009.01.074.2.jpg" xlink:href="009/01/074/2.jpg" place="text"/> non refert Gnomonem, quia lateribus in&etail;qualibus con<lb/>

&longs;ponatur &longs;ic <figure id="id.009.01.074.2.jpg" place="text" xlink:href="009/01/074/2.jpg"/> non refert Gnomonem, quia lateribus in&etail;qualibus con<lb/>

&longs;tat; <expan abbr="neq;">neque</expan> &longs;i hoc modo <figure id="id.009.01.074.3.jpg" xlink:href="009/01/074/3.jpg" place="text"/> quia dee&longs;t huic figuræ angularis vnitas, quæ <lb/>illi nece&longs;&longs;aria e&longs;t. </s>

&longs;tat; <expan abbr="neq;">neque</expan> &longs;i hoc modo <figure id="id.009.01.074.3.jpg" place="text" xlink:href="009/01/074/3.jpg"/> quia dee&longs;t huic figuræ angularis vnitas, quæ <lb/>illi nece&longs;&longs;aria e&longs;t. </s>

<s id="id.001377">Pythagorici igitur dicebant, numerum parem ideò e&longs;&longs;e <lb/>

infinitum ip&longs;um, quia videbant ip&longs;um e&longs;&longs;e cau&longs;am perpetuæ diui&longs;ionis, cum <lb/>

quælibet res quanta &longs;it diui&longs;ibilis bifariam, ide&longs;t in duo &longs;ecundum numerum <lb/>

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metices lordani, vbi i&longs;tud idem demon&longs;trat, quæ e&longs;t hæc. </s>

<s id="id.001382">&longs;it vnitas, & &longs;uo or<lb/>

dine &longs;equantur impares, vt in &longs;equenti hac &longs;erie apparet 1. 3. 5. 7. 9. & c. <lb/>

&longs;i igitur vnitati addatur ternarius in Gnomo<lb/>

nis modum, vt vides in prima figura, produ<lb/>

cetur quaternarius numerus, qui e&longs;t numerus <lb/>

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numerus pariter quadratus e&longs;t, vt in tertia figura, & hoc modo, &longs;i in infini

<pb xlink:href="009/01/075.jpg" pagenum="75" />tum procedatur, numeri &longs;emper quadrati progignentur. </s>

<pb pagenum="75" xlink:href="009/01/075.jpg"/>tum procedatur, numeri &longs;emper quadrati progignentur. </s>

<s id="id.001384">Vides igitur, qui <lb/>

ratione Gnomonum, &longs;iue imparium additione fiat &longs;emper eadem &longs;pecies, <lb/>

&longs;cilicet quadratus numerus, quod &longs;ignum e&longs;t, inquiunt, imparem numerum <lb/>

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<s id="id.001386">quæ &longs;ic explicantur: &longs;int ab vnitate pares di&longs;po&longs;iti ordinatim <lb/>

hoc modo, 1. 2. 4. 6. &c. </s>

<s id="id.001387">&longs;i igitur vnitati binarius coaceruetur, fit numerus <lb/>

triangularis, vt in prima figura. </s>

<s id="id.001388">&longs;i huic ternario <lb/>

coaceruetur &longs;equens par, fiet altera &longs;pecies, ni<lb/>

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primo Priorum, &longs;ecto primo, cap. 23.</s>

</chap>

<chap>

<s id="id.001409"><emph type="italics"/>Ex Quinto Phy&longs;icorum.<emph.end type="italics"/></s>

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<s id="id.001425">Tex. 36. <emph type="italics"/>(Sit <expan abbr="itaq;">itaque</expan> linea, in qua A G E, infinita ad partes E; & alia vtrinque <lb/>

infinita, in qua <foreign lang="greek">b</foreign> B; &longs;i <expan abbr="itaq;">itaque</expan> de&longs;cribat circulum linea A G E, cir ca centrum G, fe-<emph.end type="italics"/><lb/>

<emph type="italics"/>retur circulariter linea A G E, &longs;ecans ali<lb/>

quando lineam <foreign lang="greek">b</foreign> B, tempore finito; totum <lb/>

enim tempus, in quo circulariter latum <lb/>

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ad alteram <expan abbr="tãtum">tantum</expan> partem in qua E: altera verò ad <expan abbr="vtramq;">vtramque</expan> partem <foreign lang="greek">b,</foreign> & B,

<pb xlink:href="009/01/077.jpg" pagenum="77" />non potuerunt tamen de&longs;cribi, ni&longs;i finitæ; appo&longs;itæ idcircò &longs;unt ad partes <lb/>

<pb pagenum="77" xlink:href="009/01/077.jpg"/>non potuerunt tamen de&longs;cribi, ni&longs;i finitæ; appo&longs;itæ idcircò &longs;unt ad partes <lb/>

illas, ad quas deberent e&longs;&longs;e infinitæ lineolæ quædam infinitatem indicantes. <lb/>

</s>

<s id="id.001428">debemus po&longs;tea, vt mentem Ari&longs;t. percipiamus concipere lineam A G E, <lb/>

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<s id="id.001446">quam vnam <expan abbr="hab&etilde;um">habentem</expan>. <lb/>

</s>

<s id="id.001447">diui&longs;io enim in plana non perinde efficitur, vt qui&longs;piam <expan abbr="diuid&etilde;s">diuidens</expan> in par<lb/>tes diuidat totum, &longs;ed vt in &longs;pecie diuer&longs;a: patet igitur &longs;phæram e&longs;&longs;e &longs;olidarum <lb/>

primam)<emph.end type="italics"/> qui &longs;olida diuidunt in plana, ca diuidunt <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> numerum &longs;uper<lb/>ficierum, quibus ambiuntur, v. g. diuidunt cubum in &longs;ex &longs;uperficies, quia <lb/>cubus &longs;ex quadratis planis &longs;uperficiebus continetur: qua ratione nequeunt <pb xlink:href="009/01/078.jpg" pagenum="78" />&longs;ohæram in plana vlla re&longs;oluere, <expan abbr="neq;">neque</expan> in alias plures &longs;uperficies, quia &longs;phæ<lb/>

primam)<emph.end type="italics"/> qui &longs;olida diuidunt in plana, ca diuidunt <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> numerum &longs;uper<lb/>ficierum, quibus ambiuntur, v. g. diuidunt cubum in &longs;ex &longs;uperficies, quia <lb/>cubus &longs;ex quadratis planis &longs;uperficiebus continetur: qua ratione nequeunt <pb pagenum="78" xlink:href="009/01/078.jpg"/>&longs;ohæram in plana vlla re&longs;oluere, <expan abbr="neq;">neque</expan> in alias plures &longs;uperficies, quia &longs;phæ<lb/>

ra ambitur vnica tantum &longs;uperficie &longs;phærica. </s>

<s id="id.001448">quando verò ex planis corpo<lb/>

ra generant, vt facit Plato in Timæo, accipíunt primò triangulum æquila<lb/>

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tione &longs;umpta, quod apta natura e&longs;t &longs;emper confluere aqua ad magis concauum: ma<lb/>

gis autem concauum e&longs;t, quod centro propinquius est. </s>

<s id="id.001457">ducantur ergo ex centro A,<emph.end type="italics"/><lb/>

<emph type="italics"/>linea A B, & linea A C, & producatur, in qua B C, <lb/>

ducta igitur ad ba&longs;im linea, in qua A D, minor e&longs;t eis, <lb/>

quæ ex centro. </s>

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locus non e&longs;t decliuior punctis B, & C. quare cum loca B, E, C, quæ &longs;unt ex

<pb xlink:href="009/01/079.jpg" pagenum="79" />trema linearum, &longs;int æquè decliuia, nece&longs;&longs;e e&longs;t aquæ &longs;uperficiem apud ip&longs;a <lb/>

<pb pagenum="79" xlink:href="009/01/079.jpg"/>trema linearum, &longs;int æquè decliuia, nece&longs;&longs;e e&longs;t aquæ &longs;uperficiem apud ip&longs;a <lb/>

con&longs;i&longs;tere, tunc enim debet quie&longs;cere, aliter nunquam quie&longs;ceret; &longs;ed vide<lb/>

mus aquam manentem, & quietam, ergo quie&longs;cit circa puncta B, E, C, à <lb/>

centro terræ æquidi&longs;tantia, per quæ tran&longs;it linea circularis coniungens illa; <lb/>et&longs;i &longs;uperficies per eiu&longs;modi loca pertran&longs;iret, e&longs;&longs;et &longs;phærica: &longs;ed &longs;uperfi<lb/>

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alijs maius corpus velocius fertur propria latione, &longs;ic, & in circularibus: maius <lb/>

enim e&longs;t eorum, quæ auferuntur ab eis, quæ ex centro, maioris circuli &longs;egmentum)<emph.end type="italics"/><lb/>

ex intellectione vltimæ periodi textus totius intelligentia pendet: &longs;it igitur <lb/>

figura præ&longs;ens, in qua cum &longs;int duo circuli concen<lb/>

trici, vnus altero maior, <expan abbr="eductæ&qacute;">eductæque</expan>; &longs;int ex <expan abbr="c&etilde;tro">centro</expan> duæ <lb/>

&longs;emidiametri A D, A E, quæ <expan abbr="vtrunq;">vtrunque</expan> circulum &longs;e<lb/>

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quædam &longs;int priora, quædam posteriora, & quomodo &longs;patijs &longs;e &abreve;<expan abbr="habeãt">habeant</expan> ad inuicem,<emph.end type="italics"/>

<pb xlink:href="009/01/080.jpg" pagenum="80" /><emph type="italics"/>ex ijs circa A&longs;trologiam, con&longs;ideretur: dicitur enim &longs;ufficienter)<emph.end type="italics"/> &longs;umit hoc loco <lb/>

<pb pagenum="80" xlink:href="009/01/080.jpg"/><emph type="italics"/>ex ijs circa A&longs;trologiam, con&longs;ideretur: dicitur enim &longs;ufficienter)<emph.end type="italics"/> &longs;umit hoc loco <lb/>

A&longs;trologiam, pro A&longs;tronomia, &longs;i iuxta recentiores loqui velimus. </s>

<s id="id.001478">Dicit igi<lb/>

tur ordinem c&oelig;lorum, ac &longs;yderum, item &longs;itum, & proportiones magnitu<lb/>dinum eorundem, cum per naturalis &longs;cientiæ principia &longs;ciri nequeant, ex <lb/>

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<s id="id.001488">intellige tamen partem illam Solis, quæ non eclyp&longs;atur, habere figu<lb/>

ram lunulæ, pars enim à Luna obumbrata non videtur, et&longs;i videretur oua<lb/>

lem quandam &longs;peciem, præ&longs;eferret: pars igitur, illa e&longs;t corniculata, quia <lb/>

cum Solis defectio ex interpo&longs;itione Lunæ inter nos, & <lb/>

Solem contingat, & Luna &longs;it &longs;phærica, nece&longs;&longs;ariò &longs;phæ<lb/>

ricè, & circulariter Solem obumbrabit; quare pars illa <lb/>

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telis e&longs;t, debere nos exi&longs;timare, quod &longs;i quæpiam grauis magnitudo de&longs;cen<lb/>dat ad centrum mundi, eam non perman&longs;uram, &longs;tatim ac ip&longs;ius extremum <lb/>

centrum mundi attigent; &longs;ed cò <expan abbr="v&longs;q;">v&longs;que</expan> de&longs;cen&longs;uram, <expan abbr="quou&longs;q;">quou&longs;que</expan> ip&longs;ius medium, <lb/>mundi medium, &longs;iue centrum affequutum &longs;it; maior enim ip&longs;ius pars, in qua <lb/>

&longs;cilicet medium e&longs;t, minorem partem propellit, donec vtrinque à centro <lb/>

mundi æquè emineat; omne enim graue <expan abbr="hucu&longs;q;">hucu&longs;que</expan> habet propen&longs;ionem, &longs;iue <pb xlink:href="009/01/081.jpg" pagenum="81" /><expan abbr="hucu&longs;q;">hucu&longs;que</expan> grauitat, v. g. &longs;i lapis illuc de&longs;cenderet, non quie&longs;ceret &longs;tatim ac <lb/>

mundi æquè emineat; omne enim graue <expan abbr="hucu&longs;q;">hucu&longs;que</expan> habet propen&longs;ionem, &longs;iue <pb pagenum="81" xlink:href="009/01/081.jpg"/><expan abbr="hucu&longs;q;">hucu&longs;que</expan> grauitat, v. g. &longs;i lapis illuc de&longs;cenderet, non quie&longs;ceret &longs;tatim ac <lb/>

prima ip&longs;ius pars ad mundi centrum pertingeret, &longs;ed reliquæ ip&longs;ius partes <lb/>

adhuc grauitarent, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; vlterius primam partem impellerent, donec lapi<lb/>dis medium, mundi medio congrueret: quo facto lapis quie&longs;ceret. </s>

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ex eo, quod Luna &longs;phæricè eclyp&longs;etur, quod innuitur illis verbis, &longs;emper

<pb xlink:href="009/01/082.jpg" pagenum="82" />curuam habet terminantem lineam, linea &longs;cilicet, quæ terminat partem <lb/>

<pb pagenum="82" xlink:href="009/01/082.jpg"/>curuam habet terminantem lineam, linea &longs;cilicet, quæ terminat partem <lb/>

eclyp&longs;atam à non eclyp&longs;ata, &longs;emper apparet circularis; cum autem hæc li<lb/>

nea &longs;it terminus vmbræ terræ, quæ lumen obumbrat, &longs;ignum <expan abbr="manife&longs;t&utilde;">manife&longs;tum</expan> e&longs;t <lb/>

vmbram ip&longs;am e&longs;&longs;e rotundam; nam cum Luna deficiat propter terræ obie<lb/>

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paruo itinere &longs;iue ad meridionalem plagam, &longs;iue ad <expan abbr="&longs;ept&etilde;trionalem">&longs;eptentrionalem</expan> (quam <lb/>

Vr&longs;am dicit) magnopere mutatur horizon: quod apparet primo ex varia<lb/>tione a&longs;trorum, nam quæ in primo loco &longs;upra no&longs;trum verticem <expan abbr="trã&longs;ibant">tran&longs;ibant</expan>, <lb/>

in &longs;ecundo loco non amplius, &longs;ed alia, <expan abbr="atq;">atque</expan> alia valde ab inuicem &longs;eiuncta <lb/>

<figure id="id.009.01.082.1.jpg" xlink:href="009/01/082/1.jpg" place="text"/><lb/>ex facto quamuis paruo itinere tran&longs;eunt. </s>

<figure id="id.009.01.082.1.jpg" place="text" xlink:href="009/01/082/1.jpg"/><lb/>ex facto quamuis paruo itinere tran&longs;eunt. </s>

<s id="id.001518">&longs;it in <lb/>

præ&longs;enti figura terra, vbi A, in qua facta parua <lb/>

mutatione ex loco F, in locum G, fieret magna <lb/>

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loco ad alterutram plagam, &longs;tatim ab&longs;conduntur; aliæ verò nouæ <expan abbr="appar&etilde;t">apparent</expan> <lb/>vt in Aegypto, & Cypro, &longs;tella, quæ dicitur Canobus &longs;upra horizontem <lb/>

a&longs;cendit; quæ &longs;i paululum Vr&longs;am, &longs;eu &longs;eptentrionem ambulaueris, &longs;tatim <lb/>

latitabit. </s>

<s id="id.001521">Demum eiu&longs;dem citæ mutationis finitoris indicium etiam &longs;it,<pb xlink:href="009/01/083.jpg" pagenum="83" />quod regiones &longs;eptentrionales incolentibus plurima &longs;unt a&longs;tra, quæ nun<lb/>quam occidunt, quamuis horizontem leuiter per&longs;tringant, quæ tamen Cy<lb/>

<s id="id.001521">Demum eiu&longs;dem citæ mutationis finitoris indicium etiam &longs;it,<pb pagenum="83" xlink:href="009/01/083.jpg"/>quod regiones &longs;eptentrionales incolentibus plurima &longs;unt a&longs;tra, quæ nun<lb/>quam occidunt, quamuis horizontem leuiter per&longs;tringant, quæ tamen Cy<lb/>

prijs, <expan abbr="atq;">atque</expan> Aegyptijs oriuntur, <expan abbr="atq;">atque</expan> occidunt. </s>

<s id="id.001522">ex quibus & rotunditas, & <lb/>

paruitas terræ colligi pote&longs;t. </s>

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per intellectum à &longs;en&longs;ibilibus affectionibus, re&longs;tat vt &longs;it tantummodo intel

<pb xlink:href="009/01/084.jpg" pagenum="84" />lectu perceptibilis. </s>

<pb pagenum="84" xlink:href="009/01/084.jpg"/>lectu perceptibilis. </s>

<s id="id.001542">Hanc eandem &longs;upponunt e&longs;&longs;e diui&longs;ibilem in infinitum, <lb/>

vt &longs;upra 3. Phy&longs;. textu 31. dictum e&longs;t.</s>

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pauimento relinquant. </s>

<s id="id.001549">huiu&longs;modi &longs;unt triangula æquilatera (de his enim <lb/>

intelligendus e&longs;t textus) quadrata, & hexagona, &longs;iue &longs;exilatera regularia; <lb/>

nam &longs;ex triangula æquilatera &longs;imul iuncta in plano paui<lb/>

re po&longs;&longs;unt, vt patet in figura præ&longs;enti; ratio huius e&longs;t, <lb/>

quia omnes anguli circa idem punctum (y. </s>

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quatuor rectis angulis, con&longs;tituti omnes circa punctum <lb/>

A, totum locum circa illud implere po&longs;&longs;unt. </s>

<s id="id.001552">Quadratum etiam replere lo<lb/>

<figure id="id.009.01.084.2.jpg" xlink:href="009/01/084/2.jpg" place="text"/><lb/>cum manife&longs;tum e&longs;t, cum enim ip&longs;ius anguli &longs;int recti, &longs;i <lb/>

<figure id="id.009.01.084.2.jpg" place="text" xlink:href="009/01/084/2.jpg"/><lb/>cum manife&longs;tum e&longs;t, cum enim ip&longs;ius anguli &longs;int recti, &longs;i <lb/>

quatuor quadrata ad idem punctum A, copulentur, vt in <lb/>

figura apparet, replebunt eadem de cau&longs;a vacuum.</s>

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idem punctum A, vt in figura adaptentur, nece&longs;&longs;ariò ni<lb/>

hil vacui inter ip&longs;a relinquetur, vt in figura hac o&longs;tenditur. </s>

<s id="id.001554">præter has tres <lb/>

<figure id="id.009.01.084.3.jpg" xlink:href="009/01/084/3.jpg" place="text"/><lb/>figuras, nulla alia reperitur, quæ i&longs;tud efficere po&longs;<lb/>

<figure id="id.009.01.084.3.jpg" place="text" xlink:href="009/01/084/3.jpg"/><lb/>figuras, nulla alia reperitur, quæ i&longs;tud efficere po&longs;<lb/>

&longs;it. </s>

<s id="id.001555">cuius demon&longs;trationem perfectam videre pote<lb/>

ris in fine commentarij P. Clauij &longs;uper 4. Elem. nos <lb/>

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<s id="id.001558">quare quartum <lb/>

<expan abbr="ab&longs;q;">ab&longs;que</expan> figura relinquetur; quod e&longs;t ab&longs;urdum.</s>

<s id="id.001559"><emph type="italics"/>Admirabilis quædam A&pgrave;um industria.<emph.end type="italics"/></s>

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<expan abbr="ait&qacute;">aitque</expan>; ip&longs;a replere locum, intelligens, planum, profectò non loquitur forma<lb/>liter, ide&longs;t de ip&longs;is, vt &longs;olida &longs;unt. </s>

<s id="id.001577">Quare Ari&longs;t. videretur &longs;ibi non con&longs;tare, <lb/>

vel perperam exi&longs;tima&longs;&longs;e plura Tetraedra complere &longs;oliditatem. </s>

<s id="id.001578">deceptus <pb xlink:href="009/01/086.jpg" pagenum="86" />fortè fuit Ari&longs;t. cò quod videret Ico&longs;aedrum con&longs;tare ex viginti pyramidi<lb/>

<s id="id.001578">deceptus <pb pagenum="86" xlink:href="009/01/086.jpg"/>fortè fuit Ari&longs;t. cò quod videret Ico&longs;aedrum con&longs;tare ex viginti pyramidi<lb/>

bus, verùm illæ non &longs;unt regulares, ide&longs;t <expan abbr="nõ">non</expan> &longs;unt Tetraedra, vt po&longs;tea o&longs;ten<lb/>

dam. </s>

<s id="id.001579">Verum quidem e&longs;t octo cubos &longs;imul adactos &longs;oliditatem conficere, <lb/>

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ramides Dodecaedron con&longs;tituentes non &longs;unt regulares, ide&longs;t, non &longs;unt Te

<pb xlink:href="009/01/087.jpg" pagenum="87" />traedra (de quibus tamen Ari&longs;t. loquitur) vt patet ex &longs;upra dictis. </s>

<pb pagenum="87" xlink:href="009/01/087.jpg"/>traedra (de quibus tamen Ari&longs;t. loquitur) vt patet ex &longs;upra dictis. </s>

