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">
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                <p>
                  <s xml:id="echoid-s3106" xml:space="preserve">
                    <pb o="246" rhead="IO. BAPT. BENED." n="258" file="0258" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0258"/>
                  præciſe ideſt interuallum inter centrum mundi, & centrum epicycli Martis in huiuſ-
                    <lb/>
                  modi ſitu.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3107" xml:space="preserve">Fingemus igitur eccenticum Martis ſignificatum per
                    <var>.p.c.m.</var>
                  cuius centrum ſit
                    <var>.r.</var>
                    <lb/>
                  & lineam augis
                    <var>.p.r.o.m.</var>
                  in qua
                    <reg norm="centrum" type="context">centrũ</reg>
                  mundi ſit
                    <var>.o.</var>
                  centrum autem verum epicycli,
                    <lb/>
                  comprehendatur ab angulo
                    <var>.p.o.c.</var>
                  qui ſit graduum .151. min .30. ſecundum ſuppoſi-
                    <lb/>
                  tum. </s>
                  <s xml:id="echoid-s3108" xml:space="preserve">Quare in puncto
                    <var>.c.</var>
                  erit centrum epicycli. </s>
                  <s xml:id="echoid-s3109" xml:space="preserve">Imaginemur ergo
                    <var>.c.o.</var>
                  productam à
                    <lb/>
                  parte
                    <var>.o.</var>
                  quouſque ab
                    <var>.r.</var>
                  centro deferentis veniat linea
                    <var>.r.k.</var>
                  perpendiculariter, faciens
                    <lb/>
                  angulum rectum in puncto. k & quoniam angulus
                    <var>.r.o.c.</var>
                  datur nobis graduum .151.
                    <lb/>
                  min .30. ideo cognoſcemus angulum
                    <var>.r.o.k.</var>
                  tanquam reliquum ex duobus rectis, qui
                    <lb/>
                  erit gra .28. min .30. & ſimiliter angu-
                    <lb/>
                    <figure xlink:label="fig-0258-01" xlink:href="fig-0258-01a" number="293">
                      <image file="0258-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0258-01"/>
                    </figure>
                  lum
                    <var>.o.r.k.</var>
                  tanquam reſiduum vnius
                    <lb/>
                  recti, qui erit gra .61. min .30. cuius ſi-
                    <lb/>
                  nus ideſt
                    <var>.o.k.</var>
                  erit partium .8788 1. et
                    <var>.k.
                      <lb/>
                    r.</var>
                  vt ſinus anguli
                    <var>.r.o.k.</var>
                  partium .47715
                    <lb/>
                  talium qualium
                    <var>.o.r.</var>
                  eſſet 100000. ſed
                    <lb/>
                  vt
                    <var>.o.r.</var>
                  eſt .6. latus
                    <var>.o.k.</var>
                  erit .5. & min .16
                    <lb/>
                  et
                    <var>.r.k.</var>
                  partium .2. min .52. & quia
                    <var>.r.c.</var>
                    <lb/>
                  cſt
                    <reg norm="partium" type="context">partiũ</reg>
                  60. eiuſmodi, ſi ab eius qua-
                    <lb/>
                  drato ſubtractum fuerit quadratum ip
                    <lb/>
                  ſius
                    <var>.r.k.</var>
                  reliquum erit nobis
                    <reg norm="quadratum" type="context">quadratũ</reg>
                    <lb/>
                  ipſius
                    <var>.k.c.</var>
                  cuius radix, ideſt
                    <var>.k.</var>
                  erit par-
                    <lb/>
                  tium .59. min .56. à qua
                    <var>.c.k.</var>
                  ſubtrahen-
                    <lb/>
                  do poſtea
                    <var>.k.o.</var>
                  partium .5. minu .16. re-
                    <lb/>
                  manebit
                    <var>.o.c.</var>
                  partium .54. min .40. pro
                    <lb/>
                  diſtantia quæſita.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3110" xml:space="preserve">Fingamus poſtea epicyclum
                    <var>.f.n.g.</var>
                    <lb/>
                  in quo argumentum verum graduum
                    <num value="149">.
