Cardano, Geronimo, Opvs novvm de proportionibvs nvmerorvm, motvvm, pondervm, sonorvm, aliarvmqv'e rervm mensurandarum, non solùm geometrico more stabilitum, sed etiam uarijs experimentis & observationibus rerum in natura, solerti demonstratione illustratum, ad multiplices usus accommodatum, & in V libros digestum. Praeterea Artis Magnae, sive de regvlis algebraicis, liber vnvs abstrvsissimvs & inexhaustus planetotius Ariothmeticae thesaurus ... Item De Aliza Regvla Liber, hoc est, algebraicae logisticae suae, numeros recondita numerandi subtilitate, secundum Geometricas quantitates inquirentis ...

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page |< < of 291 > >|
    <archimedes>
      <text>
        <front>
          <section>
            <table>
              <pb xlink:href="015/01/009.jpg"/>
              <row>
                <cell/>
                <cell>
                  <emph type="italics"/>
                ut producti ex aggregato primæ & tertiæ, in tertiam ad productum ex aggre gato tertiæ & omiotatæ ad ſecundam in ipſam quartam.
                  <emph.end type="italics"/>
                </cell>
                <cell>14</cell>
              </row>
              <row>
                <cell>XVII.</cell>
                <cell>O
                  <emph type="italics"/>
                mnes duæ proportiones conuerſæ producunt æqualem proportionem.
                  <emph.end type="italics"/>
                </cell>
                <cell>15</cell>
              </row>
              <row>
                <cell>XVIII.</cell>
                <cell>S
                  <emph type="italics"/>
                i fuerint quotlibet quantitates in continua proportione multiplici præter,
                  <expan abbr="ultimã">ultimam</expan>
                proportio uerò penultimæ ad ultimam, qualis reſidui primæ ad ſecundam, erit primæ ad aggregatum reliquarum, uelut penultimæ ad ultimam.
                  <emph.end type="italics"/>
                </cell>
                <cell>15</cell>
              </row>
              <row>
                <cell>XIX.</cell>
                <cell>S
                  <emph type="italics"/>
                i fuerint aliquot quantitates arithmeticæ omiologæ, quarum exceſſus ſit æqualis minimè, omnibus autem deficientibus ſupplementa ad æqualitatem maximè adiungantur, erunt quadrata omnium quantitatum æqualium, adiecto rurſus quadrato primæ cum eo quod fit ex minima primi ordinis in aggregatum o­mnium quantitatum eiuſdem, tripla aggregato quadratorum omnium quanti tatum primi ordinis pariter acceptis.
                  <emph.end type="italics"/>
                </cell>
                <cell>17</cell>
              </row>
              <row>
                <cell>XX.</cell>
                <cell>C
                  <emph type="italics"/>
                um fuerint quatuor quantitates, fueritque
                  <expan abbr="ſecũda">ſecunda</expan>
                æqualis tertiæ, aut prima æqualis quartæ, erit proportio primæ ad quartam, aut tertiæ ad ſecundam, producta ex proportionibus primæ ad ſecundam & tertiæ ad quartam.
                  <emph.end type="italics"/>
                </cell>
                <cell>21</cell>
              </row>
              <row>
                <cell>XXI.</cell>
                <cell>C
                  <emph type="italics"/>
                um decuſſatim ducta fuerit prima in quartam, & ſecunda in tertiam, produ­ctumque primæ in quartam, diuiſum fuerit per productum ſecundæ in tertiam, erit proportio primæ ad ſecundam, diuiſa per proportíonem tertiæ ad quar­tam.
                  <emph.end type="italics"/>
                E
                  <emph type="italics"/>
                t ſimiliter interpoſita omiologa.
                  <emph.end type="italics"/>
                </cell>
                <cell>22</cell>
              </row>
              <row>
                <cell>XXII.</cell>
                <cell>C
                  <emph type="italics"/>
                um fuerit proportio primæ ad ſecundam maior quàm tertiæ ad quartam, erit confuſa ex his maior quàm tertiæ ad quartam, minor autem quàm primæ ad ſecundam.
                  <emph.end type="italics"/>
                </cell>
                <cell>23</cell>
              </row>
              <row>
                <cell>XXIII.</cell>
                <cell>O
                  <emph type="italics"/>
                mnis motus naturalis ad locum ſuum eſt: ideò per rectam lineam fit.
                  <emph.end type="italics"/>
                </cell>
                <cell>23</cell>
              </row>
              <row>
                <cell>XXIIII.</cell>
                <cell>O
                  <emph type="italics"/>
                mnis motus circularis uoluntarius eſt.
                  <emph.end type="italics"/>
                </cell>
                <cell>23</cell>
              </row>
              <row>
                <cell>XXV.</cell>
                <cell>T
                  <emph type="italics"/>
                res ſunt motus omnino ſimplices naturalis, uoluntarius, & uiolentus.
                  <emph.end type="italics"/>
                </cell>
                <cell>24</cell>
              </row>
              <row>
                <cell>XXVI.</cell>
                <cell>M
                  <emph type="italics"/>
                otus ergo compoſiti quatuor neceſſariò ſunt ſpecies.
                  <emph.end type="italics"/>
                </cell>
                <cell>24</cell>
              </row>
              <row>
                <cell>XXVII.</cell>
                <cell>M
                  <emph type="italics"/>
                otus uoluntarius eſt in loco: naturalis ad locum: uiolentus ex loco.
                  <emph.end type="italics"/>
                </cell>
                <cell>25</cell>
              </row>
              <row>
                <cell>XXVIII.</cell>
                <cell>M
                  <emph type="italics"/>
                otus quilibet uoluntarius aut uiolentus in aliquo medio fit.
                  <emph.end type="italics"/>
                </cell>
                <cell>25</cell>
              </row>
              <row>
                <cell>XXIX.</cell>
                <cell>O
                  <emph type="italics"/>
                mnis motus uoluntarius æqualis eſt ſemper: ſimpliciter etiam quilibet alius mo­tus.
                  <emph.end type="italics"/>
                </cell>
                <cell>25</cell>
              </row>
              <row>
                <cell>XXX.</cell>
                <cell>I
                  <emph type="italics"/>
                n omni corpore mobili in medio partes medij reſiſtunt obuiæ, aliæ impel­lunt.
                  <emph.end type="italics"/>
                </cell>
                <cell>26</cell>
              </row>
              <row>
                <cell>XXXI.</cell>
                <cell>O
                  <emph type="italics"/>
                mnis motus naturalis in æquali medio ualidior eſt in fine quàm in principio.
                  <emph.end type="italics"/>
                V
                  <emph type="italics"/>
                iolentus contrà.
                  <emph.end type="italics"/>
                </cell>
                <cell>26</cell>
              </row>
              <row>
                <cell>XXXII.</cell>
                <cell>O
                  <emph type="italics"/>
                mne mobile naturaliter motum ſeu uiolenter uelocius mouetur in medio rariore quàm denſiore.
                  <emph.end type="italics"/>
                M
                  <emph type="italics"/>
                aior quoque eſt proportio finis motus in corpore rariore ad finem motus in corpore denſiore quàm principij.
                  <emph.end type="italics"/>
                I
                  <emph type="italics"/>
                n uiolento autem celerius perueniret ad finem motus in corpore denſiore.
                  <emph.end type="italics"/>
                </cell>
                <cell>27</cell>
              </row>
              <row>
                <cell>XXXIII.</cell>
                <cell>O
                  <emph type="italics"/>
                mnia duo mobilia æqualis undique magnitudinis quæ æquali in tempore æqualia ſpacia pertranſeunt in diuerſis ſubſtantia medijs neceſſe eſt, ut ſit ponderis ad pondus, quem ad modum medij ad medium proportio duplicata.
                  <emph.end type="italics"/>
                </cell>
                <cell>27</cell>
              </row>
              <row>
                <cell>XXXIIII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportio corporis cubi ad ſuam ſuperficiem quadratam, eſt uelut eiuſdem ſuperfi ciei, ad latus eiuſdem uerò ad monadem.
                  <emph.end type="italics"/>
                </cell>
                <cell>28</cell>
              </row>
              <row>
                <cell>XXXV.</cell>
                <cell>V
                  <emph type="italics"/>
                ocum magnitudines excreſcunt in acumine, non in grauitate, finis autem eſt in utroque extremo.
                  <emph.end type="italics"/>
                P
                  <emph type="italics"/>
                ropter hoc minima facta uariatione in hypate acutæ uix ferunt.
                  <emph.end type="italics"/>
                </cell>
                <cell>29</cell>
              </row>
              <row>
                <cell>XXXVI.</cell>
                <cell>S
                  <emph type="italics"/>
                i proportio per proportionem minorem æquali ducatur, proportio minor pro­
                  <emph.end type="italics"/>
                </cell>
                <cell/>
              </row>
            </table>
          </section>
        </front>
      </text>
    </archimedes>
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