<s id="id.001589">Indul<lb/>

geas Lector, &longs;i hoc loco nece&longs;&longs;e fuit in Geometriæ penetralia ingredi: ope<lb/>

ræpretium enim e&longs;t aliquando ip&longs;is Mathematicis &longs;atisfacere. </s>

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est ferri ad medium. </s>

<s id="id.001606">boc autem vtrum accidit ad ip&longs;um terræ medium, <lb/>

an ad vniuer&longs;i, quoniam idem ip&longs;orum &longs;it, alius &longs;ermo e&longs;t)<emph.end type="italics"/> cum vellet <lb/>

probare Ari&longs;toteles dari <expan abbr="p&utilde;ctum">punctum</expan> quoddam in medio <lb/>

mundi, ad quod grauia de&longs;cendant, & concurrent: <lb/>

& à quo leuia a&longs;cendat; vtitur, præter alias, etiam <lb/>

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ra præ&longs;enti circulus E C D, cuius medium, &longs;ine cen

<pb xlink:href="009/01/088.jpg" pagenum="88" />trum A. via, qua a&longs;cendit ignis &longs;it in linea A C B, quæ facit angulos in &longs;u<lb/>

<pb pagenum="88" xlink:href="009/01/088.jpg"/>trum A. via, qua a&longs;cendit ignis &longs;it in linea A C B, quæ facit angulos in &longs;u<lb/>

perficie terræ æquales, nimirum angulos B C D, B C E. &longs;imiliter terra per <lb/>eandem lineam <expan abbr="faci&etilde;s">faciens</expan> eo&longs;dem angulos æquales de&longs;cendit. </s>

<s id="id.001608">linea autem, quæ <lb/>

facit tales angulos tendit ad centrum &longs;phæræ A, vt patet ad &longs;en&longs;um in figu<lb/>

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per ip&longs;um Solem, & Zodiacum ab ortu in occa&longs;um circa mundum.</s>

</chap>

<chap>

<s id="id.001629"><emph type="italics"/>EX PRIMO METEORORVM.<emph.end type="italics"/></s>

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quà &longs;it illuminatum, vmbram proijci fa&longs;tigiatam: cum deinde Solem val<lb/>

de a terra di&longs;tare certum &longs;it, optimè infertur, eum re&longs;pectu terræ e&longs;&longs;e maxi<lb/>

mum: quanto enim duæ lineæ, &longs;iue radij B A, B C. à terra ad partes Solis <lb/>

magis elongantur, tan<lb/>

to maius corpus <expan abbr="illu-minãs">illu<lb/>

minans</expan> intercipiunt. </s>

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<s id="id.001642">Eodem cap. <emph type="italics"/>(Con&longs;iderantes vtique, quæ nunc o&longs;tenduntur per Mathematica<emph.end type="italics"/> <pb xlink:href="009/01/090.jpg" pagenum="90" /><emph type="italics"/>&longs;ufficienter, fortè vtique de&longs;isterent ab hac puerili opinione; valde enim &longs;implex <lb/>

<s id="id.001642">Eodem cap. <emph type="italics"/>(Con&longs;iderantes vtique, quæ nunc o&longs;tenduntur per Mathematica<emph.end type="italics"/> <pb pagenum="90" xlink:href="009/01/090.jpg"/><emph type="italics"/>&longs;ufficienter, fortè vtique de&longs;isterent ab hac puerili opinione; valde enim &longs;implex <lb/>

e&longs;t putare <expan abbr="vnumquodq;">vnumquodque</expan> eorum quæ feruntur e&longs;&longs;e paruum magnitudinibus, quia vi<lb/>detur a&longs;picientibus, hinc nobis &longs;ic)<emph.end type="italics"/> vtinam i&longs;ta, necnon alia his &longs;imilia, quæ <lb/>

pa&longs;&longs;im apud Ari&longs;t. occurrunt, <expan abbr="pleriq;">plerique</expan> no&longs;træ ætatis con&longs;iderarent, qui nulla <lb/>

ratione probari po&longs;&longs;e exi&longs;timant, Solem, v. g. terra e&longs;&longs;e centies &longs;exagies &longs;e<lb/>

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<s id="id.001660">quando verò ad Boream &longs;ubdefecerit, <lb/>accipere comam, quia magna e&longs;t circunferentia, quæ e&longs;t &longs;upra horizontem; quæ au-<emph.end type="italics"/>

<pb xlink:href="009/01/091.jpg" pagenum="91" /><emph type="italics"/>tem e&longs;t &longs;ubtus, pars circuli parua; facilè enim vi&longs;um hominum pertingere tunc ad <lb/>

<pb pagenum="91" xlink:href="009/01/091.jpg"/><emph type="italics"/>tem e&longs;t &longs;ubtus, pars circuli parua; facilè enim vi&longs;um hominum pertingere tunc ad <lb/>

Solem)<emph.end type="italics"/> cur cometa in regione au&longs;trali vltra Solis, <expan abbr="anni&qacute;">annique</expan>; vias con&longs;titutus <lb/>non appareret, cau&longs;am referebat Hippocrates paruitatem circuli, quem <lb/>

motu diurno cometa de&longs;cribebat, ob quam adeò parum &longs;upra horizontem <lb/>

attolleretur, vt <expan abbr="nõ">non</expan> po&longs;&longs;et vi&longs;us no&longs;ter ab ip&longs;o ad Solem reflecti; quod &longs;ecun<lb/>

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<s id="id.001675">Prima. </s>

<s id="id.001676">&longs;ed vt ab auctoritate, in quam obiter incidimus <expan abbr="initi&utilde;">initium</expan> faciamus, <lb/>non e&longs;t exi&longs;timandum nonnullos &longs;olum ex recentioribus id con&longs;tanter a&longs;&longs;e<pb xlink:href="009/01/092.jpg" pagenum="92" />uera&longs;&longs;e, &longs;ed &longs;uperiori etiam ætate id ip&longs;um Hieron. </s>

<s id="id.001676">&longs;ed vt ab auctoritate, in quam obiter incidimus <expan abbr="initi&utilde;">initium</expan> faciamus, <lb/>non e&longs;t exi&longs;timandum nonnullos &longs;olum ex recentioribus id con&longs;tanter a&longs;&longs;e<pb pagenum="92" xlink:href="009/01/092.jpg"/>uera&longs;&longs;e, &longs;ed &longs;uperiori etiam ætate id ip&longs;um Hieron. </s>

<s id="id.001677">Cardan. libro de &longs;ubtili<lb/>

tate conatus e&longs;t, <expan abbr="neq;">neque</expan> irrito conatu, demon&longs;trare; qui præterea idem cum <lb/>&longs;e ip&longs;o &longs;en&longs;i&longs;&longs;e ait Albumazar. </s>

<s id="id.001678">quibus etiam ex antiquis Seneca annumeran<lb/>

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reret, quam &longs;tella qu&etail;dam: <expan abbr="id&qacute;">idque</expan>; propter propinquitatem; a&longs;tra enim ob ni<lb/>

miam di&longs;tantiam videntur tardè moueri, quamuis veloci&longs;&longs;imè moueantur.</s>

<s id="id.001684">Quod melius ex &longs;equenti figura <lb/>

<expan abbr="cõuincitur">conuincitur</expan>, vbi circulus interior e&longs;t <lb/>

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tem &longs;pectatur, ea figura terræ &longs;emidiametrum A B. toties multiplicabit, vt <lb/>

ip&longs;i Lunæ circuitui proximè accedat.</s>

<s id="id.001688">Præterea aiunt, quis &longs;anæ mentis dixerit, Meteoron vllum ex materia <lb/>

vaga, ac fluxa con&longs;tans, po&longs;&longs;e tanta pernicitate moueri, vt diurnam con<lb/>

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<s id="id.001701"><expan abbr="Atq;">Atque</expan> hæ &longs;unt rationes, quibus plurimi a&longs;tronomorum recentiorum, co

<pb xlink:href="009/01/094.jpg" pagenum="94" />metas ho&longs;ce motum æthereæ regioni conformem, contrà quam Ari&longs;t. opi<lb/>natus e&longs;t, obtinui&longs;&longs;e, manife&longs;tum e&longs;&longs;e volunt; ac proinde eorum locum, & <lb/>

<pb pagenum="94" xlink:href="009/01/094.jpg"/>metas ho&longs;ce motum æthereæ regioni conformem, contrà quam Ari&longs;t. opi<lb/>natus e&longs;t, obtinui&longs;&longs;e, manife&longs;tum e&longs;&longs;e volunt; ac proinde eorum locum, & <lb/>

cur&longs;um in c&oelig;le&longs;ti mundi parte extiti&longs;&longs;e, &longs;e comproba&longs;&longs;e exi&longs;timant: qua de <lb/>

re prudentis Lectoris e&longs;to iudicium: <expan abbr="neq;">neque</expan> enim, vt ille cecinit, no&longs;trum e&longs;t, <lb/>

tantas componere lites.</s>

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<s id="id.001719">Eodem cap. <emph type="italics"/>(Amplius autem e&longs;t tertia quædam opinio de ip&longs;o, dicunt enim<emph.end type="italics"/> <pb xlink:href="009/01/095.jpg" pagenum="95" /><emph type="italics"/>quidam lac e&longs;&longs;e reflexionem no&longs;tri vi&longs;us ad Solem; &longs;icut & &longs;tellam comatam; im<lb/>

<s id="id.001719">Eodem cap. <emph type="italics"/>(Amplius autem e&longs;t tertia quædam opinio de ip&longs;o, dicunt enim<emph.end type="italics"/> <pb pagenum="95" xlink:href="009/01/095.jpg"/><emph type="italics"/>quidam lac e&longs;&longs;e reflexionem no&longs;tri vi&longs;us ad Solem; &longs;icut & &longs;tellam comatam; im<lb/>

po&longs;&longs;ibile autem e&longs;t & hoc, &longs;i enim videns quieuerit & &longs;peculum, & quod videtur <lb/>

omne in eodem puncto &longs;peculi eadem apparebit <expan abbr="vtiq;">vtique</expan> pars imaginis, &longs;i autem mo<lb/>

ueatur &longs;peculum, & quod videtur, in eadem quidem di&longs;tantia ad videns, & quie<lb/>

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a&longs;tronomis a&longs;&longs;eruatur: quando igitur Sol e&longs;t in apogæo, maiori multo in

<pb xlink:href="009/01/096.jpg" pagenum="96" />teruallo di&longs;tat à nobis, quàm quando e&longs;t in perigæo, interuallum enim illud <lb/>

<pb pagenum="96" xlink:href="009/01/096.jpg"/>teruallo di&longs;tat à nobis, quàm quando e&longs;t in perigæo, interuallum enim illud <lb/>

con&longs;tat diametris terræ duobus, & quadraginta, hoc e&longs;t milliarijs 208000. <lb/>

ferè, ide&longs;t octonis millibus &longs;upra ducenta millia. </s>

<s id="id.001731">quæ differentia facit vt Sol <lb/>

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nionem, non &longs;olum Ari&longs;toteli imponerent, verum etiam ip&longs;i <expan abbr="tãquam">tanquam</expan> veram

<pb xlink:href="009/01/097.jpg" pagenum="97" />a&longs;truerent: huiu&longs;modi patiuntur incommoda, qui <expan abbr="ab&longs;q;">ab&longs;que</expan> Mathematicarum <lb/>

<pb pagenum="97" xlink:href="009/01/097.jpg"/>a&longs;truerent: huiu&longs;modi patiuntur incommoda, qui <expan abbr="ab&longs;q;">ab&longs;que</expan> Mathematicarum <lb/>

auxilio Philo&longs;ophiam aggrediuntur.</s>

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orientale mare, quæ extrema indigenæ particulatim nominant Poropami&longs;

<pb xlink:href="009/01/098.jpg" pagenum="98" />&longs;um, Emodum, Imauum, & alijs nominibus: Macedones verò Cauca&longs;um <lb/>

<pb pagenum="98" xlink:href="009/01/098.jpg"/>&longs;um, Emodum, Imauum, & alijs nominibus: Macedones verò Cauca&longs;um <lb/>

vocant.</s>

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fe&longs;tumque</expan>; reddit, quàm nece&longs;&longs;ariæ &longs;int Mathematicæ ad philo&longs;ophicæ veri

<pb xlink:href="009/01/099.jpg" pagenum="99" />tatis in&longs;pectionem. </s>

<pb pagenum="99" xlink:href="009/01/099.jpg"/>tatis in&longs;pectionem. </s>

<s id="id.001787">Is igitur &longs;ect. </s>

<s id="id.001788">3. cap. 5. de hoc Ari&longs;t. loco &longs;ie loquitur: <lb/>hic locus diligenter expendendus videtur tum quia difficillimus e&longs;t, <expan abbr="t&utilde;">tum</expan> quia <lb/>

multis an&longs;am dedit reprehendendi Ari&longs;t. tanquam puerilia effutientem. </s>

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vt totius montis altitudo perpendicularis &longs;it 78. mill. &longs;ed papè in quos acu

<pb xlink:href="009/01/100.jpg" pagenum="100" />leos imprudens me conieci? </s>

<pb pagenum="100" xlink:href="009/01/100.jpg"/>leos imprudens me conieci? </s>

<s id="id.001801">rident enim hoc Ari&longs;t. dictum Mathematici, <lb/>

putant enim eum pueriliter lap&longs;um e&longs;&longs;e. </s>

<s id="id.001802">Cæterum ego pro præceptoris tu<lb/>tela, dico eum &longs;equutum e&longs;&longs;e famam. </s>

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52. milliaria, non tamen &longs;equitur ip&longs;am &longs;olam eminere, &longs;ed alia etiam pars <lb/>

eminere pote&longs;t, quod &longs;ic geometricè demon&longs;trabo. </s>

<s id="id.001805">de&longs;cribatur enim figura <lb/>

<pb xlink:href="009/01/101.jpg" pagenum="101" />illa, qua ad vaporum altitudines indagandas vtuntur Alhazenus, Vitellio, <lb/>

<pb pagenum="101" xlink:href="009/01/101.jpg"/>illa, qua ad vaporum altitudines indagandas vtuntur Alhazenus, Vitellio, <lb/>

& Clauius, in qua terræ globus e&longs;t F L G E, regiò vaporum, & exhalatio<lb/>

num M X N T. horizon a&longs;tronomicus O P. phy&longs;icus Q R, tangens terram <lb/>

in puncto F, vbi etiam ponendus e&longs;t huius horizontis habitator, vnà cum. <lb/>

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tertiæ partis noctis apicem montis illu&longs;trari, altitudo eius erit tantum

<pb xlink:href="009/01/102.jpg" pagenum="102" />modo 180. quot continet latus F V. vt vidimus, quæ quamuis illa minor &longs;it, <lb/>

<pb pagenum="102" xlink:href="009/01/102.jpg"/>modo 180. quot continet latus F V. vt vidimus, quæ quamuis illa minor &longs;it, <lb/>

adhuc tamen ab&longs;urda e&longs;t.</s>

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<s id="id.001851">Ad finem eiu&longs;dem cap. <emph type="italics"/>(Et circa Ligu&longs;ticam non minor Rhodano ab&longs;orbetur <lb/>

quidam fluuius, & iterum egreditur &longs;ecundum alium locum)<emph.end type="italics"/> <expan abbr="incompert&utilde;">incompertum</expan> & hoc <pb xlink:href="009/01/103.jpg" pagenum="103" />Ari&longs;t. vt &longs;uperiora, ob Geographiæ illius &longs;eculi imperfectionem, nu&longs;quam <lb/>

quidam fluuius, & iterum egreditur &longs;ecundum alium locum)<emph.end type="italics"/> <expan abbr="incompert&utilde;">incompertum</expan> & hoc <pb pagenum="103" xlink:href="009/01/103.jpg"/>Ari&longs;t. vt &longs;uperiora, ob Geographiæ illius &longs;eculi imperfectionem, nu&longs;quam <lb/>

enim in tota Liguria quidpiam tale reperitur.</s>

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&longs;unt <expan abbr="quã">quam</expan> exordio mundi, vt paulò po&longs;t <expan abbr="o&longs;t&etilde;dam">o&longs;tendam</expan>. </s>

<s id="id.001869">Illud autem liquidò apparet <lb/>

ex &longs;ignis, &longs;eu &longs;ymbolis, &longs;eu ex &longs;imilitudine terræ, aut lapidis, quæ in alti&longs;&longs;imis <lb/>

fluminum ripis hinc inde pa&longs;&longs;im <expan abbr="vid&etilde;tur">videntur</expan>, quæ indicio &longs;unt montes illos iam <pb xlink:href="009/01/104.jpg" pagenum="104" />olim fui&longs;&longs;e continuos, <expan abbr="atq;">atque</expan> vnam, <expan abbr="eandem&qacute;">eandemque</expan>; terram <expan abbr="contin&etilde;tem">continentem</expan>, antequam <lb/>

fluminum ripis hinc inde pa&longs;&longs;im <expan abbr="vid&etilde;tur">videntur</expan>, quæ indicio &longs;unt montes illos iam <pb pagenum="104" xlink:href="009/01/104.jpg"/>olim fui&longs;&longs;e continuos, <expan abbr="atq;">atque</expan> vnam, <expan abbr="eandem&qacute;">eandemque</expan>; terram <expan abbr="contin&etilde;tem">continentem</expan>, antequam <lb/>

flumen eos ab inuicem &longs;epararet; <expan abbr="flumen&qacute;">flumenque</expan>; ip&longs;um olim altius, vbi &longs;unt &longs;igna <lb/>

illa ambula&longs;&longs;e; quemadmodum in Pyramo Ciliciæ amne ob&longs;eruauit Strabo, <lb/>

dum libro 12. de illius ripis hæc tradit, mira præterea e&longs;t montis cæ&longs;ura, <lb/>

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<s id="id.001880">&longs;ic <lb/>

etiam templa Epi&longs;copalia, quæ <expan abbr="plerunq;">plerunque</expan> &longs;atis peruetu&longs;ta &longs;unt, admodum <lb/>

infra terram con&longs;piciuntur. </s>

<s id="id.001881">Idem affirmant c&oelig;mentarij, & architectores <pb xlink:href="009/01/105.jpg" pagenum="105" />omnes, quibus <expan abbr="vbiq;">vbique</expan> terrarum, dum in planis ædeficiorum fundamenta ex<lb/>

<s id="id.001881">Idem affirmant c&oelig;mentarij, & architectores <pb pagenum="105" xlink:href="009/01/105.jpg"/>omnes, quibus <expan abbr="vbiq;">vbique</expan> terrarum, dum in planis ædeficiorum fundamenta ex<lb/>

canant, occurrit primò terra quædam, quam ip&longs;i motam appellant, quæ li<lb/>

gnis, ruderibus, ferramentis, numi&longs;matis, &longs;epulturis, <expan abbr="varijs&qacute;">varijsque</expan>; rebus per<lb/>

mixta e&longs;t; qua eruta, reperitur terra alia, quam nunquam fui&longs;&longs;e motam, ap<lb/>

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<s id="id.001895"><expan abbr="quart&utilde;">quartum</expan> e&longs;t illi Bo&longs;phorus Tracius; quod <lb/>

vnà cum præcedentibus &longs;atius e&longs;t apud ip&longs;um, vel potius apud eius expo&longs;i<lb/>

torem Vicomercatum videre, vt breuitati con&longs;ulatur. </s>

<s id="id.001896">Accedit & Plinij te<lb/>&longs;timonium, qui tradit multas terras na&longs;ci, non &longs;olum fluminum inuectu, &longs;ed <pb xlink:href="009/01/106.jpg" pagenum="106" />etiam marium rece&longs;&longs;u; &longs;ic mare ab Ambraciæ portu 10. millia pa&longs;&longs;uum; ab <lb/>

<s id="id.001896">Accedit & Plinij te<lb/>&longs;timonium, qui tradit multas terras na&longs;ci, non &longs;olum fluminum inuectu, &longs;ed <pb pagenum="106" xlink:href="009/01/106.jpg"/>etiam marium rece&longs;&longs;u; &longs;ic mare ab Ambraciæ portu 10. millia pa&longs;&longs;uum; ab <lb/>

Athenarum verò <expan abbr="quinq;">quinque</expan> millia, & alijs in locis plus minu&longs;uè rece&longs;&longs;i&longs;&longs;e &longs;cri<lb/>

bit. </s>

<s id="id.001897">Huc facit locus quidam Strabonis ex lib. 12. de Pyramo Ciliciæ fluuio: <lb/>

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mundus interiturus e&longs;&longs;et. </s>

<s id="id.001913">&longs;ed de his hactenus.</s>

<s id="id.001914">Quoad magnum illud Diluuium, quod Ari&longs;t. hoc capite exi&longs;timat po&longs;t <lb/>

multa &longs;ecula reuolui, hoc veritati e&longs;&longs;e con&longs;entaneum argumento &longs;unt, ac <lb/>

