Cardano, Girolamo Opus novum de proportionibus 1570

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<p type="main"> <s id="id003888">Dixi quod in hipomochlio parua uarietas fit in motu: igitur &agrave; <lb/>
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leui cau&longs;a magnum nauigium impellitur aut uariatur. </s> <s id="id003889">Cum enim a <lb/>
<expan abbr="tr&atilde;sfertur">transfertur</expan> ad b, fit minima uarietas in e, igitur a parua poterit tran&longs;&shy;<lb/>
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ferri, tum uero quod debuit <expan abbr="tr&atilde;sferri">transferri</expan> ad c, transfertur ad <lb/>
d, nam motus ip&longs;e ab alia cau&longs;a fit, uelut <expan abbr="u&etilde;to">uento</expan> aut remis, <lb/>
ita non e&longs;t difficultas ni&longs;i propter motum aqu&aelig;, &longs;cilicet <lb/>
ut tabula &longs;cindat illam. </s> <s id="id003890">Ad hoc autem contulit illud <lb/>
quod intra nauim prominet ut uectis rationem habeat, <lb/>
&amp; ob id facilius uerti.</s> </p>

<p type="margin"> <s id="id003891"><margin.target id="marg749"/>C<emph type="italics"/>o<emph.end type="italics"/>^&lcub;m}.</s> </p>

<p type="main"> <s id="id003892">Similiter uarietas in puppi exigua e&longs;t cau&longs;a magn&aelig; <lb/>
uarietatis in prora, quod autem pote&longs;t fieri paucioribus <lb/>
&amp; faciliori modo id debet fieri, hac igitur cau&longs;a in pup&shy;<lb/>
pi temonem con&longs;tituere oportet &longs;eu guberna culum.</s> </p>

<p type="main"> <s id="id003893">Cum autem impellatur &agrave; mari, nece&longs;&longs;e e&longs;t, ut &agrave; latere excipiat <lb/>
aquam ita ut tantum pendeat in unam partem, quantum nauis in <lb/>
aduer&longs;am, nam &longs;i nauis non penderet, gubernaculum rect&egrave; dirige&shy;<lb/>
<figure id="id.015.01.248.2.jpg" xlink:href="carda_propo_015_la_1570/015-01-figures/015.01.248.2.jpg"/><lb/>
retur. </s> <s id="id003894">Vt ergo ex duobus obliquis <expan abbr="un&utilde;">unum</expan> rectum con&longs;titui<lb/>
tur, ita ex naui &amp; gubernaculo, nam &longs;int a b &amp; c b &amp; im&shy;<lb/>
pellatur ad d, impelletur per mediam lineam b e &amp; non <lb/>
per a b neque c b, igitur oportet temonem pendere ex ad <lb/>
uer&longs;o inclinationis nauis. </s> <s id="id003895">E&longs;t etiam alia ratio, quoniam <lb/>
nauis &longs;ecurior redditur, nam quemadmodum quod in <lb/>
medio e&longs;t, facilius impellitur tran&longs;uer&longs;im, qu&agrave;m quod pendet in <lb/>
contrarium, ita &amp; in gubernaculo. </s> <s id="id003896">E&longs;t &amp; id ob nece&longs;sitatem, quoni&shy;<lb/>
am motus aqu&aelig; plerumque e&longs;t in partem, uelut &amp; uentus ad la&shy;<lb/>
tus eius &longs;itus, &longs;ecundum quem moueri debet nauis. </s> <s id="id003897">Sicut igitur &amp; <lb/>
uela &amp; malus inclinantur, ut motum directum efficiant, quia ali&ograve; <lb/>
dirigitur nauis quam qui mouet uentus, ita de temone compara&shy;<lb/>
tione aqu&aelig;.</s> </p>

<p type="main"> <s id="id003898">Propo&longs;itio ducente&longs;ima prima.</s> </p>

<p type="main"> <s id="id003899">Si du&aelig; line&aelig; non &longs;ecantes circuli peripheriam in <expan abbr="un&utilde;">unum</expan> <expan abbr="punct&utilde;">punctum</expan>, ex <lb/>
ea co&euml;ant, exterius nece&longs;&longs;e e&longs;t illas peripheria <expan abbr="c&otilde;tenta">contenta</expan> e&longs;&longs;e maiores.</s> </p>

<p type="head"> <s id="id003900">LEMMA PRIMVM.</s> </p>

<p type="main"> <s id="id003901">Si fuerit proportio primi ad &longs;ecundum maior qu&agrave;m tertij ad <lb/>
quartum, erit primi ad tertium maior qu&agrave;m &longs;ecundi ad quartum.<lb/>
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<p type="margin"> <s id="id003902"><margin.target id="marg750"/>C<emph type="italics"/>o<emph.end type="italics"/>^&lcub;m}.</s> </p>

<p type="main"> <s id="id003903">Quamuis hoc demon&longs;tretur &agrave; Campano, quia </s> </p>

<p type="main"> <s id="id003904"><arrow.to.target n="marg751"/><lb/>
tamen facile e&longs;t hic adijcietur. </s> <s id="id003905">Sit igitur maior a <lb/>
ad b quam c ad d, dico maiorem e&longs;&longs;e a ad c quam <lb/>
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b ad d, quia enim maior e&longs;t a ad b quam c ad d fiat e ad b ut c ad e <lb/>
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eritque e minu&longs; quam a, e igitur ad c ut b ad d &longs;ed maior a ad c quam <lb/>
e ad e igitur maior a ad c quam b ad d.<lb/>
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