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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<
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xml:space
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">QVod diebus præteris tibi ſignificaui, idem nunc confirmo, ſcilicet ſphærico-
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rum triangulorum operationem ſæpe nos fallere, vt exempli gratia, ſi pro
<
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poſitus nobis fuiſſet triangulus
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cuius angulus
<
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nobis datus eſſet graduum
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114.</
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mi
<
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& eius latus
<
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var
>
B, graduum .67. min .5. & latus
<
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>
graduum .45. mi .10.
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ſi reliquos angulos cum tertio latere etiam cognoſcere voluerimus, ex methodo .11
<
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primi Copernici propoſitum obtinebimus. </
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<
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eſſet graduum .89. min
<
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value
="
30
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<
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30.</
num
>
angulus vero
<
var
>.C.</
var
>
graduum .57. min .14. angulus autem
<
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var
>
grad .48. min .38. </
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re vltimus hic angulus
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falſus eſſet, eo quod operatio paruorum triangulorum in
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cauſa eſt, quotieſcunque eorum latera tam breuia ſint, ut non eccedant vnum gra-
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dum, quare ipſorum angulorum veram quantitatem non tribuunt. </
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<
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cum voluerimus veram
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ipſius anguli
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oportet poſt quam inuenerimus
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angulum
<
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var
>
mediante arcu
<
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ſupponere alium polum in
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deinde producere. </
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A. vſque ad
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et
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vſque ad
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var
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imaginando
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et
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duas quartas eſſe magno-
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rum circulorum, extendendo poſtea
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vſque ad interſectionem cum
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>
&
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dem ordinem proſequendo, </
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nobis oſtendet angulum
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eſſe gra .40. mi .22
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quæ erit eius vera quantitas. </
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<
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cere, hoc modo, eſto, exempli gratia, quod nobis datus ſit angulus
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>
graduum .57.
<
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min .14. cum latere
<
var
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>
gra .45. min .10. & latus
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>
gra .89. min .30. </
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nem .11. dicti lib. ſe quemur, obtinebimus intentum, hoc modo ſcilicet ſupponendo
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in
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polum, & non in
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ducendo etiam
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et
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ſed
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ad gra .90. du-
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cendo poſtea
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ita quod ab omni parte concurrat cum latere
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producto, vn
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de tam
<
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quam
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erunt ſemicirculi magnorum circulorum. </
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<
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D.</
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nobis cognitus erit gra .44. min .50. & ſic etiam angulus
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gra .57. min .14. ex
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4. dicti lib. poſtea habebimus
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gra .60. min .54. & angulum
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gra .53. mi .24. aggre
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gatum poſtea
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cum
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habebimus
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gra .150. min .24. qui ſi a ſemicirculo
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ptus fuerit, nobis remanebit
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gra .29. mi .36. cum angulo
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cognito
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ſit æqua-
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lis
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eius oppoſito. </
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gnoſcemus angulum
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gra .40. min .31.
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qui ferè æ qualis eſt ſuperiori iam inuen-
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to, nec ab ipſo differt niſi per min .9. quæ
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quidem differentia parua eſt reſpectu al </
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