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<s id="id.001930">nam cùm ip&longs;a Sol, quippe il<lb/>

lis velocior primum a&longs;&longs;equitur, ea &longs;uo lumine obtegit, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; hic occa&longs;us eo<lb/>

rum heliacus: cum verò eadem præterierit, ac po&longs;t &longs;e reliquerit fit, vt mo<lb/>

tu diurno toto c&oelig;lo conuer&longs;o, mane ante Solem effulgeant, &longs;iue heliacè <lb/>oriantur: & cum quotidie magis Sol ab illis recedat, ip&longs;aque magis à Sole <pb xlink:href="009/01/108.jpg" pagenum="108" />elongentur, fit, vt quotidie magis ortum Solis anticipent, & citius mane au<lb/>

tu diurno toto c&oelig;lo conuer&longs;o, mane ante Solem effulgeant, &longs;iue heliacè <lb/>oriantur: & cum quotidie magis Sol ab illis recedat, ip&longs;aque magis à Sole <pb pagenum="108" xlink:href="009/01/108.jpg"/>elongentur, fit, vt quotidie magis ortum Solis anticipent, & citius mane au<lb/>

te Solem videantur. </s>

<s id="id.001931"><expan abbr="&longs;ic&qacute;">&longs;icque</expan>; tanto in dies citius, vt deinde media etiam nocte <lb/>

oriantur; tum ante mediam noctem po&longs;tea paulò ante occa&longs;um Solis. </s>

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<s id="id.001947">Eodem cap. <emph type="italics"/>(Ete&longs;iæ autem flant post ver&longs;iones, & Canis ortum)<emph.end type="italics"/> per ver&longs;io<lb/>

nes intelligit tropicos, quod & tropici etymon confirmat, <expan abbr="c&utilde;">cum</expan> tropicus idem <lb/>

valeat, ac conuer&longs;iuus. </s>

<s id="id.001948">circa Canis ortum eadem &longs;unt notanda, quæ &longs;upra <lb/>de ortu Orionis annotaui; intelligit enim eum Canis ortum, qui mane fiat <pb xlink:href="009/01/109.jpg" pagenum="109" />primum paulò ante Solis ortum, cum &longs;cilicet incipit apparere.</s>

<s id="id.001948">circa Canis ortum eadem &longs;unt notanda, quæ &longs;upra <lb/>de ortu Orionis annotaui; intelligit enim eum Canis ortum, qui mane fiat <pb pagenum="109" xlink:href="009/01/109.jpg"/>primum paulò ante Solis ortum, cum &longs;cilicet incipit apparere.</s>

<s id="id.001949">Cum porrò in c&etail;lo &longs;it Canis maior, & Canis minor, qui & Procyon, ide&longs;t <lb/>

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<s id="id.001956">eodem autem modo ad inferiorem polum alij duo coni terræ &longs;egmenta fa<lb/>

ciunt)<emph.end type="italics"/> vt benè duas ha&longs;ce terræ portiones, quas &longs;olas habitabiles putat Ari<lb/>

&longs;tot. concipias, <expan abbr="reliquaq;">reliquaque</expan> huius loci intelligas, in&longs;pice &longs;equentem figuram. <lb/>

Maior circulus &longs;it c&oelig;lum, in quo polus L, articus; M, antarticus, ille eleua<lb/>

tus &longs;upra no&longs;trum horizontem S N, 45. gradibus, i&longs;te verò totidem infra <lb/>

depre&longs;&longs;us. </s>

<s id="id.001957"><expan abbr="&longs;int&qacute;">&longs;intque</expan>; diametri circuli &longs;emper apparentium maximi S R, necnon <pb xlink:href="009/01/110.jpg" pagenum="110" />diametri &longs;emper occultorum maximi Y N: tropicorum item T Q, Cancri, <lb/>

<s id="id.001957"><expan abbr="&longs;int&qacute;">&longs;intque</expan>; diametri circuli &longs;emper apparentium maximi S R, necnon <pb pagenum="110" xlink:href="009/01/110.jpg"/>diametri &longs;emper occultorum maximi Y N: tropicorum item T Q, Cancri, <lb/>

X O, Capricorni, vt vides in figura. </s>

<s id="id.001958">Terra &longs;it A B C H G F E D Z K. à cu<lb/>

ius centro Z, educantur primo duæ lineæ rectæ Z R, Z S. ad circulum &longs;em<lb/>

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<s id="id.001981">Eodem cap. <emph type="italics"/>(Et quidem ad latitudinem <expan abbr="v&longs;q;">v&longs;que</expan> ad inhabitabilia &longs;cimus habita-<emph.end type="italics"/>

<pb xlink:href="009/01/111.jpg" pagenum="111" /><emph type="italics"/>tam, hic enim propter frigus non amplius habitant, illic autem propter æ&longs;tum)<emph.end type="italics"/><lb/>

<pb pagenum="111" xlink:href="009/01/111.jpg"/><emph type="italics"/>tam, hic enim propter frigus non amplius habitant, illic autem propter æ&longs;tum)<emph.end type="italics"/><lb/>

illic autem, ide&longs;t &longs;ub Zona torrida, compertum autem e&longs;t nunc totam ferè <lb/>

torridam Zonam, & quidem alicubi percommodè habitari, cuius cau&longs;æ &longs;unt <lb/>

quatuor, quæ ip&longs;um latuerunt. </s>

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rotundus)<emph.end type="italics"/> vt in &longs;equenti figura circulus A G B H, de&longs;criptus horizontem <lb/>

referret,</s>

<s id="id.001993"><emph type="italics"/>Oportet autem ip&longs;ius alteram portionem intelligere, quæ nobis habitatur; quæ <lb/>

eodem modo diuidi poterit)<emph.end type="italics"/> ide&longs;t oportet intelligere ip&longs;ius horizontis, vel ter<lb/>

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enim e&longs;t Cæciæ, & Aparetiæ. </s>

<s id="id.002008">Diameter autem K I, iuxta circulum &longs;emper con&longs;pi<lb/>

cuum e&longs;&longs;e &longs;olet, non tamen exactè)<emph.end type="italics"/> ide&longs;t linea K I, &longs;olet in horizonte referre <lb/>

diametrum circuli omnium &longs;emper apparentium maximi, eo quod &longs;it ferè <lb/>&longs;ub diametro illius, in qualibet enim &longs;phæra obliqua, ide&longs;t, in qua polus ele<pb xlink:href="009/01/113.jpg" pagenum="113" />uatur, intelligunt A&longs;tronomi circulum quendam &longs;emper apparentium ma<lb/>ximum, quem de&longs;cribunt ex ip&longs;o polo, tanquam centro, & interuallo v&longs;que <lb/>

diametrum circuli omnium &longs;emper apparentium maximi, eo quod &longs;it ferè <lb/>&longs;ub diametro illius, in qualibet enim &longs;phæra obliqua, ide&longs;t, in qua polus ele<pb pagenum="113" xlink:href="009/01/113.jpg"/>uatur, intelligunt A&longs;tronomi circulum quendam &longs;emper apparentium ma<lb/>ximum, quem de&longs;cribunt ex ip&longs;o polo, tanquam centro, & interuallo v&longs;que <lb/>

ad horizontem, circa ip&longs;um polum: hunc appellant &longs;emper apparentium, <lb/>

maximum, quia intra hunc alios quamplurimos concipiunt circa eundem <lb/>

polum, quorum minores &longs;emper &longs;unt polo propinquiores. </s>

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<s id="id.002022">Notandum etiam Aream, de qua mox dicam explicari po&longs;&longs;e tam per re<lb/>

flexionem, quàm per refractionem: per reflexionem, quia &longs;upponunt Philo<lb/>&longs;ophi e&longs;&longs;e in acre rorido innumera &longs;pecula parua inuicem valdè proxima, <lb/>ide&longs;t guttulas, per quas reflectatur ad oculum no&longs;trum &longs;pecies &longs;yderis. </s>

<s id="id.002023">per <lb/>refractionem verò, vt vult Vitellio, quia &longs;umit totum illum aerem humi<lb/>

dum magis den&longs;um e&longs;&longs;e aere paro, qui e&longs;t circa oculos no&longs;tros, & hoc modo <lb/>con&longs;tituit diuer&longs;a media in den&longs;itate, per quam fiat vi&longs;io; corpus inquam <pb xlink:href="009/01/114.jpg" pagenum="114" />illud humidum den&longs;ius, & aerem deinde circa oculum rarius. </s>

dum magis den&longs;um e&longs;&longs;e aere paro, qui e&longs;t circa oculos no&longs;tros, & hoc modo <lb/>con&longs;tituit diuer&longs;a media in den&longs;itate, per quam fiat vi&longs;io; corpus inquam <pb pagenum="114" xlink:href="009/01/114.jpg"/>illud humidum den&longs;ius, & aerem deinde circa oculum rarius. </s>

<s id="id.002024">Vicomerca<lb/>

tus igitur quamuis vtatur voce reflexionis in Halone, non tamen ex prædi<lb/>ctis videtur reprehendendus.</s>

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dem enim &longs;igno ad idem &longs;ignum æquales frangentur &longs;uper circuli lineam &longs;emper. </s>

<s id="id.002030">&longs;it <emph.end type="italics"/><lb/>

<emph type="italics"/>enim à puncto, in quo A, ad B, fracta, & ea, quæ est <lb/>

A C B, & quæ A F B, & quæ A D B, æquales autem <lb/>& hæ A C, A F, A D, inuicem. </s>

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nit igitur primò Ari&longs;t. lineas vi&longs;uales à &longs;ydere B, ad oculos no&longs;tros A, per <lb/>

nubem roridam C D F, procedentes, in nube con&longs;imiliter refrangi, ide&longs;t <expan abbr="vn-diq;">vn<lb/>

dique</expan> circa Solem, Lunamuè facere angulos refractionis æquales. </s>

<s id="id.002036">quod etiam <pb xlink:href="009/01/115.jpg" pagenum="115" />patet ex 48. 10. Vitellionis; vt in figura, in qua &longs;ydus B, oculus A, nubes <lb/>

<s id="id.002036">quod etiam <pb pagenum="115" xlink:href="009/01/115.jpg"/>patet ex 48. 10. Vitellionis; vt in figura, in qua &longs;ydus B, oculus A, nubes <lb/>

C D F, radij vi&longs;uales tres refracti in nube &longs;int B C A, B D A, B E A, facien<lb/>

tes con&longs;imilem refractionem, ide&longs;t angulos refractos B C A, B D A, B E A, <lb/>

æquales in punctis C, D, F: <expan abbr="atq;">atque</expan> hoc e&longs;t con&longs;imilem facere refractionem. <lb/>

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pulatæ refrangantur ab hemi&longs;phærio ad G, &longs;uper maiorem angulum, circuli circun<lb/>

ferentiam incident lineæ, quæ à K, & &longs;i quidem in ortu, aut in occa&longs;u a&longs;tri reflexio <lb/>

fiat, &longs;emicirculus ab <expan abbr="horizõte">horizonte</expan> a&longs;&longs;umetur &longs;uper terram factus. </s>

<s id="id.002050">&longs;i autem &longs;upra, minor<emph.end type="italics"/> <pb xlink:href="009/01/116.jpg" pagenum="116" /><figure id="id.009.01.116.1.jpg" xlink:href="009/01/116/1.jpg" place="text"/><lb/>

<s id="id.002050">&longs;i autem &longs;upra, minor<emph.end type="italics"/> <pb pagenum="116" xlink:href="009/01/116.jpg"/><figure id="id.009.01.116.1.jpg" place="text" xlink:href="009/01/116/1.jpg"/><lb/>

<emph type="italics"/>&longs;emper &longs;emicirculo, minus autem, <lb/>

cum in meridie fuerit a&longs;trum)<emph.end type="italics"/> quod <lb/>

&longs;upra monui, iterum moneo, <expan abbr="re-tin&etilde;dam">re<lb/>

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<s id="id.002063">Ibidem <emph type="italics"/>(Sit enim in <expan abbr="ori&etilde;te">oriente</expan> pri<lb/>

mum vbi G, & refracta &longs;it K M, <lb/>

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tur circunferentiam tanget M, fit <expan abbr="itaq;">itaque</expan> bæc in qua M N, quare &longs;ectio circunferen-<emph.end type="italics"/>

<pb xlink:href="009/01/117.jpg" pagenum="117" /><emph type="italics"/>tiarum data e&longs;t. </s>

<pb pagenum="117" xlink:href="009/01/117.jpg"/><emph type="italics"/>tiarum data e&longs;t. </s>

<s id="id.002066">apud autem aliud punctum, quam ip&longs;ius M N, circunferentiæ, ab <lb/>

ij&longs;dem punctis, eadem ratio in eodem plano non con&longs;i&longs;tit)<emph.end type="italics"/> eorum omnium, quæ <lb/>

demon&longs;tranda &longs;unt, præmittenda &longs;unt duo nece&longs;&longs;aria fundamenta. </s>

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tum; ea &longs;cilicet, quæ per reflexionem (de quorum numero e&longs;t Iris) viden<lb/>

tur, videri, tunc &longs;olum, quando angulus incidentiæ fuerit æqualis angulo <lb/>

reflexionis, quia tunc breui&longs;&longs;imis lineis fit vi&longs;io; quibus &longs;oli, natura (&longs;i fieri <lb/>

pote&longs;t) vtitur. </s>

<s id="id.002070">v. g. in figura præ&longs;enti &longs;it &longs;pe<lb/>

culum C D E, obiectum A, oculus B, linea in<lb/>

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magnum, vt totum &longs;ecet hemi&longs;phærium, faciet in &longs;uperficie hemi&longs;phærij &longs;e

<pb xlink:href="009/01/118.jpg" pagenum="118" />ctionem, quæ erit portio maximi circuli, per 6. Theodo&longs;ij, cum planum &longs;e<lb/>

<pb pagenum="118" xlink:href="009/01/118.jpg"/>ctionem, quæ erit portio maximi circuli, per 6. Theodo&longs;ij, cum planum &longs;e<lb/>

cans hemi&longs;phærium, tran&longs;eat per <expan abbr="centr&utilde;">centrum</expan> ip&longs;ius, quæ &longs;ectio, &longs;iue circuli por<lb/>tio repræ&longs;entatur in figura, per &longs;emicirculum in quo A, &longs;iue in quo G A M <lb/>

R O. nihil autem refert quodcunque intelligas planum &longs;uper axem G K O, <lb/>

tran&longs;iens &longs;iue per triangulum G K M, &longs;iue per aliud illi &longs;imile. </s>

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</s>

<s id="id.002087">Iam &longs;i <expan abbr="triãgulum">triangulum</expan> G M K, prioris figuræ circumuoluatur circa axem G K O, <lb/>

punctum ip&longs;ius M, de&longs;cribit prædictum ambitum L M N. hunc ambitum <lb/>inquit Ari&longs;tot. linea K M, attinget, <expan abbr="erit&qacute;">eritque</expan>; hic ambitus datus, vt dictum e&longs;t. <lb/>

Erit præterea &longs;ectio circunferentiarum ho<lb/>rizontis, & huius ambitus data, cuius extre<lb/>

ma puncta e&longs;&longs;ent L, & N. &longs;i enim <expan abbr="cõcipiamus">concipiamus</expan> <lb/>

in figura non &longs;olum horizontis diametrum <lb/>

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circunferentia e&longs;&longs;ent duo illa puncta L, & N, <lb/>vt in præ&longs;enti de&longs;criptione melius intellige<lb/>

tur, in qua horizon G N O L, & ambitus <lb/>

prædictus e&longs;t L M N, qui debet intelligi ele<lb/>

uatus &longs;upra horizontem perpendiculariter) <lb/>tunc &longs;ectio ip&longs;ius mutua cum horizonte e&longs;&longs;et <pb xlink:href="009/01/119.jpg" pagenum="119" />linea N P L, cuius extrema puncta &longs;unt L, N, quæ data erunt, cum &longs;int ex<lb/>

uatus &longs;upra horizontem perpendiculariter) <lb/>tunc &longs;ectio ip&longs;ius mutua cum horizonte e&longs;&longs;et <pb pagenum="119" xlink:href="009/01/119.jpg"/>linea N P L, cuius extrema puncta &longs;unt L, N, quæ data erunt, cum &longs;int ex<lb/>

trema lineæ K M, circumlatæ; & quemadmodum dabatur &longs;uperius punctum <lb/>

M. eadem ratione ex Datis, dabitur punctum N, & L. quare etiam &longs;ectio <lb/>

N P L, quæ inter data puncta continetur, data erit ex 26. Datorum.</s>

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<s id="id.002095">Prædicta omnia &longs;unt &longs;ecundum Ari&longs;tot. di&longs;cur&longs;um, & figurationem dicta, <lb/>

nam &longs;ecundum veritatem po&longs;&longs;unt in eadem nube con&longs;titui plures anguli <lb/>

æquales, nec tamen in eodem orbe, &longs;ed vnus &longs;upra <expan abbr="alter&utilde;">alterum</expan>; vt in figura præ<lb/>

&longs;enti, &longs;i nubes e&longs;&longs;et vbi B D. <lb/>

oculus in C, Sol in A. e&longs;&longs;ent <lb/>

duo anguli A B C, A D C, æ<lb/>

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<s id="id.002098">Ita vt non &longs;o

<pb xlink:href="009/01/120.jpg" pagenum="120" />lum requiratur idem angulus, &longs;ed etiam tanta Iridis altitudo, <expan abbr="quãta">quanta</expan> requi<lb/>

<pb pagenum="120" xlink:href="009/01/120.jpg"/>lum requiratur idem angulus, &longs;ed etiam tanta Iridis altitudo, <expan abbr="quãta">quanta</expan> requi<lb/>

ritur vt angulus in orbem con&longs;tituatur, ex quo Iris po&longs;&longs;it apparere. </s>

nemine hactenus animaduer&longs;a placuit addere, vt ex ijs demon&longs;tratio Iridis <lb/>

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<s id="id.002106">Dicit <expan abbr="itaq;">itaque</expan> Ari&longs;t. cum data &longs;it proportio linearum K M, & M G, in &longs;upe<lb/>

riori &longs;ecunda figura numeri 164. quam nunc iterum in&longs;picere opertet; ex<lb/>

ponatur alia linea recta B D. quæ diui<lb/>

datur in partes B, & D. proportionales <lb/>

cum lineis K M, G M, per 10. 6. cum <lb/>

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habet autem & quæ M G, ad M K, eam rationem, quam quæ D, ad eam quæ B, <lb/>quare ambæ à punctis G K, non &longs;olum ad circunferentiam M N, con&longs;tituentur ean<lb/>dem habentes rationem, &longs;ed & alibi, quod quidem impo&longs;&longs;ibile)<emph.end type="italics"/> incipit, vt dixi,

<pb xlink:href="009/01/121.jpg" pagenum="121" />probare P, e&longs;&longs;e polum prædicti ambitus, &longs;ic. </s>

<pb pagenum="121" xlink:href="009/01/121.jpg"/>probare P, e&longs;&longs;e polum prædicti ambitus, &longs;ic. </s>

<s id="id.002113">Primò enim &longs;ciendum in præ<lb/>

mi&longs;&longs;a con&longs;tructione e&longs;&longs;e, vt F, ad G K, & B, ad K P, ita D, ad P M. nam &longs;i non <lb/>

&longs;it eadem ratio D, ad P M, cum alijs prædictis, erit eadem ratio eiu&longs;dem D, <lb/>ad aliam maiorem, vel minorem ip&longs;a P M. &longs;it ad minorem P R. nihil enim <lb/>

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quo per puncta M, vbi &longs;it reflexio, de&longs;cribitur arcus attingens omnes Iridis <lb/>

reflexiones.</s>

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<s id="id.002132">Porrò &longs;ciendum po&longs;&longs;e nos breuius polum prædictum inuenire, &longs;i nimirum <lb/>

ad M, ducatur M P, faciens angulum K P M, æqua<lb/>

lem angulo G M K, per 23. primi, erunt enim duo <lb/>

triangula <expan abbr="æquiãgula">æquiangula</expan> G P M, K P M, angulus enim <lb/>

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centrum vtique erit &longs;ub horizonte priori eius, in quo A C, in linea K P, in quo <foreign lang="greek">w,</foreign><emph.end type="italics"/>

<emph type="italics"/>Quare minor erit &longs;uperior &longs;ectio &longs;emicir<lb/>

culo, in qua S T, (nam Q S T, &longs;emicir<lb/>

culus est, nunc autem inter&longs;ectus e&longs;t ab <lb/>

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<s id="id.002150">Aduertendum præterea Vicomercatum inordinatè citare librum Dato<lb/>

rum Euclidis, & <expan abbr="quandoq;">quandoque</expan> etiam malè citare Euclidem ip&longs;um. </s>

<s id="id.002151">peius verò <pb xlink:href="009/01/124.jpg" pagenum="124" />faciunt ij, qui has demon&longs;trationes <expan abbr="ab&longs;q;">ab&longs;que</expan> vlla libri Datorum mentione ex<lb/>

<s id="id.002151">peius verò <pb pagenum="124" xlink:href="009/01/124.jpg"/>faciunt ij, qui has demon&longs;trationes <expan abbr="ab&longs;q;">ab&longs;que</expan> vlla libri Datorum mentione ex<lb/>

plicare conantur, cum manife&longs;tè illo innitantur.</s>

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accommodata, nullo negotio li<lb/>

cebit intueri.</s>

<s id="id.002161"><emph type="italics"/>Additio de Iride.<emph.end type="italics"/></s>

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in rece&longs;&longs;u, vt pictores aiunt, depictum. </s>

<s id="id.002168">non in hoc &longs;itu, & ouali figura, &longs;ed <lb/>

e&longs;&longs;e perfectè &longs;emicircularem, <expan abbr="habere&qacute;">habereque</expan>; talem po&longs;itionem, vt pars ip&longs;ius B F, <lb/>

&longs;it citra chartam eleuata, <expan abbr="ip&longs;i&qacute;">ip&longs;ique</expan>; perpendicularis, pars verò E B, vltra pagi

<pb xlink:href="009/01/126.jpg" pagenum="126" />nam rectà recedat, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; diameter Iridis E F, faciat angulos rectos cum <lb/>

<pb pagenum="126" xlink:href="009/01/126.jpg"/>nam rectà recedat, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; diameter Iridis E F, faciat angulos rectos cum <lb/>

linea horizontali A C L, in quo &longs;itu oculo C, totus ex oppo&longs;ito directè &longs;pe<lb/>

ctaretur, non aliter ac Iridem ip&longs;am con&longs;picere &longs;olemus. </s>

<s id="id.002169">Quod autem ne<lb/>

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huiu&longs;modi angulo repre&longs;entari) non po&longs;&longs;unt aliter quàm in gyrum <expan abbr="cõ&longs;titui">con&longs;titui</expan>,

<pb xlink:href="009/01/127.jpg" pagenum="127" />quem gyrum optimè concipiemus, &longs;i imaginemur triangulum A B C, cir<lb/>

<pb pagenum="127" xlink:href="009/01/127.jpg"/>quem gyrum optimè concipiemus, &longs;i imaginemur triangulum A B C, cir<lb/>

cumuerti circa lineam horizontalem A C L, fixam, tanquam circa axem. </s>

hac enim conuer&longs;ione angulus Iridis B, de&longs;cribet circulum, qui erit Iris, & <lb/>pertran&longs;ibit omnes angulos, qui in tali Solis, oculi, ac nubis &longs;itu, arcum ef<lb/>

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<s id="id.002195">Octauo loco Problemata nonnulla re&longs;oluemus.</s>

<s id="id.002196"><emph type="italics"/>Problema Primum.<emph.end type="italics"/></s>

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<s id="id.002202">Maior quidem, imò etiam integer circulus, &longs;ed ab oculo in &longs;ummitate <lb/>

montis con&longs;tituto, <expan abbr="Sole&qacute;">Soleque</expan>; iam multum eleuato videri pote&longs;t, vt in <lb/>

hac &longs;ecunda figura cernitur, vbi euecto Sole ad locum E, &longs;upra horizontem <lb/>

A B, poterit oculus in vertice montis C, po&longs;itus Iridem F G H I, comple<lb/>

tam videre, quia infra lineam E C D, in qua exi&longs;tunt Sol, oculus, & Iridis <lb/>

centrum, nihil e&longs;t ad partes D, vbi nubes irrorat, quod Iridis apparitioni <lb/>

&longs;it impedimento.</s>

<s id="id.002203">Cur quanto Sol altior e&longs;t, tanto inferior, <expan abbr="tanto&qacute;">tantoque</expan>; &longs;emicir<lb/>

culo minor appareat Iris?</s>

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<s id="id.002205">Qvia eleuato Sole ad E, vt in hac tertia figura, nece&longs;&longs;ario centrum Iri<lb/>

dis D, infra horizontem A B, deprimetur, cum in eadem recta E C D. <lb/>

Sol E, oculus C, <expan abbr="centr&utilde;&qacute;">centrumque</expan>; Iridis D, exi&longs;tant: vnde nece&longs;&longs;ariò &longs;equitur Iridis <lb/>

portionem F G H, &longs;upra horizontem extantem, &longs;emicirculo minorem e&longs;&longs;e.</s>

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<s id="id.002209">Ex dictis pr&etail;tere a patet, &longs;impliciter nimis eos hallucinari, qui exi&longs;timant <lb/>

in plana, aut concaua nubis &longs;uperficie Iridem tantummodo apparere po&longs;&longs;e.</s>

<s id="id.002210">Cur lunares Irides fiunt rariores?</s>

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deatur &longs;upra Solem, quamuis non ei quadret, pote&longs;t enim aliqua nubes vi

<pb xlink:href="009/01/131.jpg" pagenum="131" />deri &longs;upra Solem, quæ tamen remotior &longs;it à Sole, quam illa, in qua Parelium <lb/>

<pb pagenum="131" xlink:href="009/01/131.jpg"/>deri &longs;upra Solem, quæ tamen remotior &longs;it à Sole, quam illa, in qua Parelium <lb/>

gignitur. </s>

<s id="id.002227">Ait po&longs;tea <emph type="italics"/>(A latere autem, &c.)<emph.end type="italics"/> cur appareat in nube fatis Soli <lb/>

à latere vicina, in di&longs;tantiam à Sole refert: &longs;ed quæ dudum dicta &longs;unt, i&longs;tud <lb/>

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&longs;icut recto in quantum rectum multa accidunt, vt tangere æneam &longs;phæram &longs;ecun<lb/>

dum punctum, non tamen tanget hoc, rectum ip&longs;um &longs;eparatum: in&longs;eparabile enim, <lb/>

&longs;i quidem cum corpore quodam &longs;emper e&longs;t)<emph.end type="italics"/> Propo&longs;itio 2. tertij Elem. &pacute;robat li<lb/>

neam rectam, duo quælibet puncta <expan abbr="quãtumuis">quantumuis</expan> pro<lb/>

pinqua in circuli ambitu a&longs;&longs;umpta coniungentem <lb/>

cadere intra circulum. </s>

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&longs;ed &longs;ecans, quia vt modo dixi, pars lineæ rectæ, quæ <expan abbr="cõiungeret">coniungeret</expan> puncta E F,

<pb xlink:href="009/01/132.jpg" pagenum="132" />intra circulum per &longs;ecundam præallegatam caderet, quod e&longs;t ab&longs;urdum, <lb/>

<pb pagenum="132" xlink:href="009/01/132.jpg"/>intra circulum per &longs;ecundam præallegatam caderet, quod e&longs;t ab&longs;urdum, <lb/>

quia contra hypothe&longs;im, cum &longs;upponamus illam &longs;olùm tangere, non autem <lb/>

&longs;ecare circulum. </s>

<s id="id.002245">Ex hac Euclidis doctrina Theodo&longs;ius primo &longs;phæricorum, <lb/>

propo&longs;itione 3. probat planum, &longs;iue &longs;uperficiem planam tangere &longs;phæram <lb/>

in vnico puncto, vt hoc loco innuit Philo&longs;ophus. </s>

<s id="id.002246">probat autem hac ferè ra<lb/>

tione. </s>

<s id="id.002247">&longs;it &longs;phæra A B C, quæ tangat quodpiam planum <lb/>

in duobus punctis A, B, &longs;i fieri pote&longs;t. </s>

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ne circuli, quæ huc &longs;pectant. </s>

<s id="id.002260">propterea nunc tantum propria huius loci <expan abbr="de-clarãda">de<lb/>

claranda</expan> re&longs;tant. </s>

<s id="id.002261">loquitur igitur hic Philo&longs;ophus non de quadratione circuli,<pb xlink:href="009/01/133.jpg" pagenum="133" />&longs;ed figuræ rectilineæ illius, quæ dicitur Altera parte longior, qualis e&longs;t præ<lb/>

<s id="id.002261">loquitur igitur hic Philo&longs;ophus non de quadratione circuli,<pb pagenum="133" xlink:href="009/01/133.jpg"/>&longs;ed figuræ rectilineæ illius, quæ dicitur Altera parte longior, qualis e&longs;t præ<lb/>

&longs;ens figura A B C D, cuius quadrandæ ratio e&longs;t huiu&longs;modi. </s>

niatur recta linea media proportionalis inter <lb/>

duo latera figuræ A B, B C, <expan abbr="ea&qacute;">eaque</expan>; &longs;it B D, in &longs;e<lb/>

quenti figura. </s>

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<s id="id.002264">quadratum autem li<lb/>

neæ B D, æquale e&longs;t rectangulo dato A B C D, per 17.6. Inuentio porrò hu<lb/>

ius mediæ proportionalis, quia facilis e&longs;t, & &longs;citu iucunda, eam &longs;ic habeto. <lb/>

accipe duo latera A B, & B C, <expan abbr="quadrãdi">quadrandi</expan> rectan<lb/>

guli, <expan abbr="ea&qacute;">eaque</expan>; in directum con&longs;titue, vt vnicam re<lb/>

ctam con&longs;tituant A C, vt apparet in figura; de<lb/>

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latera A B, B D, quam nimirum habitudinem habet A B, ad B D, eam quo<lb/>

que obtinet B D, ad B C. </s>

<s id="id.002265">Quadratum igitur huius B D, hoc e&longs;t quadratum, <lb/>cuius quatuor latera &longs;int æqualia lineæ B D, quale e&longs;t præ&longs;ens, æquale erit <lb/>

dato &longs;uperiori rectangulo A B C D, <expan abbr="atq;">atque</expan> hoc modo per<lb/>

acta erit quadratio, &longs;eu tetragoni&longs;mus dati quadrilateri <lb/>

A B C D. </s>

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<s id="id.002273">Verum occurrit illa dubitatio; quod cum Ari&longs;t. ibi dicat <lb/>

<emph type="italics"/>(Vox acuta quidem velox)<emph.end type="italics"/> hic autem <emph type="italics"/>(Non igitur velox e&longs;t acutum<emph.end type="italics"/>) repugnan<lb/>

tia dicere videtur. </s>

<s id="id.002274">cui dubitationi &longs;ic occurrendum; vt dicamus ibi Philo<lb/>&longs;ophum dicere vocem acutam e&longs;&longs;e velocem, quatenus acumen vocis oritur <pb xlink:href="009/01/134.jpg" pagenum="134" />ex velocitate motus aerem impellentis. </s>

<s id="id.002274">cui dubitationi &longs;ic occurrendum; vt dicamus ibi Philo<lb/>&longs;ophum dicere vocem acutam e&longs;&longs;e velocem, quatenus acumen vocis oritur <pb pagenum="134" xlink:href="009/01/134.jpg"/>ex velocitate motus aerem impellentis. </s>

<s id="id.002275">hic verò di&longs;tinguere acutum à ve<lb/>

loci, tanquam effectum à cau&longs;a.</s>

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<s id="id.002302">ex quibus <lb/>

&longs;en&longs;us verberum Ari&longs;t. manife&longs;tus e&longs;t.</s>

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<s id="id.002305">Eodem cap. <emph type="italics"/>(Velut Diapa&longs;on, & Diapente)<emph.end type="italics"/> quid &longs;it con&longs;onantia Diapa<lb/>

&longs;on, explicaui in primo Po&longs;ter. tex. 1. Diapente verò e&longs;t con&longs;onantia ex duo<lb/>

bus &longs;onis coale&longs;cens, quorum proportio &longs;it vt <lb/>

3. ad 2. quæ dicitur &longs;e&longs;quialtera. </s>

<s id="id.002306">v. g. &longs;int duæ <lb/>chordæ æqualis cra&longs;&longs;itiei, <expan abbr="atq;">atque</expan> æquè ten&longs;æ: vna <lb/>

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pellimus, ita vt oculi propterea varient &longs;itum re&longs;pectu obiecti, &longs;iue non eo

<pb xlink:href="009/01/136.jpg" pagenum="136" />dem &longs;itu vterque obiectum intueatur, hoc e&longs;t, vt optici aiunt, axes vi&longs;uales <lb/>

<pb pagenum="136" xlink:href="009/01/136.jpg"/>dem &longs;itu vterque obiectum intueatur, hoc e&longs;t, vt optici aiunt, axes vi&longs;uales <lb/>

non amplius concurrunt &longs;imul in rem vi&longs;am. </s>

<s id="id.002330">Vnde &longs;equitur &longs;peciem rei in<lb/>

tentionalem oculis vario &longs;itu affectis imprimi, ac proinde eam eundem &longs;i<lb/>

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Problem. 7. &longs;ectionis 31.</s>

</chap>

<chap>

<s id="id.002334">EX PRIMO <lb/>

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detur minimum, &longs;eu indiui&longs;ibile, videtur enim omne diui&longs;ibile po&longs;&longs;e men&longs;u

<s id="id.002352">po&longs;tea tamen cum in Geometria ver&longs;atus fuerit, maximè admirare<lb/>

tur, &longs;i audiret diametrum e&longs;&longs;e lateri commen&longs;urabilem.</s>

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<s id="id.002376">Mu&longs;ica practica, qua quotidie ip&longs;i oblecta

<pb xlink:href="009/01/139.jpg" pagenum="139" />mur; <expan abbr="Deo&qacute;">Deoque</expan>; Optimo Maximo laudes debitas concinimus. </s>

<pb pagenum="139" xlink:href="009/01/139.jpg"/>mur; <expan abbr="Deo&qacute;">Deoque</expan>; Optimo Maximo laudes debitas concinimus. </s>

<s id="id.002377">Mechanica pra<lb/>

ctica, cuius ope ingentia pondera, vel exigua vi, <expan abbr="inuita&qacute;">inuitaque</expan>; natura &longs;u&longs;q; <expan abbr="de&qacute;">deque</expan>; <lb/>

commouentur. </s>

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&longs;urabilitate tractata &longs;unt.</s>

</chap>

<chap>

<s id="id.002401"><emph type="italics"/>Ex Quinto Metaphy&longs;icæ.<emph.end type="italics"/></s>

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<s id="id.002420">Tex. 3. (<emph type="italics"/>Et ip&longs;ius Diapa&longs;on duplum, & numerus<emph.end type="italics"/>) &longs;cilicet cau&longs;æ formales <lb/>

&longs;unt, quemadmodum &longs;upra tex. 2. huius cap. explicatum e&longs;t.</s>

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<s id="id.002431">Tex. 17. <emph type="italics"/>(Veluti diametrum commen&longs;urabilem e&longs;&longs;e impo&longs;&longs;ibile est)<emph.end type="italics"/> huius expo<lb/>

&longs;itionem inuenies 1. Priorum, &longs;ecto 1. cap. 23.</s>

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<s id="id.002454">Tex. 20. (<emph type="italics"/>De&longs;criptiones <expan abbr="quoq;">quoque</expan> actu inueniuntur, diuidentes nanque <lb/>inuenirent, quod &longs;i diui&longs;æ e&longs;&longs;ent, manife&longs;iè e&longs;&longs;ent, nunc autem in&longs;unt potentia, cur <lb/>

triangulus duo recti? </s>

<s id="id.002455">quia qui circa vnum punctum anguli duobus rectis æquales<emph.end type="italics"/> <pb xlink:href="009/01/142.jpg" pagenum="142" /><emph type="italics"/>&longs;unt, &longs;i igitur quæ ad latus educeretur, videnti mox e&longs;&longs;et manife&longs;tum<emph.end type="italics"/>) per de&longs;cri<lb/>

<s id="id.002455">quia qui circa vnum punctum anguli duobus rectis æquales<emph.end type="italics"/> <pb pagenum="142" xlink:href="009/01/142.jpg"/><emph type="italics"/>&longs;unt, &longs;i igitur quæ ad latus educeretur, videnti mox e&longs;&longs;et manife&longs;tum<emph.end type="italics"/>) per de&longs;cri<lb/>

ptiones, vel figurationes, vel de&longs;ignationes intelligendas e&longs;&longs;e demon&longs;tra<lb/>

tiones Geometricas &longs;æpius &longs;upra dictum e&longs;t, & pariter ex hoc loco com<lb/>

probatur. </s>

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con&longs;cripta &longs;unt (<emph type="italics"/>Cur triangulus duo recti?<emph.end type="italics"/>) ide&longs;t, cur triangulus habet tres <lb/>

angulos æquales duobus rectis angulis (<emph type="italics"/>Quia qui circa vnum punctum anguli <lb/>

duobus rectis angulis æquales &longs;unt<emph.end type="italics"/>) ni&longs;i hoc dictum ad bonum trahatur &longs;en&longs;um, <lb/>

fal&longs;um e&longs;t, nam omnes anguli, qui circa vnum <lb/>

punctum, v. g. A, &longs;unt con&longs;tituti, æquales &longs;unt <lb/>

non duobus, vt e&longs;t in textu, &longs;ed quatuor rectis, <lb/>

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etiam patere pote&longs;t ex corollario 2. 15. eiu&longs;dem. </s>

<s id="id.002457">tales &longs;unt quatuor anguli <lb/>

ad &longs;uperiores partes lineæ B C, & ad punctum A, con&longs;tituti, qui, vt patet, <lb/>

&longs;unt æquales duobus rectis B A D, D A C, <lb/>

tales etiam &longs;unt in hac &longs;ecunda figura tres <lb/>

anguli B C A, A C D, D C E, qui quidem <lb/>

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<s id="id.002464">quia &longs;i tres æquales, & quæ <lb/>

ba&longs;is e&longs;t duo, & quæ ex medio &longs;upra stat recta, videnti manifestum erit ei, qui illud <lb/>

&longs;ciat<emph.end type="italics"/>) In 2. Po&longs;ter. tex. 11. inuenies huius loci expo&longs;itionem. </s>

<s id="id.002465">nunc &longs;olùm <pb xlink:href="009/01/143.jpg" pagenum="143" /><figure id="id.009.01.143.1.jpg" xlink:href="009/01/143/1.jpg" place="text"/><lb/>

<s id="id.002465">nunc &longs;olùm <pb pagenum="143" xlink:href="009/01/143.jpg"/><figure id="id.009.01.143.1.jpg" place="text" xlink:href="009/01/143/1.jpg"/><lb/>

hæc addenda &longs;unt. </s>

<s id="id.002466">Re&longs;pondet Ari&longs;t. quæ<lb/>

&longs;ito pr&etail;cedenti, cur &longs;cilicet angulus in &longs;e<lb/>

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nimum enim tempus hic habet. </s>

<s id="id.002485">quapropter in A&longs;trologia tale vn&ubreve; prin<lb/>

cipium, & men&longs;ura e&longs;t. </s>

<s id="id.002486">motum enim æqualem, & veloci&longs;&longs;im&ubreve; c&oelig;li &longs;up<lb/>ponunt, ad quem cæteros iudicant<emph.end type="italics"/>) intelligit motum diurnum, quam <lb/>primo c&oelig;lo, &longs;eu mobili a&longs;cribunt, hic enim veloci&longs;&longs;imus e&longs;t omnium reli<pb xlink:href="009/01/144.jpg" pagenum="144" />quorum c&oelig;le&longs;tium motuum, ac &longs;implici&longs;&longs;imus, & valdè vniformis, ac regu<lb/>

<s id="id.002486">motum enim æqualem, & veloci&longs;&longs;im&ubreve; c&oelig;li &longs;up<lb/>ponunt, ad quem cæteros iudicant<emph.end type="italics"/>) intelligit motum diurnum, quam <lb/>primo c&oelig;lo, &longs;eu mobili a&longs;cribunt, hic enim veloci&longs;&longs;imus e&longs;t omnium reli<pb pagenum="144" xlink:href="009/01/144.jpg"/>quorum c&oelig;le&longs;tium motuum, ac &longs;implici&longs;&longs;imus, & valdè vniformis, ac regu<lb/>

laris, & propterea minimum habet tempus, ide&longs;t tempus vnius diei natura<lb/>

lis, quo tempore totum primum mobile circulationem integram perficit. <lb/>

</s>

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<s id="id.002509">duæ ctiam, exempli gratia, lineæ rectæ &longs;unt inuicem &longs;imiles, quamuis vna <lb/>

&longs;it maior altera.</s>

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<s id="id.002537">Ex &longs;ententia tamen Tychonis Brahe hos or<lb/>

bes, ac circulos tanquam ab inuicem di&longs;tinctos abrogare debemus.</s>

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per paraphra&longs;im &longs;ic explico; Calippus igitur eundem quidem ordinem, at<lb/>

que di&longs;tantiam &longs;phærarum cum Eudoxo ponebat: <expan abbr="eandem&qacute;">eandemque</expan>; pluralitatem <lb/>orbium mouentium Saturnum, ac Iouem; quatuor <expan abbr="nimir&utilde;">nimirum</expan> <expan abbr="vnicuiq;">vnicuique</expan> eorum. <lb/>

</s>

<s id="id.002565">&longs;ed putabat &longs;oli duas addendas, ac Lunæ &longs;imiliter, &longs;i quis eorum <expan abbr="appar&etilde;tias">apparentias</expan> <pb xlink:href="009/01/147.jpg" pagenum="147" />&longs;aluare vellet. </s>

<s id="id.002565">&longs;ed putabat &longs;oli duas addendas, ac Lunæ &longs;imiliter, &longs;i quis eorum <expan abbr="appar&etilde;tias">apparentias</expan> <pb pagenum="147" xlink:href="009/01/147.jpg"/>&longs;aluare vellet. </s>

<s id="id.002566">cæteris verò errantium, Marti, Veneri, & Mercurio <expan abbr="vnicuiq;">vnicuique</expan> <lb/>

vnam. </s>

<s id="id.002567">nece&longs;&longs;e præterea exi&longs;timabat e&longs;&longs;e, vt prædictæ omnes &longs;phæræ &longs;imul <lb/>

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carum commendationem, ac defen&longs;ionem apponere, cum non de&longs;int hac <lb/>no&longs;tra tempe&longs;tate ageometreti complures, qui cas libenter &longs;ugillare &longs;olent.</s>

</chap>

<chap>

<s id="id.002583"><emph type="italics"/>IN MECHANICAS QVÆSTIONES.<emph.end type="italics"/></s>

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tiæ huius naturam per&longs;pectam <lb/>

haberemus.</s>

<s id="id.002600">De dignitatibus, <expan abbr="admirandis&qacute;">admirandisque</expan>; Circuli proprietatibus.</s>

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<s id="id.002618">Præter prædicta aliud tandem mirum ip&longs;i ine&longs;t, quia nimirum cum innu<lb/>

mera &longs;int puncta in vna <expan abbr="eadem&qacute;">eademque</expan>; linea, quæ &longs;emidiameter e&longs;t, omnia tamen <pb xlink:href="009/01/150.jpg" pagenum="150" />quando &longs;emidiameter circa centrum mouetur, quamuis cum ip&longs;a mouean<lb/>tur, inæquali velocitate mouentur; Nam punctum illud &longs;emper velocius <lb/>

mera &longs;int puncta in vna <expan abbr="eadem&qacute;">eademque</expan>; linea, quæ &longs;emidiameter e&longs;t, omnia tamen <pb pagenum="150" xlink:href="009/01/150.jpg"/>quando &longs;emidiameter circa centrum mouetur, quamuis cum ip&longs;a mouean<lb/>tur, inæquali velocitate mouentur; Nam punctum illud &longs;emper velocius <lb/>

mouetur, quod remotius e&longs;t à centro circuli, &longs;eu à manente &longs;emidiametri <lb/>

termino, & proinde illud tardius, quod centro proximius e&longs;t. </s>

<s id="id.002619"><expan abbr="Atq;">Atque</expan> ex hac <lb/>

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<s id="id.002620">Quoniam autem &longs;ecundum contrarias &longs;imul motiones mouetur circulus, <lb/>

& alterum quidem diametri extremum vbi A, in figura præ&longs;enti antror&longs;um <lb/>

mouetur; alterum verò vbi B, retror<lb/>

&longs;um, efficiunt nonnulli, vt ab vnica mo<lb/>

tione multi contrariò &longs;imul mouean<lb/>

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tu feratur ver&longs;us C. quod fiet &longs;i cogitemus latus A B, <expan abbr="de&longs;c&etilde;dere">de&longs;cendere</expan> ver&longs;us M C,

<pb xlink:href="009/01/151.jpg" pagenum="151" /><figure id="id.009.01.151.1.jpg" xlink:href="009/01/151/1.jpg" place="text"/><lb/>ip&longs;i æquidi&longs;tanter, dum punctum A, mouetur <lb/>

<pb pagenum="151" xlink:href="009/01/151.jpg"/><figure id="id.009.01.151.1.jpg" place="text" xlink:href="009/01/151/1.jpg"/><lb/>ip&longs;i æquidi&longs;tanter, dum punctum A, mouetur <lb/>

ad B. his duabus lationibus A, latum. </s>

<s id="id.002629">nece&longs;&longs;a<lb/>riò motu mixto progredietur per diametrum <lb/>

A M, quod &longs;ic probari pote&longs;t; &longs;it iam A, mo<lb/>

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extremo circumagitur, duabus &longs;imul feratur lationibus, ex quibus motus <lb/>

orbicularis oriatur, manife&longs;tum e&longs;t ex &longs;uperioribus, quia & antror&longs;um, & <lb/>

retror&longs;um impellitur; tùm etiam, quia &longs;i rectà tenderet recta <expan abbr="de&longs;crib&etilde;s">de&longs;cribens</expan> cir<lb/>

culum, nunquam ad diametri perpendiculum <lb/>

perueniret, &longs;ed tamen peruenit, ita vt &longs;it ip&longs;a <lb/>

à centro perpendicularis diametro. </s>

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ad C. &longs;i igitur B, feretur duabus lationibus <lb/>

aliquo modo proportionatis, v. g. vt e&longs;t pro<lb/>

portio lateris B E, ad E C, latus, &longs;equeretur <lb/>

ex demon&longs;tratis ip&longs;um B, ferri per <expan abbr="rectã">rectam</expan> B C, <lb/>quæ diameter e&longs;&longs;et quadrilateri B E C G. &longs;ed <pb xlink:href="009/01/152.jpg" pagenum="152" />quia in nulla proportione fertur, propterea per circularem lineam B E C, <lb/>

ex demon&longs;tratis ip&longs;um B, ferri per <expan abbr="rectã">rectam</expan> B C, <lb/>quæ diameter e&longs;&longs;et quadrilateri B E C G. &longs;ed <pb pagenum="152" xlink:href="009/01/152.jpg"/>quia in nulla proportione fertur, propterea per circularem lineam B E C, <lb/>

progreditur ad C, ita vt ip&longs;a diameter B D, in po&longs;itione A C, fiat perpendi<lb/>

cularis priori diametro B D. ex quibus &longs;equitur eam moueri duobus moti<lb/>

bus nullam rationem habentibus; quod erat intentum.</s>

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uer&longs;um agitur, &longs;eu &longs;ecus centrum, ob quam cogitur in gyrum duci, minor <lb/>

autem linea &longs;ecundum hanc motionem innaturalem plus fertur, quàm ma<lb/>

ior, ide&longs;t plus ip&longs;ius progre&longs;&longs;io inflectitur in orbem; quia enim e&longs;t centro <lb/>

vicinior, quod quodammodo retra<lb/>

hit à motu naturali, propterea ma<lb/>

gis vincitur, quàm remotior. </s>

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de&longs;cribit circulum maiorem, reuer<lb/>

titur tandem ad locum B A, vnde di<lb/>

gre&longs;&longs;a e&longs;t. </s>

<s id="id.002646">&longs;imiliter M A, circumuoluta <pb xlink:href="009/01/153.jpg" pagenum="153" />redibit ad priorem po&longs;itionem in M A. </s>

<s id="id.002646">&longs;imiliter M A, circumuoluta <pb pagenum="153" xlink:href="009/01/153.jpg"/>redibit ad priorem po&longs;itionem in M A. </s>

<s id="id.002647">Tardius autem fertur M A, quàm <lb/>

B A, vt dictum e&longs;t, quia maior illi fit retractio à recta progre&longs;&longs;ione. </s>

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&longs;ophum &longs;pectet.</s>

<s id="id.002658">Mihi tamen maximè con&longs;iderandum videtur hoc ip&longs;um quod a&longs;&longs;eruit, & <pb xlink:href="009/01/154.jpg" pagenum="154" />ex &longs;e patet, remotiores &longs;cilicet partes diametrorum à centro velocius mo<lb/>

<s id="id.002658">Mihi tamen maximè con&longs;iderandum videtur hoc ip&longs;um quod a&longs;&longs;eruit, & <pb pagenum="154" xlink:href="009/01/154.jpg"/>ex &longs;e patet, remotiores &longs;cilicet partes diametrorum à centro velocius mo<lb/>

ueri, quàm viciniores; ex hac enim maiori velocitate &longs;equitur maiore etiam <lb/>

vi moueri, vnde & potentiæ mouenti in extremo eius vis augebitur, & plus <lb/>

poterit quam &longs;ola &longs;ine vecte, e&longs;t enim vectis duæ &longs;emidiametri altera alte<lb/>

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bræ de&longs;cribitur quidam circulus, cuius diameter &longs;unt ip&longs;a libræ <lb/>

brachia, centrum verò e&longs;t fpartum, &longs;iue trutina; hoc enim pun<lb/>

ctum in motu libræ manet: duo verò brachia &longs;unt veluti duæ &longs;emidiametri <lb/>

à centro exeuntes, vt in figura cerne<lb/>

re e&longs;t, in qua centrum, &longs;iue &longs;partum <lb/>

e&longs;t vbi C, reliqua &longs;unt manife&longs;ta. </s>

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<s id="id.002672"><expan abbr="Atq;">Atque</expan> hæc e&longs;t huius pri<lb/>

mæ quæ&longs;tionis paraphra&longs;is.</s>

<s id="id.002673"><emph type="italics"/>QVÆSTIO SECVNDA<emph.end type="italics"/></s>

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te plus libræ extra perpendiculum fit, &longs;partum enim e&longs;t perpendiculum, <lb/>

quare nece&longs;&longs;e est deor&longs;um ferri id, quod plus est, donec a&longs;cendat, quæ bifariam li<lb/>

bram diuidit ad ip&longs;um perpendicul&ubreve;, cum onus incumbat ad libræ partem tractam.<emph.end type="italics"/><lb/>

<emph type="italics"/>&longs;it libra vbi recta B C, &longs;partum autem <lb/>

A D: hoc igitur &longs;ur&longs;um erecto, perpendi<lb/>

culum erit vbi A D M. &longs;i igitur in ip&longs;o B, <lb/>

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<s id="id.002681">&longs;i autem deor&longs;um fuerit, id quod &longs;ub<lb/>

stat, contrarium facit; plus enim dimidio fit libræ, quæ deor&longs;um e&longs;t, pars, quàm <lb/>

quod perpendiculum &longs;ecet; quapropter non a&longs;cendit, pars enim eleuata leuior e&longs;t.<emph.end type="italics"/><lb/>

<emph type="italics"/>&longs;it libra vbi N G, perpendiculum autem <lb/>

K L M, bifariam igitur &longs;ecatur N G. im<lb/>

po&longs;ito autem onere in ip&longs;o N, erit quidem <lb/>

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quæ&longs;tionis e&longs;t a&longs;&longs;ecutus, eam tibi ex Mechanicis Guidibaldi tradam. </s>

<s id="id.002686">Ari&longs;t. <lb/>

igitur ponit duas libræ &longs;pecies, &longs;iue potius duas eiu&longs;dem libræ po&longs;itiones, <lb/>vnam, quæ habet &longs;partum, &longs;iue perpendiculum &longs;upra; alteram, quæ infra. <lb/>

vt in præ&longs;enti figura, &longs;it libra B C, cuius <lb/>

&longs;partum, &longs;iue perpendiculum A D, &longs;it &longs;ur<lb/>

&longs;um, ita vt in puncto A, &longs;it affixum perpen<lb/>

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&longs;iue perpendiculum A D, &longs;it deor&longs;um, vt in altera figura, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; circa pun

ctum A, tanquam circa <expan abbr="centr&utilde;">centrum</expan>, aut axem <lb/>

ita fixum, vt ip&longs;i libræ conuer&longs;io innita<lb/>

tur, quæ e&longs;t altera libræ po&longs;itio. </s>

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M, quæ maior pars e&longs;t D D H.</s>

<s id="id.002698">Si igitur nunc onus amoueatur libræ E H, centrum grauitatis, quod e&longs;t <pb xlink:href="009/01/157.jpg" pagenum="157" />ad D, remanet vltra priorem Directionis lineam; & quia pondus non am<lb/>

<s id="id.002698">Si igitur nunc onus amoueatur libræ E H, centrum grauitatis, quod e&longs;t <pb pagenum="157" xlink:href="009/01/157.jpg"/>ad D, remanet vltra priorem Directionis lineam; & quia pondus non am<lb/>

plius illi æ que ponderat, grauitabit, & quia libra cùm affixa &longs;it ad A, nequit <lb/>

deor&longs;um recta tendere, circumferretur circa A, trahente ip&longs;am grauitatis <lb/>

centro, cum nihil ob&longs;it, donec iterum perpendiculum A D G, priori &longs;itui <lb/>

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<s id="id.002713">Vectis porrò e&longs;t in&longs;trumentum oblongum, quo ad &longs;ubleuandum graue <lb/>

quodpiam vtuntur opifices, quod innititur cuidam fulcimento, quod græcè <lb/>hypomoclion dicitur: hypomoclion autem oneri leuando, quantum fieri <pb xlink:href="009/01/158.jpg" pagenum="158" />pote&longs;t proximum e&longs;&longs;e debet, vt vectis pars longior &longs;it ad partes potentiæ <lb/>

quodpiam vtuntur opifices, quod innititur cuidam fulcimento, quod græcè <lb/>hypomoclion dicitur: hypomoclion autem oneri leuando, quantum fieri <pb pagenum="158" xlink:href="009/01/158.jpg"/>pote&longs;t proximum e&longs;&longs;e debet, vt vectis pars longior &longs;it ad partes potentiæ <lb/>

mouentis. </s>

<s id="id.002714">vt plurimum verò fulcimentum e&longs;t inter pondus, & potentiam: <lb/>

aliquando etiam e&longs;t ex altero vectis extremo, ita vt onus &longs;it inter fulturam, <lb/>

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cies exi&longs;tunt. </s>

<s id="id.002715">vt in &longs;ubiectis figuris apparet. </s>

<s id="id.002716">In prima, vectis e&longs;t A B, fultu<lb/>

ra E, onus C. potentia autem &longs;eu vis, <lb/>

&longs;eu aliud pondus <expan abbr="mou&etilde;s">mouens</expan> &longs;it vbi D. quæ <lb/>

deor&longs;um in D, præmens eleuabit &longs;ur<lb/>

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<s id="id.002726">In hac quæ&longs;tione re&longs;pexit Ari&longs;t. &longs;olùm ad primam vectis &longs;peciem. </s>

<s id="id.002727">Illud <lb/>

demum, quod dixit eandem habere rationem potentiam ad pondus, quàm <lb/>partes vectis inuicem demon&longs;tratum e&longs;t po&longs;tea acuti&longs;&longs;imè ab Archimede <pb xlink:href="009/01/159.jpg" pagenum="159" />propo&longs;itione 6. & 7. de æqueponderantibus: & no&longs;tra <expan abbr="t&etilde;pe&longs;tate">tempe&longs;tate</expan> alio quam<lb/>

demum, quod dixit eandem habere rationem potentiam ad pondus, quàm <lb/>partes vectis inuicem demon&longs;tratum e&longs;t po&longs;tea acuti&longs;&longs;imè ab Archimede <pb pagenum="159" xlink:href="009/01/159.jpg"/>propo&longs;itione 6. & 7. de æqueponderantibus: & no&longs;tra <expan abbr="t&etilde;pe&longs;tate">tempe&longs;tate</expan> alio quam<lb/>

uis modo, & vnica demon&longs;tratione à Guido Vbaldo in &longs;uis Mechanicis pro<lb/>

po&longs;itione 1. de Vecte, quæ e&longs;t huiu&longs;modi; Potentia &longs;u&longs;tinens pondus vecti <lb/>

appen&longs;um, eandem ad ip&longs;um pondus proportionem habet, quam vectis di<lb/>

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tas, atque prolixitas &longs;olutionis manauit. </s>

<s id="id.002743">E&longs;t enim propriè Temo, &longs;iue gu<lb/>

bernaculum nauis, vectis &longs;ecundi generis, vt mox explicabo, e&longs;t enim temo <lb/>

in&longs;trumentum in extrema nanis par<lb/>te, &longs;eu puppi affixum, vt in figura pre<lb/>

&longs;enti vides tabellam, in qua B C D, <lb/>

cuius manubrium A B, intra nauim <lb/>

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ta A B, e&longs;t ip&longs;a Vectis longitudo, cuius hypomoclion e&longs;t mare, cui contra

<pb xlink:href="009/01/160.jpg" pagenum="160" />nititur tabella B E; onus autem e&longs;t puppis, quod onus præ&longs;ertim in cardini<lb/>

<pb pagenum="160" xlink:href="009/01/160.jpg"/>nititur tabella B E; onus autem e&longs;t puppis, quod onus præ&longs;ertim in cardini<lb/>

bus C D, mouenti re&longs;i&longs;tit, & quod præcipuè mouere gubernator intendit. <lb/>

</s>

<s id="id.002745">cum igitur motum onus &longs;it intra vectis extrema, hypomoclion in extremo <lb/>

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uis priorem æqua velocitate con&longs;equatur, non tamen tanto impetu, cum ip<lb/>&longs;a ad alterius impetum moueatur, & propterea latio ip&longs;ius e&longs;t admodum <lb/>

imbecillis.</s>

<s id="id.002757">Si quis &longs;agittam per aerem latam à &longs;uo motu vellet deflectere, eam faci<lb/>

lius in po&longs;teriore parte à &longs;uo cur&longs;u deuiaret, quàm in anteriore. </s>

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eiu&longs;dem rationem, quia nimirum parua motione facta in puppi multo ma<lb/>

ius interuallum cogitur mutare prora; nam idem angulus, quo eius lineæ <lb/>

&longs;unt longiores, eò maiorem &longs;ubten&longs;am &longs;ibi lineam re&longs;picit, quod facilè in <lb/>

ad&longs;cripta figura intueri licet; in qua duæ <lb/>

lineæ A B, A C, continent angulum A, cui <lb/>

angulo &longs;ubtenduntur tres lineæ parallelæ <lb/>

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tem triangula &longs;unt ea, quorum anguli vnius &longs;unt æquales angulis alterius, <lb/>

quo po&longs;ito &longs;unt etiam latera vnius proportionalia lateribus alterius, vt pa<lb/>

tet ex prima definitione 6. necnon ex quarta eiu&longs;dem demon&longs;tratione. </s>

quidem duo triangula &longs;unt &longs;imi<lb/>

lia, & rectè concluditur F Y, mi<lb/>

nus e&longs;&longs;e quàm D Y, &longs;ed tamen <lb/>

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auctor remi palmulam retrocedere, quoties nauigium in anteriora progre

<pb xlink:href="009/01/163.jpg" pagenum="163" />ditur, <expan abbr="locum&qacute;">locumque</expan>; &longs;calmi, &longs;uper quo circulari motu remus vertitur, in medio <lb/>

<pb pagenum="163" xlink:href="009/01/163.jpg"/>ditur, <expan abbr="locum&qacute;">locumque</expan>; &longs;calmi, &longs;uper quo circulari motu remus vertitur, in medio <lb/>

ip&longs;ius remi po&longs;itum e&longs;&longs;e, vt &longs;cilicet tantum di&longs;tet à manubrio, quantum à <lb/>

palmula. </s>

<s id="id.002789">Duæ <expan abbr="itaq;">itaque</expan> rectæ lineæ ponantur æquales A B, & D E, quæ quidem <lb/>

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<expan abbr="&longs;it&qacute;">&longs;itque</expan>; A, manubrium; B, palmula; C, verò &longs;ealmus. </s>

<s id="id.002790">Cum igitur A, remi ca<lb/>

put in fine ip&longs;ius remigationis eò tran&longs;latum fuerit D, non erit B, vbi E; &longs;i <lb/>

enim ibi fuerit; remus igitur po&longs;itionem <lb/>

habebit rectam lineam D E; & quoniam <lb/>

contrapo&longs;iti anguli, qui ad C, æquales &longs;unt, <lb/>

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trianguli B T Z, latere T Z, maius erit: tota igitur recta linea A B, tota <lb/>

D Z, maior erit: & idcircò cum remus po&longs;itionem habuerit rectam lineam <lb/>

D Z palmula erit vltra Z. </s>

<s id="id.002802">E&longs;to igitur in K, & connectantur rectæ lineæ B D, <lb/>& B K: &longs;patium igitur decur&longs;um ab ip&longs;a palmula non erit B Z, &longs;ed B K: quod <pb xlink:href="009/01/164.jpg" pagenum="164" />quidem minus etiam o&longs;tendemus e&longs;&longs;e ip&longs;o D A. </s>

<s id="id.002802">E&longs;to igitur in K, & connectantur rectæ lineæ B D, <lb/>& B K: &longs;patium igitur decur&longs;um ab ip&longs;a palmula non erit B Z, &longs;ed B K: quod <pb pagenum="164" xlink:href="009/01/164.jpg"/>quidem minus etiam o&longs;tendemus e&longs;&longs;e ip&longs;o D A. </s>

<s id="id.002803">Nam quoniam duo latera <lb/>

B D, & D K, trianguli B D K, duobus lateribus B D, & D E, <expan abbr="triãguli">trianguli</expan> B E D, <lb/>æqualia &longs;unt, &longs;ed minor e&longs;t angulus B D K, angulo B D E: minor igitur erit <lb/>

ba&longs;is B K, ba&longs;e B E, per 24. primi, quod demon&longs;trandum erat</s>

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<s id="id.002812">Sit enim remus A C, manubrium A, &longs;calmus B, qui propter nauigij <lb/>motum &longs;patium percurrat à B, in D, in quo loco ip&longs;e remus A C, &longs;i<lb/>

tum rectitudinis habeat E F. </s>

<s id="id.002813">Spatium <lb/>itaque, quod A, conficit, curua linea <lb/>

&longs;it A E, cui recta linea re&longs;pondeat A Z, in re<lb/>ctam E F, perpendicularis. </s>

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manubrij de&longs;cripta e&longs;t; po&longs;terior verò æqualis e&longs;t rectæ B D, quæ motu na<lb/>

uigij decur&longs;a e&longs;t.</s>

<s id="id.002818"><emph type="italics"/>PROPOSITIO SECVNDA.<emph.end type="italics"/></s>

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&longs;patium igitur permeet C D, ad po&longs;teriora: quo quidem decur&longs;o, <lb/>remus A C, po&longs;itionem rectitudinis habeat F D, &longs;calmus <expan abbr="itaq;">itaque</expan> B, tran&longs;latus <lb/>

erit in G. </s>

<s id="id.002822">Excitetur autem à puncto B, in <expan abbr="vtramq;">vtramque</expan> partem linea E B R, ad <lb/>

rectos angulos &longs;uper B G, & à <expan abbr="p&utilde;cto">puncto</expan> A, recta A H, <lb/>

