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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381369EPISTOL AE. gentiæ gratia cogita ſilum illum (exempli adducti ab illis doctiſſimis viris) cui pon
dus appenſum eſt, æqualem eſſe axi orizontis, hoc eſt eius extremitatem immobi-
lem eſſe in primo mobili, & in ipſo zenit tui orizontis,
tunc arcus motionis ipſius la
pidis per tantum interuallum, quantum eſt diameter terræ, inſenſibiliter differret à
linea recta, & cum lapis diſtans à centro mundi per ſemidiametrum terræ, iret re-
diretque;, vt ſcis, ergo idem faceret ſi ſilum longius eſſet per dictum terræ ſemidia-
metrum, ita vt poſſetipſum centrum attingere, nam differentia illa ſemidiametri
terræ, ferè nulla eſt reſpectu ſemidiametri ipſius primi mobilis.
AN PENTAGONVS AB ALBERTO DVRERO
deſcriptus æquiangulus ſit.
Conrado Neubart.
SI non credis Pentagonum ab Alberto Durero ſuper datam lineam deſi-
gnatum, æquiangulum non eſſe.
Fingamus hic ſubiectam ſiguram ſimi-
lem ei quæ à Durero ponitur, in qua primò, ducta ſit linea .o.a. & habe
bimus angulum .a.o.b. graduum .60. talium qualium duo recti fuerint gra .
360.
vel .30. talium qualium duo recti fuerint .180. nam ex ſuppoſito, arcus .a.b. eſt
ſexta pars totius circunferentiæ, angulus vero .b.o.d. rectus eſt, eo quod .b.o.q. rectus
etiam ſit,
quare angulus .d.o.a. reſiduus ex recto erit graduum .60. talium, ut rectus
eſt .90. angulus verò .o.a.c. erit gra .15. eorundem.
Ducatur deinde perpendicularis .a.e. ad .o.d. quæ vt ſinus anguli .a.o.e. erit par-
tium .86602. talium qualium .a.o. erit .100000. quæ quidem .o.a. vt chorda arcus .a.
o.
eſt partium .51762. talium qualium .a.d. vel .a.c. ſemidiameter eſt .100000.
Nam ſinus dimidij arcus .a.o. (exi
ſtente .a.o. graduum .30.) eſt partium .
423[Figure 423] 25881.
ex quo .a.e. erit partium .
44827.
talium qualium .a.d. erit
100000. vnde angulus .a.d.o. cuius ſi
nus eſt .a.e. erit graduum .26. min .38
qui quidem angulus, ſumptus cum an
gulo .a.o.d. erit gra .86. min .38.
Dem
pta denique hac ſumma ex duobus
rectis gra .180. reliquum erit gra .93.
min .22. ideſt angulus .o.a.d. cui addi
tus cum fuerit angulus .o.a.c. gra .15.
talium, habebimus angulum .c.a.d.
graduum .108. min .22. exuperantem
verum angulum pentagoni per min .
22.
vel ſic, cum inuentus fuerit angu-
lus .a.d.o. gra .26. min .38. ſi ex vno re
cto demptus fuerit, relinquetur an-
gulus .d.a.e. gra .63. min .22. qui qui-
dem collectus cum fuer it cum angu-
lo .e.a.o. reſiduo ex re cto dempto angulo .a.o.e. grad .60. qui .e.a.o. eſt grad .30. &

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