Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div495" type="section" level="3" n="5">
              <div xml:id="echoid-div500" type="letter" level="4" n="2">
                <pb o="250" rhead="IO. BAPT. BENED." n="262" file="0262" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0262"/>
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              <div xml:id="echoid-div501" type="letter" level="4" n="3">
                <head xml:id="echoid-head376" style="it" xml:space="preserve">De falacia operationis triangulorum ſphericorum.</head>
                <head xml:id="echoid-head377" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3154" xml:space="preserve">QVod diebus præteris tibi ſignificaui, idem nunc confirmo, ſcilicet ſphærico-
                    <lb/>
                  rum triangulorum operationem ſæpe nos fallere, vt exempli gratia, ſi pro
                    <lb/>
                  poſitus nobis fuiſſet triangulus
                    <var>.A.B.C.</var>
                  cuius angulus
                    <var>.A.</var>
                  nobis datus eſſet graduum
                    <num value="114">.
                      <lb/>
                    114.</num>
                  mi
                    <var>.o.</var>
                  & eius latus
                    <var>.A.</var>
                  B, graduum .67. min .5. & latus
                    <var>.A.C.</var>
                  graduum .45. mi .10.
                    <lb/>
                  ſi reliquos angulos cum tertio latere etiam cognoſcere voluerimus, ex methodo .11
                    <lb/>
                  primi Copernici propoſitum obtinebimus. </s>
                  <s xml:id="echoid-s3155" xml:space="preserve">vnde latus
                    <var>.B.C.</var>
                  eſſet graduum .89. min
                    <num value="30">.
                      <lb/>
                    30.</num>
                  angulus vero
                    <var>.C.</var>
                  graduum .57. min .14. angulus autem
                    <var>.B.</var>
                  grad .48. min .38. </s>
                  <s xml:id="echoid-s3156" xml:space="preserve">Qua-
                    <lb/>
                  re vltimus hic angulus
                    <var>.B.</var>
                  falſus eſſet, eo quod operatio paruorum triangulorum in
                    <lb/>
                  cauſa eſt, quotieſcunque eorum latera tam breuia ſint, ut non eccedant vnum gra-
                    <lb/>
                  dum, quare ipſorum angulorum veram quantitatem non tribuunt. </s>
                  <s xml:id="echoid-s3157" xml:space="preserve">propterea igitur
                    <lb/>
                  cum voluerimus veram
                    <reg norm="quantitatem" type="context">quãtitatem</reg>
                  ipſius anguli
                    <var>.B.</var>
                  oportet poſt quam inuenerimus
                    <lb/>
                  angulum
                    <var>.C.</var>
                  mediante arcu
                    <var>.D.E.</var>
                  ſupponere alium polum in
                    <var>.B.</var>
                  deinde producere. </s>
                  <s xml:id="echoid-s3158" xml:space="preserve">B
                    <lb/>
                  A. vſque ad
                    <var>.d.</var>
                  et
                    <var>.B.C.</var>
                  vſque ad
                    <var>.e.</var>
                  imaginando
                    <var>.B.d.</var>
                  et
                    <var>.B.e.</var>
                  duas quartas eſſe magno-
                    <lb/>
                  rum circulorum, extendendo poſtea
                    <var>.d.e.</var>
                  vſque ad interſectionem cum
                    <var>.A.C.</var>
                  &
                    <reg norm="eum" type="context">eũ</reg>
                    <lb/>
                  dem ordinem proſequendo, </s>
                  <s xml:id="echoid-s3159" xml:space="preserve">tunc
                    <var>.e.d.</var>
                  nobis oſtendet angulum
                    <var>.B.</var>
                  eſſe gra .40. mi .22
                    <lb/>
                  quæ erit eius vera quantitas. </s>
                  <s xml:id="echoid-s3160" xml:space="preserve">Cuius quidem rei experientiam poſſumus etiam fa-
                    <lb/>
                  cere, hoc modo, eſto, exempli gratia, quod nobis datus ſit angulus
                    <var>.C.</var>
                  graduum .57.
                    <lb/>
                  min .14. cum latere
                    <var>.A.C.</var>
                  gra .45. min .10. & latus
                    <var>.B.C.</var>
                  gra .89. min .30. </s>
                  <s xml:id="echoid-s3161" xml:space="preserve">Tunc ſi ordi-
                    <lb/>
                  nem .11. dicti lib. ſe quemur, obtinebimus intentum, hoc modo ſcilicet ſupponendo
                    <lb/>
                  in
                    <var>.A.</var>
                  polum, & non in
                    <var>.B.</var>
                  ducendo etiam
                    <var>.A.B.</var>
                  et
                    <var>.A.C.</var>
                  ſed
                    <var>.A.B.</var>
                    <reg norm="vſque" type="simple">vſq;</reg>
                  ad gra .90. du-
                    <lb/>
                  cendo poſtea
                    <var>.D.E.</var>
                  ita quod ab omni parte concurrat cum latere
                    <var>.B.C.</var>
                  producto, vn
                    <lb/>
                  de tam
                    <var>.f.C.B.F.</var>
                  quam
                    <var>.f.D.E.F.</var>
                  erunt ſemicirculi magnorum circulorum. </s>
                  <s xml:id="echoid-s3162" xml:space="preserve">quare
                    <var>.C.
                      <lb/>
                    D.</var>
                  nobis cognitus erit gra .44. min .50. & ſic etiam angulus
                    <var>.D.C.f.</var>
                  gra .57. min .14. ex
                    <lb/>
                  4. dicti lib. poſtea habebimus
                    <var>.F.l.</var>
                  gra .60. min .54. & angulum
                    <var>.f.</var>
                  gra .53. mi .24. aggre
                    <lb/>
                  gatum poſtea
                    <var>.f.C.</var>
                  cum
                    <var>.C.B.</var>
                  habebimus
                    <var>.f.B.</var>
                  gra .150. min .24. qui ſi a ſemicirculo
                    <reg norm="dem" type="context">dẽ</reg>
                    <lb/>
                  ptus fuerit, nobis remanebit
                    <var>.B.F.</var>
                  gra .29. mi .36. cum angulo
                    <var>.F.</var>
                  cognito
                    <reg norm="cum" type="context">cũ</reg>
                  ſit æqua-
                    <lb/>
                    <figure xlink:label="fig-0262-01" xlink:href="fig-0262-01a" number="295">
                      <image file="0262-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0262-01"/>
                    </figure>
                    <figure xlink:label="fig-0262-02" xlink:href="fig-0262-02a" number="296">
                      <image file="0262-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0262-02"/>
                    </figure>
                  lis
                    <var>.f.</var>
                  eius oppoſito. </s>
                  <s xml:id="echoid-s3163" xml:space="preserve">Vnde ex dicta .4. co-
                    <lb/>
                  gnoſcemus angulum
                    <var>.B.</var>
                  gra .40. min .31.
                    <lb/>
                  qui ferè æ qualis eſt ſuperiori iam inuen-
                    <lb/>
                  to, nec ab ipſo differt niſi per min .9. quæ
                    <lb/>
                  quidem differentia parua eſt reſpectu al­ </s>
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