Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

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            <s xml:id="echoid-s12568" xml:space="preserve">
              <pb o="369" file="0407" n="408" rhead="Conicor. Lib. VII."/>
            datæ diametri I L: </s>
            <s xml:id="echoid-s12569" xml:space="preserve">oportet autem vt data diameter cadat inter axim
              <lb/>
            maiorem A C, & </s>
            <s xml:id="echoid-s12570" xml:space="preserve">diametrum a b æqualem ſuo erecto a c.</s>
            <s xml:id="echoid-s12571" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12572" xml:space="preserve">Sit C E latus diametri I L, & </s>
            <s xml:id="echoid-s12573" xml:space="preserve">diuidatur H D in V, vt habeat H V ad V
              <lb/>
            D eandem proportionem, quàm H E habet ad E D, & </s>
            <s xml:id="echoid-s12574" xml:space="preserve">ducta vt prius ad axim
              <lb/>
            perpendiculari V X occurrens ſectioni in X, & </s>
            <s xml:id="echoid-s12575" xml:space="preserve">coniuncta A X, quam bifa-
              <lb/>
            riam ſecet diameter T S, cuius erectus S Z; </s>
            <s xml:id="echoid-s12576" xml:space="preserve">dico hanc eſſe quæſitam. </s>
            <s xml:id="echoid-s12577" xml:space="preserve">Quo-
              <lb/>
              <note position="right" xlink:label="note-0407-01" xlink:href="note-0407-01a" xml:space="preserve">Lem. 17.
                <lb/>
              huius.</note>
            niam H V ad V D eandem proportionem habet, quàm H E ad E D, igitur
              <lb/>
            differentia quadratorum ex T S, & </s>
            <s xml:id="echoid-s12578" xml:space="preserve">ex S Z æqualis eſt differentiæ quad
              <unsure/>
            ratorum
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            ex I L, & </s>
            <s xml:id="echoid-s12579" xml:space="preserve">ex I K, quod propoſitum fuerat.</s>
            <s xml:id="echoid-s12580" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s12581" xml:space="preserve">Deducitur ex 9. </s>
            <s xml:id="echoid-s12582" xml:space="preserve">propoſitione additarum, atque ex propoſit. </s>
            <s xml:id="echoid-s12583" xml:space="preserve">51. </s>
            <s xml:id="echoid-s12584" xml:space="preserve">huius, quod
              <lb/>
            in ellypſi exceſſus quadrati cuiuſlibet diametri tranſuerſæ ſupra quadratum ere-
              <lb/>
            cti eius ſucceſſiue decreſcit ab axi maiori A C vſque ad diametrum a b æqua-
              <lb/>
            lem ſuo erecto, atque ab hac diametro defectus quadrati cuiuſlibet tranſuerſæ
              <lb/>
            diametri à quadrato erecti eius ſucceſſiue augetur, quouſque perueniatur ad dia-
              <lb/>
            metrum f d, cuius differentia quadratorum figuræ eius æqualis ſit differentiæ
              <lb/>
              <note position="right" xlink:label="note-0407-02" xlink:href="note-0407-02a" xml:space="preserve">ex Prop.
                <lb/>
              50. huius.</note>
            quadratorum figuræ axis maioris A C, & </s>
            <s xml:id="echoid-s12585" xml:space="preserve">vltra diametrum f d differentiæ præ-
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            dictæ ſemper magis augentur quouſque perueniatur ad axim minorem γ O cuius
              <lb/>
            differentia quadratorum figuræ eius maxima eſt omnium differentiarum inter
              <lb/>
            quadrata laterum figuræ cuiuſlibet diametri eiuſdem ellypſis.</s>
            <s xml:id="echoid-s12586" xml:space="preserve"/>
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            <s xml:id="echoid-s12587" xml:space="preserve">Conſtat quoque ex 9. </s>
            <s xml:id="echoid-s12588" xml:space="preserve">propoſitione additarum, quod in ellypſi tres diametri
              <lb/>
            reperiri poßunt, quarum differentia quadratorum figurarum laterum earum
              <lb/>
            æquales ſint inter ſe.</s>
            <s xml:id="echoid-s12589" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12590" xml:space="preserve">Et ex 10. </s>
            <s xml:id="echoid-s12591" xml:space="preserve">additarum reperiri poſſunt quatuor diametri, quarum differentiæ
              <lb/>
            quadrat orum laterum figurarum earum æquales ſint inter ſe: </s>
            <s xml:id="echoid-s12592" xml:space="preserve">in hyperbole verò
              <lb/>
            hoc non contingit, nam ab axi differentiæ quadratorum laterum figuræ cuiuſli-
              <lb/>
              <note position="right" xlink:label="note-0407-03" xlink:href="note-0407-03a" xml:space="preserve">ex Prop.