&longs;uper D F: itemque à puncto E, recta C E, &longs;uper <lb/>

E R; ip&longs;arum verò rectarum linearum E R, & <lb/>

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<s id="id.002827">Remus enim incipiente motu po&longs;itionem habeat A C, de&longs;inente <lb/>

verò rectitudinis &longs;itum F G. &longs;calmus igitur B, propter nauigij <lb/>motum, &longs;patium conficiet B D. </s>

<s id="id.002828">Excitetur à puncto B, in <expan abbr="vtramq;">vtramque</expan> <lb/>

partem perpendicularis E Z, in quam veniant a punctis A, & C, <lb/>ad rectos angulos rectæ lineæ A E, & C Z: &longs;patium autem A E, à manubrio <pb xlink:href="009/01/166.jpg" pagenum="166" /><figure id="id.009.01.166.1.jpg" xlink:href="009/01/166/1.jpg" place="text"/><lb/>

partem perpendicularis E Z, in quam veniant a punctis A, & C, <lb/>ad rectos angulos rectæ lineæ A E, & C Z: &longs;patium autem A E, à manubrio <pb pagenum="166" xlink:href="009/01/166.jpg"/><figure id="id.009.01.166.1.jpg" place="text" xlink:href="009/01/166/1.jpg"/><lb/>

decur&longs;um motu proprio &longs;patij B D, duplum <lb/>

&longs;it: recta verò linea C H, curuæ re&longs;pondeat <lb/>

C G, quæ à remi palmula de&longs;cripta e&longs;t. </s>

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maius &longs;patium decurrat, quàm nauigium, &longs;iue id &longs;it duplum, &longs;iue mi

<pb xlink:href="009/01/167.jpg" pagenum="167" />nus duplo, &longs;iue maius duplo, &longs;patium, quod nauigium interim decurrit ad <lb/>

<pb pagenum="167" xlink:href="009/01/167.jpg"/>nus duplo, &longs;iue maius duplo, &longs;patium, quod nauigium interim decurrit ad <lb/>

anteriora, & quod palmula remi in contrarium &longs;imul iuncta, ei quod ip&longs;um <lb/>

remi manubrium motu proprio conficit, æqualia erunt. </s>

<s id="id.002844">&longs;emper enim B D, <lb/>

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<s id="id.002850">Habeat enim remus incipiente motu po&longs;itionem A C: de&longs;inente <lb/>

verò <expan abbr="&longs;it&utilde;">&longs;itum</expan> rectitudinis F G. &longs;cal<lb/>

mus igitur B, propter nauigij <lb/>

motum tran&longs;latus, erit in D, &longs;it <lb/>

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ver&longs;us I, circa &longs;calmum. </s>

<s id="id.002855">Atqui per hypo<lb/>

the&longs;im celerius fertur nauigium, quam A. <lb/>

in H, celerius igitur ip&longs;um nauigium fer<lb/>tur, quàm C, ver&longs;us I. &longs;ed mouetur idem <pb xlink:href="009/01/168.jpg" pagenum="168" />C. ip&longs;a nauigij celeritate ver&longs;us K; celerius igitur ferretur C, ad K, quam <lb/>

in H, celerius igitur ip&longs;um nauigium fer<lb/>tur, quàm C, ver&longs;us I. &longs;ed mouetur idem <pb pagenum="168" xlink:href="009/01/168.jpg"/>C. ip&longs;a nauigij celeritate ver&longs;us K; celerius igitur ferretur C, ad K, quam <lb/>

ad I, quapropter nihil vnquam retrocedet ip&longs;um C, imò verò in vlteriora <lb/>

progredietur, <expan abbr="&longs;patium&qacute;">&longs;patiumque</expan>; decurret C K, quod quidem relinquitur detracto <lb/>

I C, ex I K. &longs;i enim remi palmula tota ip&longs;a nauigij celeritate moueretur, vl<lb/>

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potentia e&longs;t ventus, qui mouet in antenna F C G. quanto igitur &longs;ublimior <lb/>

e&longs;t antenna, tanto longior euadit vectis E C, <expan abbr="tanto&qacute;">tantoque</expan>; maiores fiunt venti <lb/>

vires. </s>

<s id="id.002877">dixi autem onus e&longs;&longs;e in D, quia &longs;i nauis vento ob&longs;i&longs;teret, ip&longs;a inuerte<lb/>retur hac ratione, vt puppis A, eleuata, prora B, demergeretur, manente <pb xlink:href="009/01/169.jpg" pagenum="169" /><figure id="id.009.01.169.1.jpg" xlink:href="009/01/169/1.jpg" place="text"/><lb/>

<s id="id.002877">dixi autem onus e&longs;&longs;e in D, quia &longs;i nauis vento ob&longs;i&longs;teret, ip&longs;a inuerte<lb/>retur hac ratione, vt puppis A, eleuata, prora B, demergeretur, manente <pb pagenum="169" xlink:href="009/01/169.jpg"/><figure id="id.009.01.169.1.jpg" place="text" xlink:href="009/01/169/1.jpg"/><lb/>

veluti centro parte E. quia ve<lb/>

rò ob maris liquiditatem na<lb/>uis minimè ob&longs;i&longs;tit, &longs;ed facilè <lb/>

cedens à ventis vrgetur, hinc <lb/>

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<s id="id.002889">Præterea circulares etiam, &longs;i cui obuiam fiunt corpori, illud &longs;imi<lb/>liter &longs;ecundum pu&longs;illum tangunt: rectilineæ verò figuræ, rectitudine &longs;ua <lb/>

plani multum contingerent. </s>

<s id="id.002890">Ad hæc motor mouens huiu&longs;modi rotas, eas <lb/>

mouet, quò nutant: nam quando rota erecta e&longs;t &longs;uper pauimentum, dia<lb/>meter ip&longs;ius, quæ à contactu pauimenti ad angulos rectos, ad &longs;upremum <pb xlink:href="009/01/170.jpg" pagenum="170" />rotæ perducitur totum rotæ pondus in duas æquas partes diuidit, ita vt ta<lb/>

mouet, quò nutant: nam quando rota erecta e&longs;t &longs;uper pauimentum, dia<lb/>meter ip&longs;ius, quæ à contactu pauimenti ad angulos rectos, ad &longs;upremum <pb pagenum="170" xlink:href="009/01/170.jpg"/>rotæ perducitur totum rotæ pondus in duas æquas partes diuidit, ita vt ta<lb/>

le pondus in æquilibrio con&longs;tituatur, cum ex vna parte tantum &longs;it, quantum <lb/>

ex altera; ex quo fit, vt vel exigua vis ip&longs;am impellere valeat: quando enim <lb/>

duo æqualia pondera &longs;unt in æquilibrio, quelibet vis pote&longs;t ea ab æquilibrio <lb/>

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motæ moueant cæteras intra &longs;e contentas. </s>

<s id="id.002895">quod dictum e&longs;t de nutu anguli <lb/>

maioris circuli ad angulum minoris ex appo&longs;ita figura facilè patebit, vbi <lb/>

pro minore angulo intelligendus e&longs;t arcus C B, <lb/>

pro maiore autem arcus D E, quorum <expan abbr="vterq;">vterque</expan> vo<lb/>

catur angulus, quoniam angulo A, qui e&longs;t in cen<lb/>

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<s id="id.002900">altera latio e&longs;t, &longs;ecundum quam cir

<pb xlink:href="009/01/171.jpg" pagenum="171" />culus à &longs;eip&longs;o &longs;ecundum diametrum mouetur, ide&longs;t circa &longs;uum centrum re<lb/>

<pb pagenum="171" xlink:href="009/01/171.jpg"/>culus à &longs;eip&longs;o &longs;ecundum diametrum mouetur, ide&longs;t circa &longs;uum centrum re<lb/>

trahit continuò extrema diametri; ne recta &longs;ecundum naturalem lationem <lb/>

ferantur, &longs;ed in orbem circulariter circa centrum gyrentur. </s>

<s id="id.002901">hæc Ari&longs;t. </s>

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e&longs;t ad libram vnam &longs;u&longs;tinendam, & non amplius. </s>

<s id="id.002912">vt autem clarè appareat <lb/>

vectis in trochlea, & hypomoclion, & æquales di&longs;tantiæ, &longs;it figura, in qua <lb/>

pondus D, ductario funi D C B E, alligatum. </s>

<s id="id.002913">poten<lb/>

tia <expan abbr="&longs;u&longs;tin&etilde;s">&longs;u&longs;tinens</expan> E. axis autem erit diameter rotulæ B A C, <lb/>

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<s id="id.002916">hæc & præ&longs;enti loco, & <lb/>

&longs;equentibus lucem afferre po&longs;&longs;unt.</s>

<s id="id.002917"><emph type="italics"/>QVÆSTIO NONA<emph.end type="italics"/></s>

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tam, & aliter complicatam Imperatori mittebant, re&longs;olutio autem mem

<pb xlink:href="009/01/173.jpg" pagenum="173" />branæ literas truncas, atque mutilas reddebat; cum partim continerentur <lb/>

<pb pagenum="173" xlink:href="009/01/173.jpg"/>branæ literas truncas, atque mutilas reddebat; cum partim continerentur <lb/>

citra iuncturas, partim vltra: eæquè partes, quæ &longs;imul fuerant &longs;criptæ, & <lb/>continuatæ, po&longs;t re&longs;olutionem erant ab inuicem valde di&longs;&longs;itæ. </s>

<s id="id.002936">quapropter <lb/>

Imperator commenti totius con&longs;cius, eandem membranam &longs;cytali alteri <lb/>

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vt Geometræ dicunt, Cylindrum; in cuius tamen extremitatibus e&longs;&longs;ent <lb/>

margines duo aliquantulum prominentes, ceu binæ rotæ, cum ip&longs;o tamen <lb/>

continuæ, & connexæ, vt cum ip&longs;o &longs;imul conuoluerentur; non tamen tan<lb/>

quam circa axem. </s>

<s id="id.002939">cuius hanc accipe fi<lb/>

guram. </s>

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<s id="id.002952">Contra quam re&longs;pon&longs;ionem &longs;ic fortè obijcies; in præcedenti enim quæ

<pb xlink:href="009/01/174.jpg" pagenum="174" />&longs;tione dictum e&longs;t ab Ari&longs;t. maiores trochleas, & &longs;cytalas, minoribus facilius <lb/>

<pb pagenum="174" xlink:href="009/01/174.jpg"/>&longs;tione dictum e&longs;t ab Ari&longs;t. maiores trochleas, & &longs;cytalas, minoribus facilius <lb/>

commoueri, hic autem dicit maiorem rotam difficilius quàm minorem mo<lb/>

ueri. </s>

<s id="id.002953">Hanc obiectionem Piccolomineus di&longs;&longs;imula&longs;&longs;e videtur, cui ego, inge<lb/>

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<s id="id.002969">Crediderim ego facilius portari magna onera per &longs;cytalas, propter ip&longs;a<lb/>

rum firmitatem, currus enim <expan abbr="ip&longs;orumq;">ip&longs;orumque</expan> rotæ &longs;unt multò debiliores, neque <lb/>

maioribus oneribus &longs;ufficiunt. </s>

<s id="id.002970">Concludit po&longs;tea quæ&longs;tionem dicens, quia <pb xlink:href="009/01/175.jpg" pagenum="175" />igitur &longs;cytalæ ab ip&longs;o onere non ita premuntur quin moueri melius po&longs;&longs;int <lb/>

<s id="id.002970">Concludit po&longs;tea quæ&longs;tionem dicens, quia <pb pagenum="175" xlink:href="009/01/175.jpg"/>igitur &longs;cytalæ ab ip&longs;o onere non ita premuntur quin moueri melius po&longs;&longs;int <lb/>

quàm currus, imò ab ip&longs;o onere iam commoto, ip&longs;æ quoque incitentur, & <lb/>

præterea à potentia per planum infernè, benè &longs;ub&longs;tratum, & complanatum <lb/>

trahantur, fit, vt qua&longs;i in duobus locis ip&longs;arum rotæ impellantur ab onere <lb/>

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<s id="id.002991">Ratio e&longs;t, quia collops, quemadmodum etiam iugum, reducitur ad vectem,

cuius hypomoclion e&longs;t in medio <lb/>

&longs;ucculæ, &longs;iue in axe ip&longs;ius &longs;ucculæ; <lb/>

potentia verò e&longs;t in &longs;ummitatibus <lb/>

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<s id="id.003012">In minori autem ligno, onus ligni in D,

fultura manus in E, potentia alterius ma<lb/>nus in F. iam inquit Ari&longs;t. maius lignum <lb/>

A B C, magis flectitur, quamuis cra&longs;&longs;ius <lb/>

&longs;it, quàm lignum D E F, quod e&longs;t tenuuius, <lb/>

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magna vi percutit, quia motus mouet, &longs;eu quia mouens malleum, mouet <lb/>

ip&longs;um etiam dum e&longs;t in ip&longs;a latione, vnde ip&longs;a lationis celeritate malleus <lb/>

fit valentior: <expan abbr="hoc&qacute;">hocque</expan>; modo paruos cunei vectes maiores con&longs;equuntur vires, <lb/>

quàm ip&longs;a vectium magnitudo po&longs;tulet. <lb/>

</s>

<s id="id.003024">&longs;it cuneus A B C. lignum autem &longs;cinden<lb/>

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vectem e&longs;t in malleo, dum &longs;uperius latus <lb/>

cunei A B, percutit. </s>

<s id="id.003026">alter huic auer&longs;us <lb/>

vectis e&longs;t latus A C, cuius fultura e&longs;t C, <lb/>eadem cum priori, onus propul&longs;atum D,<pb xlink:href="009/01/178.jpg" pagenum="178" />potentia cum altero communis e&longs;t in latere A B, à malleo validè percu&longs;&longs;o. <lb/>

vectis e&longs;t latus A C, cuius fultura e&longs;t C, <lb/>eadem cum priori, onus propul&longs;atum D,<pb pagenum="178" xlink:href="009/01/178.jpg"/>potentia cum altero communis e&longs;t in latere A B, à malleo validè percu&longs;&longs;o. <lb/>

</s>

<s id="id.003027">cunei igitur virtus partim ex vectibus, partim ex percu&longs;&longs;ione con&longs;tat.</s>

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<s id="id.003036">Auxilio huius in&longs;trumenti machinato<lb/>

res parua vi attollunt ingentia pondera. </s>

<s id="id.003037">communiter autem con&longs;tat ex plu<lb/>

ribus orbiculis, qui partim &longs;uperiori loculamento, <lb/>partim inferiori inditi &longs;unt, per quos orbiculos cer<lb/>

ta lege circumductus e&longs;t ductarius funis, qui deinde <lb/>

in &longs;ui po&longs;trema parte à potentia tractus omnes illos <lb/>

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clauo D, e&longs;t religatus, & immobilis. </s>

<s id="id.003043">&longs;ed vbinam hic <lb/>

vectis? </s>

<s id="id.003044">con&longs;idera diametrum M L, inferioris orbiculi, hæc enim ea e&longs;t, quæ <pb xlink:href="009/01/179.jpg" pagenum="179" />vectem gerit. </s>

<s id="id.003044">con&longs;idera diametrum M L, inferioris orbiculi, hæc enim ea e&longs;t, quæ <pb pagenum="179" xlink:href="009/01/179.jpg"/>vectem gerit. </s>

<s id="id.003045">huius enim extrema L M, à fune tanguntur, & ab eius medio <lb/>B, onus pendet, & grauitat; & quia funis in M, &longs;ur&longs;um trahitur, <expan abbr="&longs;ecum&qacute;">&longs;ecumque</expan>; ex <lb/>parte illa &longs;ur&longs;um elenat diametrum L M, erit potentia mouens, & eleuans <lb/>

in M. pondus verò intra vectem ad B, medium vectis; quare fulcimentum <lb/>

erit in reliquo extremo L, vbi funis &longs;u&longs;tinet loculamentum, & vbi diameter, <lb/>

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munera; vt en&longs;es, gladij, mucrones, &longs;ecures, terebræ, & &longs;imilia: &longs;erra <expan abbr="quoq;">quoque</expan> <lb/>

ad hoc reducitur, dentes enim percutiunt, <expan abbr="cunei&qacute;">cuneique</expan>; in&longs;tar exi&longs;tunt.</s>

<s id="id.003069"><emph type="italics"/>Additio de veteri Securi, & Bipenne.<emph.end type="italics"/></s>

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<s id="id.003077">Ex his autem po&longs;tremis verbis de&longs;criptio<lb/>

nem antiquæ &longs;ecuris, &longs;ic puto eruendam. </s>

<s id="id.003078">Ducatur primo recta A C, quæ <lb/>

erit in&longs;tar manubrij &longs;ecuris. </s>

inde ex centro C, interuallo. </s>

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<s id="id.003081">Quod autem tam angulus E, quàm angulus F, &longs;int æquales duabus tertijs <lb/>vnius anguli recti, &longs;iue quod idem e&longs;t angulo trianguli æquilateri, manife<lb/>&longs;tum erit hoc modo. </s>

<s id="id.003082">De&longs;cribatur iterum &longs;ecuralis figura prædicto modo, <lb/>

&longs;<expan abbr="itq;">itque</expan> ea A B C. ducantur præterea ad &longs;ingulos angulos tres rectæ A B, B C, <lb/>C A, quæ con&longs;tituunt triangulum æquilaterum A B C, tria enim ip&longs;ius late<lb/>

ra &longs;ubtendunt tres arcus æquales A B, B C, C A, <lb/>

&longs;unt enim tres &longs;extantes æqualium circulorum, <lb/>

ut facilè colligi pote&longs;t ex 15. 4. ex quo etiam &longs;e<lb/>quitur tres illas circulorum portiones, quas re<lb/>

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&longs;arum e&longs;&longs;e inuicem æquales, angulos, v.g. A B E, <lb/>

C B D, mixtos e&longs;&longs;e æquales, quod facilè e&longs;t per imaginatiam &longs;uperpo&longs;itio<lb/>

nem demon&longs;trare. </s>

<s id="id.003083">cum igitur prædicti duo anguli &longs;int æquales, &longs;itque inter <lb/>eos medius alius angulus E B C, qui pariter mixtus e&longs;t, &longs;i ip&longs;e addatur tam <lb/>angulo C B D, quàm angulo A B E, inuicem æqualibus, erunt duo anguli <pb xlink:href="009/01/181.jpg" pagenum="181" />A B C, rectilineus, & E B D, curuilineus æquales. </s>

<s id="id.003083">cum igitur prædicti duo anguli &longs;int æquales, &longs;itque inter <lb/>eos medius alius angulus E B C, qui pariter mixtus e&longs;t, &longs;i ip&longs;e addatur tam <lb/>angulo C B D, quàm angulo A B E, inuicem æqualibus, erunt duo anguli <pb pagenum="181" xlink:href="009/01/181.jpg"/>A B C, rectilineus, & E B D, curuilineus æquales. </s>

<s id="id.003084">ille autem e&longs;t angulus <lb/>

æquilateri, qui æqualis e&longs;t duabus tertijs vnius recti ex corollario 32. primi. <lb/>

</s>

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<s id="id.003088">Re&longs;tat, vt de antiquæ bipennis etiam figura di&longs;&longs;eramus; quæ nihil aliud <lb/>

erat, quàm duplex &longs;ecuris, &longs;iue &longs;ecuris anceps, qualis e&longs;t præ&longs;ens figura, vt <lb/>

propterea etiam &longs;æpius <expan abbr="bip&etilde;nis">bipennis</expan> ip<lb/>

&longs;a &longs;ecuris appelletur. </s>

<s id="id.003089">dicitur enim <lb/>

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tiquitatis &longs;tudio tenentur, la<lb/>

tere nolui.</s>

<s id="id.003103"><emph type="italics"/>Simmiæ Rhodij <lb/>

Bipennis.<emph.end type="italics"/></s>

<s id="id.003104"><emph type="italics"/>QVÆSTIO XX.<emph.end type="italics"/></s>

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bito: <expan abbr="atq;">atque</expan> hinc etiam ineptas, <expan abbr="atq;">atque</expan> ad&longs;cititias textus huius figuras tanquam <lb/>

adulterinas reijcere; <expan abbr="in&qacute;">inque</expan>; earum locum veras re&longs;tituere licebit. </s>

<s id="id.003109">erat igitur <lb/>

&longs;tatera, quantum ex Ari&longs;t. conijcio <lb/>

primum ha&longs;ta oblonga, qualis e&longs;t in <lb/>

præ&longs;enti figura A B, ex cuius altero <lb/>

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<s id="id.003122">Vnde videas contrario ab illis modo in no

<pb xlink:href="009/01/184.jpg" pagenum="184" />&longs;tris &longs;tateris æquipondium totam ha&longs;tam percurrere; in illis verò manentè <lb/>

<pb pagenum="184" xlink:href="009/01/184.jpg"/>&longs;tris &longs;tateris æquipondium totam ha&longs;tam percurrere; in illis verò manentè <lb/>

æquipondio trutinam quodammodo per ha&longs;tam moueri.</s>

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quia digiti propter carnis mollitiem cedentem nequeunt dentem <lb/>firmiter circumplecti; ferrum verò, cum vndique durum æque &longs;it, nec ce<lb/>dens, melius dentem comprehendit. </s>

<s id="id.003140">Aut tandem, quia forceps hæc duos <lb/>

in &longs;e continet contrarios vectes; quorum, vnum tantum e&longs;t hypomoclion, <lb/>

<figure id="id.009.01.184.1.jpg" xlink:href="009/01/184/1.jpg" place="text"/><lb/>eorum &longs;cilicet connexio; Virtute igitur <lb/>

<figure id="id.009.01.184.1.jpg" place="text" xlink:href="009/01/184/1.jpg"/><lb/>eorum &longs;cilicet connexio; Virtute igitur <lb/>

vectis arctius dentem per&longs;tringunt, <expan abbr="atq;">atque</expan> <lb/>

adeò obtinent, <expan abbr="atq;">atque</expan> hinc etiam facilius <lb/>

commouent. </s>

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concurrentibus dentem arctè <expan abbr="cõ&longs;tringit">con&longs;tringit</expan>,

<pb xlink:href="009/01/185.jpg" pagenum="185" />& commouet. </s>

<pb pagenum="185" xlink:href="009/01/185.jpg"/>& commouet. </s>

<s id="id.003142">Vectis vnus e&longs;t A G D, alter B G C, communis fultura e&longs;t G, <lb/>

vbi e&longs;t ip&longs;orum decu&longs;&longs;ata connexio; dens loco ponderis e&longs;t; vtroque igitur <lb/>

C, & D, tanquam manubrijs vectium dentem Medici compræhendentes ip<lb/>

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<s id="id.003157">vecte autem facilè onera quælibet <expan abbr="obuiãtia">obuiantia</expan> diuelluntur. <lb/>

</s>

<s id="id.003158">qui duo vectes vnicum habent hypomoclion ip&longs;am &longs;cilicet connexionem <lb/>

A. vectes &longs;unt binæ in&longs;trumenti ha&longs;tæ, F A D, <lb/>

E A C. <expan abbr="dilatãdo">dilatando</expan> igitur extrema C D, deducun<lb/>

tur etiam alia extrema F, E, & impo&longs;ita nuce in <lb/>

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<s id="id.003160">Ex quibus præ&longs;enti quæ&longs;tioni &longs;atisfactum videtur.</s>

<s id="id.003161"><emph type="italics"/>QVÆSTIO XXIII.<emph.end type="italics"/></s>

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<s id="id.003165">Rhombus ex definitione 23. primi Elem. e&longs;t figura æquilatera qui<lb/>

dem, &longs;ed non æquiangula, habet enim <lb/>

binos oppo&longs;itos angulos acutos, & alies <lb/>

binos oppo&longs;itos obtu&longs;os, talis e&longs;t præ<lb/>

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illi occurret in E, proprio motu: &longs;ed alieno à latere B A, proueniente erit

<pb xlink:href="009/01/187.jpg" pagenum="187" />in K, vbi etiam ob alterum motum erit A: erit igitur B, in linea B C, vt vo<lb/>

<pb pagenum="187" xlink:href="009/01/187.jpg"/>in K, vbi etiam ob alterum motum erit A: erit igitur B, in linea B C, vt vo<lb/>

lebamus. </s>

<s id="id.003177">à quo po&longs;tea di&longs;cedens ver&longs;us C, motu pariter compo&longs;ito &longs;i&longs;titur <lb/>

tandem in C, extremo lineæ pariter B C. eodem ergo tempore duo rhombi <lb/>

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quamuis duplici pellatur motu, vnus <lb/>

tamen ab altero inhibetur.</s>

<s id="id.003186"><emph type="italics"/>QVÆSTIO XXIIII.<emph.end type="italics"/></s>

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cundum æqualem conuoluuntur, quando circa idem po&longs;iti fuerint centrum, <lb/>

manife&longs;tum e&longs;t, ita tamen, vt aliquando ambæ æquales &longs;int ei, &longs;ecundum <lb/>

quam &longs;olus maior conuolueretur; aliquando verò &longs;ecundum quam minor. <lb/>

&longs;it enim circulus maior quidem vbi <lb/>

D F C, minor verò vbi E G B, <expan abbr="vtriq;">vtrique</expan> <lb/>

autem centrum A, linea, &longs;ecundum <lb/>

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G B, F C. &longs;i autem quadrantes hoc præ&longs;tant, manife&longs;tum e&longs;t, quod & toti <lb/>

ambitus idem efficiunt, quare quando tota periphæria G B E G, fuerit re<lb/>

uoluta etiam tota F C D F, &longs;uum orbem <expan abbr="complet&utilde;">completum</expan> habebit. </s>

<s id="id.003196">&longs;imiliter &longs;i ma<lb/>iorem quis mouerit, cui minor &longs;it annexus eodem exi&longs;tente centro, &longs;imul ac <pb xlink:href="009/01/189.jpg" pagenum="189" />diameter A C, erit perpendicularis ad F I, in puncto I, erit etiam A B, per<lb/>

<s id="id.003196">&longs;imiliter &longs;i ma<lb/>iorem quis mouerit, cui minor &longs;it annexus eodem exi&longs;tente centro, &longs;imul ac <pb pagenum="189" xlink:href="009/01/189.jpg"/>diameter A C, erit perpendicularis ad F I, in puncto I, erit etiam A B, per<lb/>

pendicularis ip&longs;i G M, in M; &longs;unt autem G M, & F I, æquales, quare quan<lb/>

do F C, quadrans maioris pertran&longs;iuerit rectam F C, etiam C B, quadrans <lb/>

minoris tran&longs;actam habebit illi parem G M. hoc autem accidit nulla inter<lb/>

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<s id="id.003210">Huic obiectioni <expan abbr="re&longs;pond&etilde;dum">re&longs;pondendum</expan> e&longs;t, quod quamuis prædicti orbes &longs;int con<lb/>

centrici, nihilominus non mouentur ambo &longs;uamet motione, &longs;ed ille, qui ab <lb/>

alio fertur mouetur &longs;ecundum motionem illam, tanquam &longs;i nullam ad eam <lb/>haberet aptitudinem; quamuis enim po&longs;&longs;it moueri circa centrum illud A,<pb xlink:href="009/01/190.jpg" pagenum="190" />propria natura, in præ&longs;enti tamen ca&longs;u minimè vtitur illa aptitudine; & <lb/>

alio fertur mouetur &longs;ecundum motionem illam, tanquam &longs;i nullam ad eam <lb/>haberet aptitudinem; quamuis enim po&longs;&longs;it moueri circa centrum illud A,<pb pagenum="190" xlink:href="009/01/190.jpg"/>propria natura, in præ&longs;enti tamen ca&longs;u minimè vtitur illa aptitudine; & <lb/>

propterea motus debet moueri, quantum mouens, nec plus, nec minus.</s>

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<s id="id.003222">Tertia demum ratio e&longs;t, quia hac ratione minus re&longs;tium ab&longs;umitur, quæ <lb/>

<figure id="id.009.01.190.1.jpg" xlink:href="009/01/190/1.jpg" place="text"/><lb/>vt benè intelligatur, de&longs;criba<lb/>

<figure id="id.009.01.190.1.jpg" place="text" xlink:href="009/01/190/1.jpg"/><lb/>vt benè intelligatur, de&longs;criba<lb/>

tur lectuli figura A F G K, & <lb/>

bifariam diuidatur latus F G, <lb/>

in B. & quia tota F G, dupla <lb/>

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ducunt ad B, po&longs;tea per C, re

<pb xlink:href="009/01/191.jpg" pagenum="191" />uertuntur ad D; hinc flectunt per H, v&longs;que ad E, & per G, angulum iterum <lb/>

<pb pagenum="191" xlink:href="009/01/191.jpg"/>uertuntur ad D; hinc flectunt per H, v&longs;que ad E, & per G, angulum iterum <lb/>

de&longs;cendunt ad M, à quo recta tendunt in F, hinc per 2. deducunt ad 3. à quo <lb/>

foramine, per foramen 4. reflexum faciunt ad 5. à quo iterum per B, de&longs;cen<lb/>

dunt ad angulum K, <expan abbr="ibi&qacute;">ibique</expan>; alterum funis extremum de&longs;init: <expan abbr="hoc&qacute;">hocque</expan>; modo duo <lb/>

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<s id="id.003230">&longs;i autem &longs;eeundum diame<lb/>

trum extendantur re&longs;tes, vti factum e&longs;t in lectulo A B C D, neutiquam re<lb/>

&longs;tes omnes &longs;imul &longs;uperiori quantitati adæquabuntur, &longs;ed illam longè &longs;upe<lb/>

rabunt. </s>

<s id="id.003231">Sit igitur lectus A B<lb/>

C D, in quo diametraliter du<lb/>

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<s id="id.003233"><expan abbr="Atq;">Atque</expan> hic e&longs;t &longs;en&longs;us Ari&longs;t. quamuis tex. ip&longs;ius propter nimiam tam in græ<lb/>

cis, quàm in latinis codicibus corruptionem, totus re&longs;titui nequiuerit.</s>

<s id="id.003234"><emph type="italics"/>QVÆSTIO XXVI.<emph.end type="italics"/></s>

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<s id="id.003242">pondus enim totius ligni vergit ferè ad alteram ligni <lb/>medietatem, quæ ab hypomoclio productior euadit, quapropter ad onus <lb/>

i&longs;tud æquilibrandum, opus e&longs;t alia potentia in altero extremo. </s>

<s id="id.003243">&longs;it lignum <lb/>

A B, &longs;u&longs;pen&longs;um ex medio C. <lb/>

hoc modo lignum ponderi<lb/>

bus libratum &longs;uis manet in <lb/>

æquilibrio, pote&longs;tque à &longs;ola <lb/>

potentia illud eleuante etiam deferri: quia A, & B, extrema &longs;e mutuò &longs;u&longs;ti<lb/>

nent. </s>

<s id="id.003244">quod &longs;i non ex medio eleuaretur, <lb/>

&longs;ed ab extremo, vt in &longs;ecunda figura, <lb/>

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ligni nunc e&longs;t: quando enim ab humero productius fuerit, magis <lb/>

vibrantur extrema, quam ob rem contingit portantem difficilius ge&longs;tare. <lb/>

</s>

<s id="id.003251">vibrationis autem cau&longs;a e&longs;t, quoniam ab eadem vi mouente magis extrema <pb xlink:href="009/01/193.jpg" pagenum="193" />huc illuc transferuntur, quanto procerius fuerit lignum, quia tunc maior <lb/>

<s id="id.003251">vibrationis autem cau&longs;a e&longs;t, quoniam ab eadem vi mouente magis extrema <pb pagenum="193" xlink:href="009/01/193.jpg"/>huc illuc transferuntur, quanto procerius fuerit lignum, quia tunc maior <lb/>

fit di&longs;tantià à centro, &longs;eu hypomoclio, quod modo e&longs;t humerus ip&longs;e. </s>

<s id="id.003252">&longs;it vt <lb/>

in prima præcedentis quæ&longs;tionis figura, humerus vbi A. di&longs;tantiæ autem ab <lb/>

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idoneum, quo ru&longs;tici pa&longs;&longs;im vtuntur: <expan abbr="id&qacute;">idque</expan>; iuxta puteos &longs;tabile, ac firmum <lb/>

con&longs;truunt, quale à figura &longs;equenti refertur. </s>

<s id="id.003260">vbi puteus F, tolleno con&longs;tat <lb/>

erecto tigno D C, & tran&longs;<lb/>

uer&longs;a ha&longs;ta A C B, vnà cum <lb/>

fune B E, & hydria E. ap<lb/>

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A B, vtens &longs;ur&longs;um hydriam plenam rapiet, <expan abbr="hac&qacute;">hacque</expan>; ratione nos labore leua<lb/>

bit, <expan abbr="totum&qacute;">totumque</expan>; hauriendi opus demi&longs;&longs;ione, <expan abbr="atq;">atque</expan> eleuatione <expan abbr="con&longs;tãs">con&longs;tans</expan>, alleuabit,</s>

<s id="id.003265"><emph type="italics"/>QVÆSTIO XXVIIII.<emph.end type="italics"/></s>

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<s id="id.003278">Cvm &longs;edemus, præcipuè &longs;i commodè &longs;edeamus, &longs;olemus duos angu<lb/>

los rectos facere, vnum quidem, quem facit thorax cum femore; <lb/>

alterum quem facit femur cum crure, vt in figura thorax &longs;it A B, <lb/>

femur B C, crus C D, anguli duo recti &longs;unt B, <lb/>

& C. </s>

<s id="id.003279">Quærit igitur, cur quando &longs;urgere volumus angu<lb/>

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rectum facit e&longs;t perpendicularis alteri lineæ, cui incumbit, <expan abbr="æqualiter&qacute;">æqualiterque</expan>; in <lb/>

<expan abbr="vtramq;">vtramque</expan> partem inclinata e&longs;t: quapropter fit, vt quæcunque con&longs;tituta &longs;int <lb/>&longs;uper &longs;uperficiem terræ ad angulos rectos non cadant, &longs;ed recta maneant. <lb/>

</s>

<s id="id.003283">pariter <expan abbr="quæcunq;">quæcunque</expan> ad angulos rectos pauimento incumbunt, non &longs;olum, quia <lb/>cum illo faciant angulos rectos, &longs;ed etiam, quia &longs;imul faciunt cum &longs;uperficie <pb xlink:href="009/01/195.jpg" pagenum="195" />terræ perpendiculum. </s>

<s id="id.003283">pariter <expan abbr="quæcunq;">quæcunque</expan> ad angulos rectos pauimento incumbunt, non &longs;olum, quia <lb/>cum illo faciant angulos rectos, &longs;ed etiam, quia &longs;imul faciunt cum &longs;uperficie <pb pagenum="195" xlink:href="009/01/195.jpg"/>terræ perpendiculum. </s>

<s id="id.003284">An quia qui &longs;urgit fit rectus; rectus autem manens, <lb/>oportet, vt &longs;it &longs;uperficiei terræ perpendicularis. </s>

<s id="id.003285">debet igitur e&longs;&longs;e &longs;ecundum <lb/>

eandem rectitudinem, ide&longs;t caput &longs;upra thoracem, thorax verò &longs;upra femo<lb/>

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pothe&longs;im inducere; &longs;ed ea prædicto Planctarum <lb/>

ordini parum, aut nihil repugnat.</s>

<s id="id.003301"><emph type="italics"/>Deæstu Maris.<emph.end type="italics"/></s>

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plures idem &longs;en&longs;erunt. </s>

<s id="id.003311">Lunam &longs;cilicet eam habere vim in mare, vt pars il<lb/>la, quæ Lunæ &longs;ubiacet, &longs;iue quam Luna radijs ferit, æ&longs;tuet, & turgeat; non <lb/>

aliter pars maris huic antipoda, & auer&longs;a, quamuis tota terræ moles inter <lb/>

ip&longs;am, & Lunam interpona<lb/>

tur, æ&longs;tuat, fluxumque, ac re<lb/>

fluxum quamuis priori mi<lb/>

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&longs;imul, vt ait hic Ari&longs;t. & ex

<pb xlink:href="009/01/197.jpg" pagenum="197" />perientia te&longs;tatur, &longs;imul cum Luna circa mundum circumaguntur. </s>

<pb pagenum="197" xlink:href="009/01/197.jpg"/>perientia te&longs;tatur, &longs;imul cum Luna circa mundum circumaguntur. </s>

<s id="id.003315">hoc e&longs;t <lb/>

&longs;i Luna, quæ modo e&longs;t in &longs;uperiori parte meridionali, venerit ad locum E, <lb/>occidentalem, eam fluxus A, &longs;ublequitur, <expan abbr="vergit&qacute;">vergitque</expan>; tumorem &longs;uum ad occi<lb/>

dentem E, vnde, & fluxus B, promouebitur ad orientem, ita vt punctum F, <lb/>

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<s id="id.003336">quod &longs;i hi æ&longs;tus à Luna minimè penderent, nulla ra<lb/>tione regulæ illæ effici potui&longs;&longs;ent, quibus per ætatem ip&longs;ius, ac &longs;itum &longs;upra <lb/>

horizontem eos prædicere tuto valerent.</s>

<s id="id.003337">Secunda verò ratio, quæ maximè eos torquet e&longs;t quanam ratione à Luna <lb/>

effici po&longs;&longs;it &longs;ecundus refluxus B, primò oppo&longs;itus, cum tota terræ moles in<lb/>

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to lumen <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> luminaris ad D, quod &longs;atis e&longs;t efficax, cùm ferè perpendi

culariter terræ D, incidat. </s>

<s id="id.003353">quamuis autem ex &longs;tellis F, E, lumen aliquod ad <lb/>

D, tran&longs;mittatur, tamen cum obliquè admodum illi accidat, nihil penè ef<lb/>

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<s id="id.003360">&longs;ydera porrò illa, quæ &longs;upra Solem exi&longs;tunt, etiam &longs;i ip&longs;orum illu

<pb xlink:href="009/01/200.jpg" pagenum="200" />minatio tota ad terras vergat, tamen in lateribus terræ prædictis nihil ef<lb/>

<pb pagenum="200" xlink:href="009/01/200.jpg"/>minatio tota ad terras vergat, tamen in lateribus terræ prædictis nihil ef<lb/>

ficiunt, quia in illa vel obliquè admodum radij incidunt, vel ea tantummo<lb/>

do tangunt. </s>

<s id="id.003361">Verum illuminatione &longs;ua ea&longs;dem maris partes, quæ &longs;unt ad G, <lb/>

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<s id="id.003374"><expan abbr="Atq;">Atque</expan> hæc e&longs;t mea de æ&longs;tu maris per reflexionem &longs;ententia. </s>

<s id="id.003375">quam iamdiu <lb/>

inuentam, <expan abbr="atq;">atque</expan> auditoribus meis &longs;æpius explicatam, reperi tandem non &longs;ine <pb xlink:href="009/01/201.jpg" pagenum="201" />gaudio fui&longs;&longs;e etiam &longs;ubtili&longs;&longs;imi Scoti opinionem, quam ip&longs;e breuiter in pri<lb/>

inuentam, <expan abbr="atq;">atque</expan> auditoribus meis &longs;æpius explicatam, reperi tandem non &longs;ine <pb pagenum="201" xlink:href="009/01/201.jpg"/>gaudio fui&longs;&longs;e etiam &longs;ubtili&longs;&longs;imi Scoti opinionem, quam ip&longs;e breuiter in pri<lb/>

mum &longs;ent. </s>

<s id="id.003376">de creatione mundi tantummodo &longs;ine vlla expo&longs;itione, <expan abbr="atq;">atque</expan> con<lb/>

firmatione proponit. </s>

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<s id="id.003397">Alterum quorumdam indiui&longs;ibilium quidem, &longs;ed tamen quantorum cu<lb/>

iu&longs;modi e&longs;&longs;ent, quædam adeò minimæ lineæ, quæ omnem effugiant diui&longs;io<lb/>nem: ex quibus antiqui opinabantur lineas totales, ac diuiduas componi. <lb/>

</s>

<s id="id.003398">atque de hoc &longs;ecundo indiuiduorum, quantorum genere videtur opu&longs;culum <pb xlink:href="009/01/202.jpg" pagenum="202" />i&longs;tud di&longs;&longs;erere. </s>

<s id="id.003398">atque de hoc &longs;ecundo indiuiduorum, quantorum genere videtur opu&longs;culum <pb pagenum="202" xlink:href="009/01/202.jpg"/>i&longs;tud di&longs;&longs;erere. </s>

<s id="id.003399">& quia partim rationibus phy&longs;icis, partim geometricis vti<lb/>

tur, ideò nec omninò phy&longs;icus nec omninò mathematicus e&longs;t. </s>

<s id="id.003400">Ego igitur, <lb/>quæ mathematica &longs;unt, ex in&longs;tituto exponere aggrediar.</s>

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men&longs;urabiles (vt aiunt Geometræ) potentia, ide&longs;t &longs;ecundum quadrata ea

<pb xlink:href="009/01/203.jpg" pagenum="203" />rum, &longs;iue dicas quadrata <expan abbr="quoq;">quoque</expan> earum e&longs;&longs;e commen&longs;urabilia, v. g. linea dua<lb/>

<pb pagenum="203" xlink:href="009/01/203.jpg"/>rum, &longs;iue dicas quadrata <expan abbr="quoq;">quoque</expan> earum e&longs;&longs;e commen&longs;urabilia, v. g. linea dua<lb/>

rum vnciarum, & linea trium vnciarum &longs;unt <lb/>

commen&longs;urabiles longitudine, & potentia, <lb/>

quia potentia lineæ duarum vnciarum, &longs;iue <lb/>

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<s id="id.003425">Propo&longs;ita igitur linea quapiam, v. g. trium palmorum qualis e&longs;t linea A, <lb/>

po&longs;&longs;unt inueniri quamplurimæ lineæ, quarum aliæ &longs;int illi longitudine com<lb/>

men&longs;urabiles, &longs;iue quæ cum expo&longs;ita A, ha<lb/>

beant communem men&longs;uram. </s>

<s id="id.003426">v. g. linea B, <lb/>

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gitudine incommen&longs;urabiles, qualis e&longs;&longs;et diameter C D, quadrati lineæ A, <lb/>

quæ e&longs;t cum latere A, incommen&longs;urabilis ex vltima 10.</s>

<s id="id.003427">Cæterum lineam primò expo&longs;itam, vt e&longs;t in præ<lb/>

&longs;entia A, quod e&longs;&longs;et notæ quantitatis, Græci appella<lb/>

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e&longs;t etiam potentia) &longs;iue potentia &longs;olùm, rationales ip&longs;æ quoque dicuntur.

Aliæ verò (quarum permultæ in decimo reperiun<lb/>

tur) quæ nec longitudine, nec potentia illi &longs;unt <lb/>

commen&longs;urabiles, irrationales appellantur, qua<lb/>

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quod ex duabus lineis rationalibus re&longs;pectu rationalis expo&longs;itæ. </s>

men&longs;urabilibus inuicem tantum potentia, componitur linea, quæ cum ea<lb/>

dem expo&longs;ita e&longs;t irrationalis, <expan abbr="vocatur&qacute;">vocaturque</expan>; ex <lb/>

duobus nominibus, &longs;iue Binomium, vt &longs;i ex <lb/>

latere A, & diametro C D, componatur li<lb/>

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rum decretis, & ex quibus Mathematici docent in contentio&longs;am pariter, ac falla<emph.end type="italics"/>

<pb xlink:href="009/01/205.jpg" pagenum="205" /><emph type="italics"/>cem diuertere argumentationem, præ&longs;ertim tam inualidam. </s>

<pb pagenum="205" xlink:href="009/01/205.jpg"/><emph type="italics"/>cem diuertere argumentationem, præ&longs;ertim tam inualidam. </s>

<s id="id.003449">nam multis modis im<lb/>becillis e&longs;t eiu&longs;modi ratio, & quouis modo licet euitare, ne aut inu&longs;itata dicere, aut <lb/>

argui videamur.<emph.end type="italics"/></s>

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<expan abbr="eadem&qacute;">eademque</expan>; determinata men&longs;ura men&longs;urari oportere, fal&longs;um omninò e&longs;t, & <lb/>

contra mathematicorum dogmata, non enim Geometræ hoc a&longs;&longs;erunt, cùm <lb/>ip&longs;orum demon&longs;trationibus aduer&longs;etur; &longs;ed <expan abbr="tant&utilde;">tantum</expan> dicunt omnes lineas, quæ <lb/>

ad inuicem &longs;unt commen&longs;urabiles, commen&longs;urari, vna <expan abbr="eadem&qacute;">eademque</expan>; men&longs;ura, <lb/>

&longs;ed non tamen vnica, ide&longs;t non vnica, ac determi<lb/>

nata. </s>

<s id="id.003452">po&longs;&longs;unt enim e&longs;&longs;e plures <expan abbr="eædem&qacute;">eædemque</expan>; men&longs;uræ <lb/>

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ac &longs;ine ratione, imò contra rationem addidit: tum quia in Græco textu non <lb/>

extant, tum quia &longs;en&longs;us totius &longs;ententiæ is e&longs;t, vt potius debui&longs;&longs;et affirmati<lb/>

uè dicere <emph type="italics"/>(Diuiduas credere)<emph.end type="italics"/> nam Ari&longs;toteles videtur &longs;ic <expan abbr="argum&etilde;tari">argumentari</expan>, quan<lb/>

do recta linea A B, vt in appo&longs;ita figura mo<lb/>

uetur intrando in &longs;emicirculum C A D B, ita <lb/>

vt primò &longs;it in &longs;itu A B, &longs;ecundò in E F, tertiò <lb/>

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ram additamentum illud factum e&longs;&longs;e, & &longs;imul ratio, & textus Ari&longs;t. eadem <lb/>

opera patefacta &longs;unt.</s>

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<s id="id.003461">Hæc e&longs;t alia ratio, qua probat totam circuli periphæriam e&longs;&longs;e diuiduam. <lb/>

&longs;int enim duo circuli æquales primum in eo<lb/>

dem loco, <expan abbr="vocentur&qacute;">vocenturque</expan>; A, & B, deinde circu<lb/>

lus B, moueatur, & di&longs;cedat à circulo A, ma<lb/>

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<s id="id.003479">indiuiduæ autem lineæ &longs;ibi ip&longs;is commen&longs;urabiles &longs;unt longitudine, cum inter &longs;e <lb/>

fiat æquales; quare potentia quoque, quod &longs;i hoc e&longs;t, diuiduum erit quadratum.<emph.end type="italics"/></s>

<s id="id.003480">Pergit adhuc nouis rationibus aduer&longs;arios refellere, dicens, &longs;i extarent <lb/>

huiu&longs;modi indiuiduæ lineæ, &longs;equeretur omnes omninò lineas e&longs;&longs;e commen<lb/>

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prauata ex græco textu, in hunc modum correxi <emph type="italics"/>(Præterea cùm circa maio<lb/>rem latitudinem facit applicata, æquale ei, quod ab indiuidua, & pedali copulatis <lb/>

circa bipedalem, minorem faciet latitudinem, quàm &longs;it indiuidua: erit minus, quod <lb/>

circa indiuiduam)<emph.end type="italics"/> ide&longs;t cùm minor linea applicata cum maiore, latitudinem <lb/>

faciat. </s>

<s id="id.003486">v. g. linea minor A B, applicata cum ma<lb/>

iori B C, vt in figura, ita vt contineant figuram <lb/>

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aduer&longs;arij velint extare huiu&longs;modi lineas ato<lb/>

mas, con&longs;tituatur figura &longs;ub vna ex illis, quæ &longs;it v. g. A B, & altera maiori, <lb/>

quæ &longs;it pedalis, v. g. B C, vt in præcedenti figura, &longs;umatur deinde linea bi<lb/>

pedalis E F, cui per 45. primi ap<lb/>

plicetur &longs;patium E F G H, æquale <lb/>

&longs;patio &longs;uperiori A B C D, nece&longs;&longs;a<lb/>

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<s id="id.003494">Ex 22. primi Elem. ex tribus datis lineis, quarum quælibet duæ &longs;int, re<lb/>

liqua maiores pote&longs;t con&longs;titui triangulum: poterit igitur ex tribus indiui<lb/>

duis con&longs;titui <expan abbr="triãgulum">triangulum</expan>, <expan abbr="illud&qacute;">illudque</expan>; æquilaterum, cum omnes in<lb/>

diuiduæ lineæ &longs;int æquales. </s>

<s id="id.003495">&longs;it igitur ex eis triangulum A B C, <lb/>

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protracta, & perpendiculari ducta, quadrati co&longs;ta potentia <expan abbr="perp&etilde;dicularem">perpendicularem</expan>, diame-<emph.end type="italics"/>

<pb xlink:href="009/01/208.jpg" pagenum="208" /><emph type="italics"/>trumqué mediam æquat: quare non erit minima. </s>

<pb pagenum="208" xlink:href="009/01/208.jpg"/><emph type="italics"/>trumqué mediam æquat: quare non erit minima. </s>

<s id="id.003499">neque duplum erit &longs;patium à diame<lb/>

tro con&longs;urgens illius, quod ab indiuidua procreatur: nans æquali ablato, reliquum <lb/>erit minus indiuidua, nam &longs;i æqualis, diameter quadruplum de&longs;criberet, &c.) <emph.end type="italics"/><lb/>

ide&longs;t &longs;i per 46 primi quadratum. </s>

tuor in&longs;ecabilibus componatur, cuius diametro B C, <lb/>

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<s id="id.003522">Decimusquintus locus <emph type="italics"/>(Adhuc etiam, vt linea &longs;ic, & &longs;uperficies, & corpus <lb/>

crit impartibile: vno quippe indiuiduo exi&longs;tente, cætera <expan abbr="quoq;">quoque</expan> con&longs;equentur, quia<emph.end type="italics"/> <pb xlink:href="009/01/209.jpg" pagenum="209" /><emph type="italics"/>vnum per aliud diuiditur, at corpus indiuiduum non e&longs;t, cum in &longs;e latitudinem, & <lb/>

crit impartibile: vno quippe indiuiduo exi&longs;tente, cætera <expan abbr="quoq;">quoque</expan> con&longs;equentur, quia<emph.end type="italics"/> <pb pagenum="209" xlink:href="009/01/209.jpg"/><emph type="italics"/>vnum per aliud diuiditur, at corpus indiuiduum non e&longs;t, cum in &longs;e latitudinem, & <lb/>

profunditatem contineat: quare nec linea pote&longs;t e&longs;&longs;e atoma. </s>

<s id="id.003523">corpus &longs;iquidem in &longs;u<lb/>perficies, &longs;uperficies verò in lineas &longs;oluitur)<emph.end type="italics"/> hoc e&longs;t: præterea, quemadmodum <lb/>linea per aduer&longs;arium extat indiuidua, &longs;ic & &longs;uperficies ab eadem linea de<lb/>

&longs;cripta erit atoma, & corpus ab hac &longs;uperficie de&longs;criptum erit impartibile. <lb/>

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ctam lineam in vnico puncto. </s>

<s id="id.003534">iam &longs;i linea con&longs;taret ex punctis indiuiduis <lb/>

tanquam partibus, po&longs;&longs;et circulus <expan abbr="tãgere">tangere</expan> rectam lineam in duobus punctis. <lb/>

Sit circulus, cuius centrum A, tangens lineam <lb/>

rectam B C, con&longs;tantem ex punctis, quorum vnus <lb/>

&longs;it in extremo D, lineæ B D, alterum verò in E, <lb/>

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tate, <expan abbr="id&qacute;">idque</expan>; rationibus aliunde, quàm <lb/>

ex Geometria deductis.</s>

<s id="id.003537"><emph type="italics"/>In Librum de Propriet. Elementorum.<emph.end type="italics"/></s>

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Arabem quempiam.</s>

</chap>

<chap>

<s id="id.003541">EX LIBRO NONO <lb/>

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minimè a&longs;&longs;entiebar, quia m Araneo nullum e&longs;&longs;et naturale in&longs;trumentum,

<pb xlink:href="009/01/212.jpg" pagenum="212" />veluti velum, in quod ventus po&longs;&longs;it impingere. </s>

<pb pagenum="212" xlink:href="009/01/212.jpg"/>veluti velum, in quod ventus po&longs;&longs;it impingere. </s>

<s id="id.003559">Alij Araneum ex vna arbo<lb/>

re de&longs;cendere, & po&longs;tea alteram con&longs;cendere, interim emi&longs;&longs;um retro filum <lb/>

raptando, ac deinde &longs;ur&longs;um attrahendo attollere, ac prætendere: &longs;ed ho<lb/>

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<s id="id.003566">Ex qua repetita &longs;æpius ob&longs;eruatione lu<lb/>

ce clarius comperi Araneum non &longs;implex filum, &longs;ed ramo&longs;um, ac multiplex <lb/>

emittere, <expan abbr="atq;">atque</expan> aliquando ex &longs;ece&longs;&longs;u etiam ip&longs;o duo &longs;imul eijcere, <expan abbr="alter&utilde;">alterum</expan> quo <lb/>

&longs;u&longs;pendatur, alterum <lb/>

verò, quod &longs;orte hac, <lb/>

<expan abbr="atq;">atque</expan> illac volitans, ali<lb/>

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E I, M O, F L, alter

<pb xlink:href="009/01/213.jpg" pagenum="213" />natim prodeunt, ac per aerem hinc inde volitant. </s>

<pb pagenum="213" xlink:href="009/01/213.jpg"/>natim prodeunt, ac per aerem hinc inde volitant. </s>

<s id="id.003569">Si ergò filum E I, dextræ <lb/>

arbori occurrerit, <expan abbr="ei&qacute;">eique</expan>; hæ&longs;erit, vt in figura, illicò Araneus huius rei con<lb/>

&longs;cius per filum A E I, a&longs;cendit, <expan abbr="&longs;e&qacute;">&longs;eque</expan>; ad prius inacce&longs;&longs;am &longs;ibi dextram arbo<lb/>

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&longs;ciendum, quod lineam hypotenu&longs;am, quemadmodum etiam Athenæus lib. <lb/>

10. te&longs;tatur, eam appellant geometræ, quæ in triangulo rectangulo recto <lb/>

angulo &longs;ubtenditur, vnde & denominata e&longs;t hypotenu&longs;a, ide&longs;t &longs;ubten&longs;a, vt <lb/>

in triangulo A B C, cuius angulus B, rectus &longs;it, recta <lb/>

A C, angulo recto B, &longs;ubten&longs;a, hypotenu&longs;a dicitur. <lb/>

</s>

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quem facit alterum crus adhuc quie&longs;cens, cum hori

<pb xlink:href="009/01/214.jpg" pagenum="214" />zonte; vt in &longs;uperiori triangulo, &longs;i concipiamus crura fui&longs;&longs;e duo latera A B, <lb/>

<pb pagenum="214" xlink:href="009/01/214.jpg"/>zonte; vt in &longs;uperiori triangulo, &longs;i concipiamus crura fui&longs;&longs;e duo latera A B, <lb/>

A D, quæ manente animali, fui&longs;&longs;ent ambo &longs;imul in &longs;itu A B, perpendicula<lb/>

ria horizonti; incipiens autem animal ambulare, proferat primo crus A D, <lb/>

A D, fiet hypotenu&longs;a trianguli A B C, & quia crus hoc A D, factum hypo<lb/>tenu&longs;a æquale e&longs;t alteri manenti A B, nequit totius veræ hypotenu&longs;æ A C, <lb/>officio fungi, quæ æquiualet toti A D, & præterea interiacenti D C, vtea au<lb/>

<figure id="id.009.01.214.1.jpg" xlink:href="009/01/214/1.jpg" place="text"/><lb/>tem hypotenu&longs;a debet e&longs;&longs;e maior, quia opponitur <lb/>

<figure id="id.009.01.214.1.jpg" place="text" xlink:href="009/01/214/1.jpg"/><lb/>tem hypotenu&longs;a debet e&longs;&longs;e maior, quia opponitur <lb/>

maiori angulo nimirum recto B, quam latus A B, <lb/>

quod angulo acuto C, opponitur per 19. primi, & <lb/>

propterea ni&longs;i alterum &longs;ub&longs;equens crus A B, incli<lb/>

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<s id="id.003594">nece&longs;&longs;e igitur refle

<pb xlink:href="009/01/215.jpg" pagenum="215" />ctere <expan abbr="vtrumq;">vtrumque</expan> crus non &longs;olum ad horixontem, &longs;ed etiam circa aliquam cor<lb/>

<pb pagenum="215" xlink:href="009/01/215.jpg"/>ctere <expan abbr="vtrumq;">vtrumque</expan> crus non &longs;olum ad horixontem, &longs;ed etiam circa aliquam cor<lb/>

poris flexuram, vel nodum, vt circa genu, aut alia. </s>

<s id="id.003595">crura enim in gre&longs;&longs;u fiunt <lb/>

latera &longs;uperiora trianguli i&longs;o&longs;celis, vt in &longs;ecunda figura patuit, cuius ba&longs;is <lb/>

e&longs;t pa&longs;&longs;us. </s>

<s id="id.003596">& tunc caput ambulantis fit inferius, quàm antequam gradere<lb/>

tur; quia tunc ambo crura erant horizonti perpen<lb/>

dicularia. </s>

<s id="id.003597">quando autem caput fuerit in linea <expan abbr="per-p&etilde;diculari">per<lb/>

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e&longs;t flexus & vna, & duæ; & recta, & flexa, quæ permutatur potentia, <lb/>

& actu, propter flexum. </s>

<s id="id.003603">cum autem flectitur, & mouetur, hoc quidem &longs;ignum mo-<emph.end type="italics"/><lb/>

<emph type="italics"/>vetur, illud autem manet in flexibus, quemadmodum <expan abbr="vtiq;">vtique</expan> &longs;i dia<lb/>

metri, quæ quidem A D, maneat, quæ cutem B, moueatur, & <lb/>

fiat A C, &longs;ed hic quidem videtur, &longs;ecundum omnem modum in<lb/>

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erit huius flexuræ centrum A, quod vt extremum lineæ D A, manentis, ma

<pb xlink:href="009/01/216.jpg" pagenum="216" />net: vt verò extremum motæ A B, mouetur. </s>

<pb pagenum="216" xlink:href="009/01/216.jpg"/>net: vt verò extremum motæ A B, mouetur. </s>

<s id="id.003612">quamuis in mathematicis hæc <lb/>

quidem duorum centrorum di&longs;tinctio nulla &longs;it, quia centrum mathemati<lb/>

cum omninò indiuiduum e&longs;t: neque in mathematicis e&longs;t propriè motus, <lb/>

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<expan abbr="vtriq;">vtrique</expan> con&longs;iderant: ille quatenus <expan abbr="&longs;ol&utilde;">&longs;olum</expan> ad opus vtile e&longs;t, hic verò cum ve<lb/>

ritatis &longs;peculator &longs;it, quid, & qualis &longs;it, indagat)<emph.end type="italics"/> Id quod dicit Ari&longs;t. <lb/>

confirmatur ex eo, quod Fabri omnes vtuntur amu&longs;&longs;i, &longs;eu norma, <lb/>

quæ nihil aliud e&longs;t quàm angulus rectus, quæ vulgò <lb/>

&longs;quadra dicitur, vt eius auxilio angulum ip&longs;um re<lb/>

ctum in opus conferant, <expan abbr="&longs;ic&qacute;">&longs;icque</expan>; normæ, aut amu&longs;&longs;is du<lb/>

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<s id="id.003634">10. primi,

<pb xlink:href="009/01/217.jpg" pagenum="217" />vt in figura, vbi linea A B, in&longs;i&longs;tens alteri D C, perpendiculariter, ide&longs;t ita <lb/>

<pb pagenum="217" xlink:href="009/01/217.jpg"/>vt in figura, vbi linea A B, in&longs;i&longs;tens alteri D C, perpendiculariter, ide&longs;t ita <lb/>

vt faciat angulos hinc inde æqualis A B D, A B C, prædictos inquam duos <lb/>

angulos con&longs;iderat e. </s>

<s id="id.003635">&longs;e rectos. </s>

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portionum, &longs;iue medietatum, Arithmetica quam modo &longs;uppo&longs;ui; Geome<lb/>

trica, & Harmonica, quas inferius oblata occa&longs;ione opportunius explicabo.</s>

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phy&longs;icæ, &longs;ed à naturalibus ab&longs;tractæ, qualis con&longs;iderat Arithmeticus: omni <lb/>tamen numero &longs;iue ab&longs;tracto, &longs;iue non, conuenit proportiones &longs;u&longs;cipere, <lb/>

id e&longs;t & numero, & rebus numeratis.</s>

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<s id="id.003681">Horum exemplum in rebus practicis &longs;it hoc: &longs;it vt Plato ad Proclum, ita <lb/>

mille aurei ad quingentos aureos, ergò alternatim ita erit Plato ad 1000. <lb/>

aureos, &longs;icuti Proclus ad 500. quare ita etiam totum erit ad totum, &longs;cilicet <lb/>

Plato, & Proclus &longs;imul ad 1000. & 500. &longs;imul, quæ duo tota, di&longs;tributio mo<lb/>ralis, ac practica diuidit, & binatim copulat, hoc modo dicens, vt Plato ad <pb xlink:href="009/01/219.jpg" pagenum="219" />Proclum, ita 1000. ad 500, & po&longs;tea, vt Plato ad 1000. ita Proclus ad 500. <lb/>

Plato, & Proclus &longs;imul ad 1000. & 500. &longs;imul, quæ duo tota, di&longs;tributio mo<lb/>ralis, ac practica diuidit, & binatim copulat, hoc modo dicens, vt Plato ad <pb pagenum="219" xlink:href="009/01/219.jpg"/>Proclum, ita 1000. ad 500, & po&longs;tea, vt Plato ad 1000. ita Proclus ad 500. <lb/>

iuxta <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> merita, & quidem i&longs;ta e&longs;t huiu&longs;modi moralis di&longs;tributio, cum <lb/>

modis argumentandi ab Euclide comprobatis, nitatur.</s>

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terminis con&longs;i&longs;tere po&longs;&longs;e, & ideo non e&longs;&longs;e continuam, &longs;ed di&longs;iunctam, vt vo<lb/>

lebat Ari&longs;tot.</s>

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duobus rectis æquales habet angulos, quadratum <expan abbr="quoq;">quoque</expan> quatuor angulis rectis ha-<emph.end type="italics"/>

<pb xlink:href="009/01/221.jpg" pagenum="221" /><emph type="italics"/>beat nece&longs;&longs;e e&longs;t. </s>

<pb pagenum="221" xlink:href="009/01/221.jpg"/><emph type="italics"/>beat nece&longs;&longs;e e&longs;t. </s>

<s id="id.003723">& &longs;i triangulum &longs;ecus, ita etiam, & quadratum commutabitur, <lb/>

ex altera parte enim ei re&longs;pondet. </s>

<s id="id.003724">& &longs;i quadratum quatuor angulis rectis æquales, <lb/>

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ratum ponere.</s>

</chap>

<chap>

<s id="id.003742"><emph type="italics"/>Ex Secundo Moralium Eudem.<emph.end type="italics"/></s>

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<s id="id.003762">cap. 10. &longs;atis de hac re dictum e&longs;t.</s>

</chap>

<chap>

<s id="id.003763"><emph type="italics"/>Ex Septimo Moralium Eudem.<emph.end type="italics"/></s>

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<s id="id.003784">Cæterum, qui plura de modis tam antiquis, quàm nouis de&longs;iderat,