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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IO. BAPT. BENED.
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                <p>
                  <s xml:id="echoid-s2951" xml:space="preserve">
                    <pb o="236" rhead="IO. BAPT. BENED." n="248" file="0248" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0248"/>
                  tali ſitu epicycli ſit baſis vnius trianguli orthogonij, cuius vnum ex illis duobus late-
                    <lb/>
                  ribus eſt ſemidiameter eccentrici partium .60. pręcisè, aliud eſt interuallum eccen-
                    <lb/>
                  tricitatis partium .6. eiuſmodi. </s>
                  <s xml:id="echoid-s2952" xml:space="preserve">Angulus ergo
                    <var>.i.o.c.</var>
                  vt dixi, erit partium .40. minu
                    <num value="55">.
                      <lb/>
                    55.</num>
                  qui angulus continuò variatur ſecundum ſitum epicycli. </s>
                  <s xml:id="echoid-s2953" xml:space="preserve">& cum centrum
                    <lb/>
                  eius eſt in auge eccentrici. eſt minimus
                    <reg norm="quam" type="context">quã</reg>
                  eſſe poſſit. </s>
                  <s xml:id="echoid-s2954" xml:space="preserve">
                    <reg norm="eſtque" type="simple">eſtq́;</reg>
                  tantum grad .36. min
                    <num value="46">.
                      <lb/>
                    46.</num>
                  & in oppoſito ipſius augis eſt grad .47. min .1. maximus quam alibi vnquam ſit,
                    <lb/>
                  & ſic continuò variatur, ſecundum ſitum, quem habet epicyclus in eccentrico. </s>
                  <s xml:id="echoid-s2955" xml:space="preserve">Qui
                    <lb/>
                  quidem angulus inuenitur per doctrinam .27. et .28. libri primi Monteregij de trian
                    <lb/>
                  gulis. </s>
                  <s xml:id="echoid-s2956" xml:space="preserve">Nam triangulus
                    <var>.c.i.o.</var>
                  eſt ſemper rectangulus in puncto
                    <var>.i.</var>
                  & latus
                    <var>.c.i.</var>
                  reſpectu
                    <lb/>
                  ſemidiametri eſt datum. </s>
                  <s xml:id="echoid-s2957" xml:space="preserve">Quod
                    <var>.c.i.</var>
                  erit veluti partium .39. cum dimidia, et dictum
                    <lb/>
                  interuallum
                    <var>.o.c.</var>
                  veluti pat
                    <unsure/>
                  cium .60. min .18. & quia datur nobis etiam eccentricitas
                    <lb/>
                  veluti partium .60. talium, & cum
                    <var>.c.o.</var>
                  ſit linea veri motus epicycli, & latus ſimiliter
                    <lb/>
                  vnius trian guli, cuius duo latera ſunt ſupradicta, ſcilicet ſemidiameter eccentrici, &
                    <lb/>
                  eccentricitas, inter ſe compræhendentes angulum datum. </s>
                  <s xml:id="echoid-s2958" xml:space="preserve">Nam ſemper præſuppo
                    <lb/>
                  nitur datus locus centri ipſius epicycli, cum ipſe eſt extra augem aut oppoſitum eius
                    <lb/>
                  quia in auge linea
                    <var>.o.c.</var>
                  conſtat ex ſemidiametro eccentrici & interualli eccentricita-
                    <lb/>
                  tis. </s>
                  <s xml:id="echoid-s2959" xml:space="preserve">& in eius oppoſito, ipſa linea
                    <var>.o.c.</var>
                  eſt minor dicto ſemidiametro eccentrici per in
                    <lb/>
                  teruallum dictæ eccentricitatis. </s>
                  <s xml:id="echoid-s2960" xml:space="preserve">Vnde etiam poſſumus extra augem, vel oppoſitum
                    <lb/>
                  eius cognoſcere
                    <var>.o.c.</var>
                  tanquam latus dicti trianguli duorum laterum
                    <reg norm="cum" type="context">cũ</reg>
                  angulo cogni
                    <lb/>
                  torum. </s>
                  <s xml:id="echoid-s2961" xml:space="preserve">
                    <reg norm="Idque" type="simple">Idq́;</reg>
                  per .49. propoſitionem libri primi
                    <reg norm="eiuſdem" type="context">eiuſdẽ</reg>
                  Monteregij cum ſcilicet dictus
                    <lb/>
                  angulus
                    <reg norm="non" type="context">nõ</reg>
                  fuerit rectus. </s>
                  <s xml:id="echoid-s2962" xml:space="preserve">Nam ſi fuerit rectus videbitur per .27. et .28. ſupra citatas.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2963" xml:space="preserve">Cum igitur hab eamus angulum
                    <var>.c.o.i.</var>
                  gra .40. mi .55. angulus
                    <var>.o.c.i.</var>
                  tanquam reli-
                    <lb/>
                  quus exrecto, erit grad .49. mi .5. cui reſpondet arcus
                    <var>.i.g.</var>
                  epicycli confectus à Marte
                    <lb/>
                  in diebus circiter .105. ad rationem min .28. aut circiter in ſingulos dies, prætermiſ-
                    <lb/>
                  ſis nunc quidem minutijs cum exigui momenti ſit error .15. aut .20. dierum ad verifi
                    <lb/>
                  cationem longæ morę Martis in vno duodecatemorio, atque per hoc tempus cen-
                    <lb/>
                  trum epicycli conficit gradus .55. min .7. aut circiter, ad rationem minutorum .31.
                    <reg norm="cum" type="context">cũ</reg>
                    <lb/>
                  dimidio in ſingulos dies. qui numerus graduum .55. min .7: differt à numero
                    <reg norm="graduum" type="context">graduũ</reg>
                  .
                    <lb/>
                  40. min .55. maximæ æquationis argumenti gradibus .14. mi .12. nec refert quod gra
                    <num value="55">.
                      <lb/>
                    55.</num>
                  min .7. habeant reſpectum ad centrum æquantis, magis quam ad centrum
                    <reg norm="mundi" type="context">mũdi</reg>
                  ,
                    <lb/>
                  quia differentia non eſt tanta, vt poſſit inducere errorem menſium. </s>
                  <s xml:id="echoid-s2964" xml:space="preserve">Hinc ſequitur
                    <lb/>
                  quod in fine dictorum dierum .105. </s>
                  <s xml:id="echoid-s2965" xml:space="preserve">Mars erit in linea
                    <var>.o.c.</var>
                  veri motus epicycli, ſed
                    <lb/>
                  gradibus .14. min .12. vlterius quam in primo loco, in quo erat in Zodiaco, & erit in
                    <lb/>
                  medio ſuæ retrogradationis. </s>
                  <s xml:id="echoid-s2966" xml:space="preserve">Sed quoniam Mars manifeſtè retrogradi non incipit
                    <lb/>
                  in puncto
                    <var>.i.</var>
                  conting entiæ, imo ab illo puncto vſque ad terminum primæ ſtationis li
                    <lb/>
                  neæ
                    <var>.o.n.</var>
                  interponitur arcus
                    <var>.i.n.</var>
                  epicycli, qui eſt graduum .32. minu .14. </s>
                  <s xml:id="echoid-s2967" xml:space="preserve">
                    <reg norm="Idque" type="simple">Idq́;</reg>
                  cogno-
                    <lb/>
                  ſcitur ſubtrahendo arcum
                    <var>.f.i.n.</var>
                  graduum .163. mi .9. qui eſt inter augem, & primam
                    <lb/>
                  ſtationem, à gradibus .180. ( qui arcus
                    <var>.f.i.n.</var>
                  erit verum argumentum, quod ſi-
                    <lb/>
                  militer variatur ſecundum ſitum epicycli, etſi eiuſmodi varietas, nobis
                    <reg norm="non" type="context">nõ</reg>
                  eſt magni
                    <lb/>
                  momenti, vnde poſſumus præſupponere, quod
                    <var>.c.</var>
                  centrum epicycli non alteret
                    <reg norm="in- teruallum" type="context">in-
                      <lb/>
                    teruallũ</reg>
                    <var>.c.o.</var>
                  à centro
                    <reg norm="mundi" type="context">mũdi</reg>
                  ,
                    <reg norm="cum" type="context">cũ</reg>
                  non posſit intercedere, error
                    <reg norm="menſium" type="context context">mẽſiũ</reg>
                  reliquum verò
                    <var>.g.
                      <lb/>
                    n.</var>
                  graduum .16. min .51. ſubtrahendo ex arcu
                    <var>.g.i.</var>
                  graduum .49. minuti .5. vnde reli-
                    <lb/>
                  quus nobis erit arcus
                    <var>.n.i.</var>
                  graduum .32. min .14. in eiuſmodi tamen ſitu mediocrium
                    <lb/>
                  longitudinum. </s>
                  <s xml:id="echoid-s2968" xml:space="preserve">Nunc hic arcus epicycli graduum .32. mi .14. fit à ſtella Martis die-
                    <lb/>
                  bus .69. ad rationem ſupradictam, omittendo quod ipſa ſtella habeat reſpectum ad
                    <lb/>
                  augem mediocrem epicycli, & quod dicta aux mediocris mutet diſtantiam à vera
                    <lb/>
                  propter motum epicycli, quod nunc quidem parui refert, in quibus diebus .69. cen- </s>
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