                <lb/>
              49. huius.</note>
            bet diametri ſucceſſiue augentur, ſi axis maior fuerit ſuo erecto, at ſi minor
              <lb/>
              <note position="right" xlink:label="note-0407-04" xlink:href="note-0407-04a" xml:space="preserve">ex Prop.
                <lb/>
              50. huius.</note>
            fuerit prædictæ differentiæ quadratorum ſucceſſiue diminuuntur.</s>
            <s xml:id="echoid-s12593" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12594" xml:space="preserve">Differentia (8. </s>
            <s xml:id="echoid-s12595" xml:space="preserve">15.) </s>
            <s xml:id="echoid-s12596" xml:space="preserve">duorum quadratorum duorum laterum figuræ axis
              <lb/>
              <note position="left" xlink:label="note-0407-05" xlink:href="note-0407-05a" xml:space="preserve">a</note>
            maior eſt in hyperbola (51.)</s>
            <s xml:id="echoid-s12597" xml:space="preserve">, & </s>
            <s xml:id="echoid-s12598" xml:space="preserve">ellypſi, quàm differentia quadratorum
              <lb/>
            duorum laterum figuræ homologæ diametri ſectionis, & </s>
            <s xml:id="echoid-s12599" xml:space="preserve">differentia ho-
              <lb/>
            mologi proximioris axi maior eſt differentia homologi remotioris: </s>
            <s xml:id="echoid-s12600" xml:space="preserve">hoc
              <lb/>
            autem ſi axis in hyperbola minor fuerit ſuo erecto (49.)</s>
            <s xml:id="echoid-s12601" xml:space="preserve">; </s>
            <s xml:id="echoid-s12602" xml:space="preserve">ſi verò fuerit
              <lb/>
            maior oppoſitum pronunciandum eſt (50.)</s>
            <s xml:id="echoid-s12603" xml:space="preserve">, & </s>
            <s xml:id="echoid-s12604" xml:space="preserve">differentia quadrati axis
              <lb/>
            inclinati, & </s>
            <s xml:id="echoid-s12605" xml:space="preserve">figuræ eius minor eſt ſemidifferentia quadratorum duorum
              <lb/>
            laterũ figuræ ſui homologi, ſi axis inclinatus minor eſt ſuo erecto (49.)
              <lb/>
            </s>
            <s xml:id="echoid-s12606" xml:space="preserve">ſi verò fuerit maior exceſſus axis maior erit dimidio exceſſus quadrato-
              <lb/>
            rum duorum laterum figuræ homologi, & </s>
            <s xml:id="echoid-s12607" xml:space="preserve">minor quàm tota, &</s>
            <s xml:id="echoid-s12608" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12609" xml:space="preserve">Legen-
              <lb/>
            dum puto: </s>
            <s xml:id="echoid-s12610" xml:space="preserve">in qualibet ellypſi, &</s>
            <s xml:id="echoid-s12611" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12612" xml:space="preserve">vt in textu apparet.</s>
            <s xml:id="echoid-s12613" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s12614" xml:space="preserve">Et ſit P Q in ellypſi vna &</s>
            <s xml:id="echoid-s12615" xml:space="preserve">hellip;</s>
            <s xml:id="echoid-s12616" xml:space="preserve">, & </s>
            <s xml:id="echoid-s12617" xml:space="preserve">educamus A B, A N, &</s>
            <s xml:id="echoid-s12618" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s12619" xml:space="preserve">
              <note position="left" xlink:label="note-0407-06" xlink:href="note-0407-06a" xml:space="preserve">b</note>
            Repleui lacunam, vt in textu videre eſt.</s>
            <s xml:id="echoid-s12620" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12621" xml:space="preserve">Ergo E H ad H A minor eſt quàm E D ad D A, nempe E X exceſſus
              <lb/>
              <note position="left" xlink:label="note-0407-07" xlink:href="note-0407-07a" xml:space="preserve">c</note>
            E G, E H ad A C exceſſum H A, A G, & </s>
            <s xml:id="echoid-s12622" xml:space="preserve">quadratum A C in omni-
              <lb/>
            bus figuris ad differentiam duorum quadratorum A G, A F, vt quadra-
              <lb/>
            tum A H ad differentiam duorum quadratorũ A G, & </s>
            <s xml:id="echoid-s12623" xml:space="preserve">E H ad H A mi-
              <lb/>
            nor in duabus primis, & </s>
            <s xml:id="echoid-s12624" xml:space="preserve">maior in duabus ſecundis, quàm E G ad G A,
              <lb/>
            & </s>
            <s xml:id="echoid-s12625" xml:space="preserve">iungamus ergo E H ad H A, nempe E H ad H A, quàm aggrega-</s>
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