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

Page concordance

< >
Scan Original
111 73
112 74
113 75
114 76
115 77
116 78
117 79
118 80
119 81
120 82
121 83
122 84
123 85
124 86
125 87
126 88
127 89
128 90
129 91
130 92
131 93
132 94
133 95
134 96
135 97
136 98
137 99
138 100
139 101
140 102
< >
page |< < (81) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div317" type="section" level="1" n="106">
          <pb o="81" file="0119" n="119" rhead="Conicor. Lib. V."/>
          <p style="it">
            <s xml:id="echoid-s3370" xml:space="preserve">Deinde patebit, quemadmodum demonſtrauimus, &</s>
            <s xml:id="echoid-s3371" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3372" xml:space="preserve">Quia D M fa-
              <lb/>
              <note position="left" xlink:label="note-0119-01" xlink:href="note-0119-01a" xml:space="preserve">f</note>
            cta eſt maior, quàm D B, & </s>
            <s xml:id="echoid-s3373" xml:space="preserve">minor quàm D A, eſtque circuli radius D N
              <lb/>
            æqualis D M; </s>
            <s xml:id="echoid-s3374" xml:space="preserve">ergo punctum M cadit intra coniſectionem, N vero extra ip-
              <lb/>
            ſam; </s>
            <s xml:id="echoid-s3375" xml:space="preserve">& </s>
            <s xml:id="echoid-s3376" xml:space="preserve">propterea circulus M L N ſectionem conicam ſecabit alicubi, vt in L,
              <lb/>
            & </s>
            <s xml:id="echoid-s3377" xml:space="preserve">portio circuli M L intra coniſectionem A L incidet: </s>
            <s xml:id="echoid-s3378" xml:space="preserve">rurſus ducatur radius
              <lb/>
            D L, & </s>
            <s xml:id="echoid-s3379" xml:space="preserve">L G coniſectionem tangens in L erit, vt priùs angulus D L G acu-
              <lb/>
              <note position="right" xlink:label="note-0119-02" xlink:href="note-0119-02a" xml:space="preserve">33. 34.
                <lb/>
              lib. 1.</note>
            tus; </s>
            <s xml:id="echoid-s3380" xml:space="preserve">& </s>
            <s xml:id="echoid-s3381" xml:space="preserve">ideo L G cadit intra circulum L M, & </s>
            <s xml:id="echoid-s3382" xml:space="preserve">propterea intra coniſectionem
              <lb/>
            A L, ſed eadem L G cadit extra ipſam, quia eam contingit in L, quod eſt ab-
              <lb/>
            ſurdum; </s>
            <s xml:id="echoid-s3383" xml:space="preserve">quare ramus D A non eſt maior, quàm D B; </s>
            <s xml:id="echoid-s3384" xml:space="preserve">ſed priùs neque illi
              <lb/>
            æqualis erat; </s>
            <s xml:id="echoid-s3385" xml:space="preserve">igitur ramus terminatus D A minor eſt quolibet ramo ſecante
              <lb/>
            D B infra ipſum poſito, & </s>
            <s xml:id="echoid-s3386" xml:space="preserve">propterea minimus erit omnium ſecantium.</s>
            <s xml:id="echoid-s3387" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3388" xml:space="preserve">Poſtea dico, quod D C maior eſt, quàm D B, &</s>
            <s xml:id="echoid-s3389" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3390" xml:space="preserve">Demonſtratio ſe-
              <lb/>
              <note position="left" xlink:label="note-0119-03" xlink:href="note-0119-03a" xml:space="preserve">g</note>
            cundæ partis huius propoſitionis, quàm Apollonius innuit (quia conſtructione,
              <lb/>
            ac progreſſu ſimili ſuperiori perſici poteſt) hac ratione reſtituitur. </s>
            <s xml:id="echoid-s3391" xml:space="preserve">Demonſtran-
              <lb/>
            dum eſt quemlibet ramum D B vertici A proximiorem eße minorem quolibet
              <lb/>
            ramo D C remotiore. </s>
            <s xml:id="echoid-s3392" xml:space="preserve">Ducantur recta C P contingens ſectionem in C, & </s>
            <s xml:id="echoid-s3393" xml:space="preserve">O B
              <lb/>
            tangens ſectionem in B, & </s>
            <s xml:id="echoid-s3394" xml:space="preserve">recta B R perpendicularis ad ramum D B; </s>
            <s xml:id="echoid-s3395" xml:space="preserve">& </s>
            <s xml:id="echoid-s3396" xml:space="preserve">ſi
              <lb/>
            quidem ramus D C non concedatur maior, quàm D B, ſit primo ei æqualis, ſi
              <lb/>
            fieri poteſt, & </s>
            <s xml:id="echoid-s3397" xml:space="preserve">centro D interuallo D C deſcribatur circulus C P R, qui tran-
              <lb/>
            ſibit per punctum B, ob æqualitatem radiorum D C, D B; </s>
            <s xml:id="echoid-s3398" xml:space="preserve">& </s>
            <s xml:id="echoid-s3399" xml:space="preserve">quia (ex Lem-
              <lb/>
            mate nono) angulus D C P verticem reſpiciens, eſt acutus, recta C P cadet
              <lb/>
            intra circulum C P R; </s>
            <s xml:id="echoid-s3400" xml:space="preserve">ſed cadit extra coniſectionem, cum ſit contingens; </s>
            <s xml:id="echoid-s3401" xml:space="preserve">igi-
              <lb/>
            tur portio circularis peripheriæ C P ducitur extra coniſectionem C Q B: </s>
            <s xml:id="echoid-s3402" xml:space="preserve">rur-
              <lb/>
            ſus, quia angulus D B O eſt obtuſus (ex nono Lemmate, cum verticem A non reſpi-
              <lb/>
            ciat) ergo R B perpendicularis ad D B cadit intra coniſectionẽ, cum B O poſita ſit eã
              <lb/>
            contingens: </s>
            <s xml:id="echoid-s3403" xml:space="preserve">cadit verò eadem B R extra circulum B R Q, cum ſit perpendicu-
              <lb/>
            laris ad circuli radium D B; </s>
            <s xml:id="echoid-s3404" xml:space="preserve">igitur circuli portio B R intra coniſectionem ca-
              <lb/>
            det: </s>
            <s xml:id="echoid-s3405" xml:space="preserve">ſed priùs eiuſdem circuli portio C P extra eandem ſectionem ducebatur;
              <lb/>
            </s>
            <s xml:id="echoid-s3406" xml:space="preserve">igitur idem circulus ſecat coniſectionem alicubi, vt in Q, ducaturque denuo
              <lb/>
            ramus D Q, & </s>
            <s xml:id="echoid-s3407" xml:space="preserve">Q O contingens ſectionem in Q; </s>
            <s xml:id="echoid-s3408" xml:space="preserve">Vnde (ex nono Lemmate)
              <lb/>
              <note position="right" xlink:label="note-0119-04" xlink:href="note-0119-04a" xml:space="preserve">33. 34.
                <lb/>
              lib. 1.</note>
            angulus D Q O erit acutus; </s>
            <s xml:id="echoid-s3409" xml:space="preserve">& </s>
            <s xml:id="echoid-s3410" xml:space="preserve">propterea recta Q O intra circuli portionem;
              <lb/>
            </s>
            <s xml:id="echoid-s3411" xml:space="preserve">Q R conſtituta intra coniſectionem cadet, quod eſt abſurdum; </s>
            <s xml:id="echoid-s3412" xml:space="preserve">recta enim Q
              <lb/>
            O extra coniſectionem Q A cadit, quàm contingit in Q; </s>
            <s xml:id="echoid-s3413" xml:space="preserve">non ergo ramus D
              <lb/>
            C æqualis eſt ipſi D B. </s>
            <s xml:id="echoid-s3414" xml:space="preserve">Sit ſecundò D C minor, quàm D B (ſi fieri poteſt) ſe-
              <lb/>
            ceturque D T minor quàm D B, ſed maior quàm D C; </s>
            <s xml:id="echoid-s3415" xml:space="preserve">& </s>
            <s xml:id="echoid-s3416" xml:space="preserve">centro D interuallo
              <lb/>
            D T deſcribatur circulus T Q S; </s>
            <s xml:id="echoid-s3417" xml:space="preserve">is quidem ad partes B cadet intra, ad par-
              <lb/>
            tes vero C extra coniſectionem; </s>
            <s xml:id="echoid-s3418" xml:space="preserve">& </s>
            <s xml:id="echoid-s3419" xml:space="preserve">propterea eam alicubi ſecabit, vt in Q; </s>
            <s xml:id="echoid-s3420" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s3421" xml:space="preserve">ducto ramo D Q, & </s>
            <s xml:id="echoid-s3422" xml:space="preserve">Q O contingente ſectionem in Q, erit angulus D Q
              <lb/>
              <note position="right" xlink:label="note-0119-05" xlink:href="note-0119-05a" xml:space="preserve">Lem. 9.</note>
            O acutus, & </s>
            <s xml:id="echoid-s3423" xml:space="preserve">ideo recta Q O cadet intra circulum T Q, & </s>
            <s xml:id="echoid-s3424" xml:space="preserve">propterea intra
              <lb/>
            coniſectionem, quod eſt abſurdum; </s>
            <s xml:id="echoid-s3425" xml:space="preserve">Q O enim cadit extra ſectionem Q A,
              <lb/>
            quàm contingit in Q; </s>
            <s xml:id="echoid-s3426" xml:space="preserve">non ergo ramus D C minor eſt, quàm D B, ſed neque
              <lb/>
            æqualis priùs oſtenſus fuit; </s>
            <s xml:id="echoid-s3427" xml:space="preserve">igitur quilibet ramus D B vertici A propinquior
              <lb/>
            minor eſt quolibet ramo remotiore D C, quod erat oſtendendum.</s>
            <s xml:id="echoid-s3428" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum