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]

Page concordance

< >
Scan Original
261 249
262 250
263 251
264 252
265 253
266 254
267 255
268 256
269 259
270 258
271 259
272 260
273 261
274 222
275 263
276 264
277 265
278 266
279 267
280 268
281 269
282 270
283 271
284 272
285 273
286 274
287 275
288 276
289 277
290 278
< >
page |< < (250) of 445 > >|
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <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"/>
              </div>
              <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>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum