<echo version="1.0"><text type="book" xml:lang="la"><div xml:id="echoid-div1" type="front" level="1" n="1"><div xml:id="echoid-div5" type="preface" level="2" n="1"><pb n="13" file="0013" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0013"/>
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<head xml:id="echoid-head15" xml:space="preserve">IO. BAPTISTAE BENEDICTI PATRITII VENETI SERENISS. CAR. EM. ALLOBROGVM DVCIS PHILOSOPHI.</head>
<head xml:id="echoid-head16" style="it" xml:space="preserve">Theoremata Arithmetica.</head>
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<s xml:id="echoid-s37" xml:space="preserve"><emph style="sc">PRaeclare</emph>
multa veteres mathematici philoſophi de numeris eorumq́ue effectibus excogitata poſteris tradide-runt, quorum cum vix vllam rationem reddiderint, aut certè per exiguam, occaſione diuerſorum problematum mihi à Sereniſſimo Sabaudiæ Duce propoſitorum præbi-ta, de ijs quæ ab antiquis propoſita fuerunt contemplanda nonnulla occurrerunt, quæ poſteritati comendare non inutile arbitratus fum, ne hæ meæ cogitationes intercide-rent, & occaſionem præberem quamplurimis abſtruſa hęc indagandi, quæ problematibus & thæorematibus inuoluta, vix aliquem qui euol-ueret nacta funt.</s>
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<s xml:id="echoid-s38" xml:space="preserve">Inter cætera vero à me queſita, hoc fuit theorema.</s>
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<head xml:id="echoid-head17" xml:space="preserve">THEOREMA PRIMVM.</head>
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<s xml:id="echoid-s39" xml:space="preserve"><emph style="sc">INterrogavit</emph>
me Sereniſſimus Dux Sabaudiæ, qua ratione cognoſci poſ-ſet ſcientificè & ſpeculatiue (vt dicitur) productum ex duobus fractis numeris, quolibet producentium minus eſſe. </s>
<s xml:id="echoid-s40" xml:space="preserve">Cui reſpondi, mente & cogitatione conci-piendum eſſe fractos producentes cum fractis productis, non vnius eiuſdemq́ue na-turæ eſſe, imò longè diuerfæ.</s>
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<s xml:id="echoid-s41" xml:space="preserve">Exempli gratia, fractis numeris propofitis et quorum integri ſint et qui tanquam lineæ cogitentur, apertum fanè eſſet productum fu-perficiale futurum, quod nomen caperet à producto ſuperficiali generato ex vno in aliud totorum linearium, nam ſi conſtitueretur octauum ipſius et dimidium multiplicato cum produceretur fextumdecimum ipſius . </s>
<s xml:id="echoid-s42" xml:space="preserve">Quare eſſet totum <reg norm="relatiuum" type="context">relatiuũ</reg>
ipſius non aliquod totum producentium. </s>
<s xml:id="echoid-s43" xml:space="preserve">Mirum itaque non eſt ſi productum minus videatur fuis producentibus, cum toto, diuerſæ naturæ à primis conferatur, fractum fiquidem ab integro eiuſdem naturæ, linearis, ſuperficialis, aut corporeæ denominatur.</s>
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<s xml:id="echoid-s44" xml:space="preserve">Quòd ſi amplioris cognitionis gratia ex ſcientiæ præceptis ſpeculari voluerit a@
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