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]

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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382370IO. BAPT. BENED. etiam collectus cum angulo .o.a.c. grad .15. hi tres anguli efficient angulum .d.a.c.
d. ctum grad .108. min .22.

Examinatio anguli .u.

Ducatur .d.n. quam quidem .d.n. cognoſcemus vt ſinus anguli .d.o.n. gra .45. nam
angulus ei contrapoſitus .q.o.p. eſt dimidium recti, quare .d.n. erit partium .70710.
talium qualium .d.o. fuerit .100000. ſed .d.o. eſt partium .115270. qualium .a.d. eſt .
100000. nam .e.d. vt ſinus anguli .e.a.d. gra .63. min .22. eſt partium .89389. o.e. ve-
ro eſt partium .50000. talium qualium .a.o. eſt .100000. vt ſinus anguli .e.a.o. gra .30.
ſed vt .a.o. eſt partium .51762. hoc eſt vt .a.d. eſt .100000. ipſa .o.e. erit partium .25881
quæ iuncta cum fuerit cum .e.d. efficiet .d.o. partium .115270. vt dictum eſt, quapro-
pter cum .d.n. ſit partium .70710. talium qualium .d.o. fuerit .100000. ipſa .d.n. erit
partium .81507. talium qualium .d.o. erit .115270. ideſt qualium .d.a. vel .d.u. erit
100000. quæ quidem .d.n. eſt ſinus anguli .d.u.n. graduum ſcilicet .54. 36. cuius du-
plum erit gra .109. mi .12. debebattamen eſſe .108. m.o.

Examinatio anguli .d.

Accipe angulum .a.d.o. gra .26.

424[Figure 424] min .38. vt ſupra, cui applica angu-
lum .o.d.n. gra .45. min .o. ſimul cum
angulo .u.d.n. reſiduo ex recto gra
duum .35. minu .24. & conficies an-
gulum .a.d.u. grad .107. minu .2. &
habebis propoſitum, quem tamen
oportebat eſſe gra .108. min .o.

Quod autem omnia rectè ſuppu-
tata ſint, ex ſumma omnium angulo
rum patere poteſt. nam collectis om
nibus quinque angulis .a.c.d.f.u. ſi-
mul, hoc eſt grad .108. minu .22. cum
gra .107. min .2. cum grad .12. effi-
cient grad .540. min .o. ſumma æqua
lis ſex angulis rectis.

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