                      <lb/>
                    149.</num>
                  minu .39. ſit arcus
                    <var>.f.n.</var>
                  vbi Mars inueniatur in
                    <var>.n.</var>
                  per quem punctum tranſeat li-
                    <lb/>
                  nea
                    <var>.o.n.</var>
                  veri motus Martis. </s>
                  <s xml:id="echoid-s3111" xml:space="preserve">Deinde inueniamus angulum
                    <var>.c.o.n.</var>
                  æquationis
                    <reg norm="argumem" type="context">argumẽ</reg>
                    <lb/>
                  ti, modo iam dicto, ideſt ducendo ſinum
                    <var>.n.h.</var>
                  arcus
                    <var>.n.g.</var>
                  qui arcus tanquam reliquus
                    <lb/>
                  argumenti veri, iam præſuppoſiti, ex dimidio circulo, erit graduum 30. minu .21. &
                    <lb/>
                    <var>n.h.</var>
                  eius ſinus partium .50528. ſinus ſimiliter anguli
                    <var>.n.c.h.</var>
                  et
                    <var>.c.h.</var>
                  tanquam ſinus an-
                    <lb/>
                  guli
                    <var>.c.n.h.</var>
                  reſtantis ex uno recto grad .59. minu .39. erit partium .86295.
                    <reg norm="talium" type="context">taliũ</reg>
                  qua-
                    <lb/>
                  lium
                    <var>.c.n.</var>
                  ſinus totus eſſet partium .100000. ſed vt partium .39. & min .30. ſinus
                    <var>.c.h.</var>
                    <lb/>
                  erit partium .34. min .5. et
                    <var>.n.h.</var>
                  partium .19. mi .57. reliquum poſtea
                    <var>.h.o.</var>
                  ex
                    <var>.o.c.</var>
                  par-
                    <lb/>
                  tium .20. min .35. quia iam ſupra inuenimus
                    <var>.o.c.</var>
                  eſſe partium eiuſmodi .54. minu .40.
                    <lb/>
                  vnde
                    <var>.o.n.</var>
                  vt radix quadrata ſummæ duorum
                    <var>.n.h.</var>
                  et
                    <var>.h.o.</var>
                  erit partium .28. minu .41.
                    <lb/>
                  talium qualium
                    <var>.n.h.</var>
                  inuenta fuit partium .19. min .57. quæ
                    <var>.n.h.</var>
                  erit poſtea partium,
                    <lb/>
                  69552. talium qualium
                    <var>.n.o.</var>
                  partium .100000. & ſumpta dicta
                    <var>.n.h.</var>
                  vt ſinus dictarum
                    <lb/>
                  partium, dabit nobis angulum
                    <var>.n.o.h.</var>
                  quæſitum gra .44. min .4. qui per tabulas Alfon
                    <lb/>
                  ſi inuentus eſt gra .44. min .2. par huic, vt dici poteſt. </s>
                  <s xml:id="echoid-s3112" xml:space="preserve">Quiangulus gra .44. minu .4.
                    <lb/>
                  collectus cum angulo veri centri iam ſuppoſito graduum .151. minu .20. & cum an-
                    <lb/>
                  gulo augis eccentrici Martis, ſimiliter ſuppoſitæ grad .135. min .5. dabit nobis ſum-
                    <lb/>
                  mam veræ diſtantiæ Martis à principio Arietis grad .330. min .29. quod aliud non
                    <lb/>
                  ſignificat, niſi quod Mars inuenietur in minu .29. primi gradus Piſcium. </s>
                  <s xml:id="echoid-s3113" xml:space="preserve">Et Stofle-
                    <lb/>
                  rus in ſuis ephemeridibus ponit eum in .22. minuto dicti primi gradus, cuius diffe- </s>
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