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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342330IO. BAPT. BENED.

QVAEDAM NOTATV DIGNA IN
Ptolomeum.

Bartolomeo Christino Serenißimi Sabaudiœ Ducis apparitore.

EX tuis literis cognoui quo erga me animo eſſes, qualique; voluntate, ſed ne
tua pulcherrima ſtudia aliquo modo imperfecta relinquantur, vel ego tibi
deeſſe videar, dum Problemata geographica Magni Ptolomei conſi-
deras, aduerte, quod ſi putares in figura .6. cap. libr .7. geographię eiuſ-
dem (vt multi credunt) lineam .V.*. ſecare circunferentiam .A.D. in puncto .G. ita
vt punctus .G. ſit tropici æſtiui, ideſt arcum .D.G. eſſe graduum .24. cum illis inci-
deres in maximum errorem. Quapropter conſidera quæ nunc tibi ſcribo.

Sit circulus .A.B.C.D. huius centrum .E. ſupponaturque; ſemidiameter .E.D. eſſe
partium 120. quarum .E.Z. in alio ſemidiametro .C.E. ei orthogonaliter coniuncto,
talium ſit .17. in ſemidiametro vero .E.A. accipiatur .E.S. talium .24. et .E.V. 64. vn
de .S.V. erit partium 40. ſimilium.

Erigatur deinde .S.*. ad rectos cum .E.A. in puncto .S. quæ terminetur ab inter-
ſectione lineę ductæ per puncta .Z.D. in puncto .*. ducatur demum .V.*. quæ ſeca-
bit circunf rentiam .A.D. in puncto .G. Quæratur nunc quantitas ipſius .G.D.
Ad quod efficiendum quærenda primum eſt quantitas ipſius .S.*. quam illico co
gnoſcemus ex regula de tribus, cum dixerimus, ſi@ 17. dat nobis .120. quid dabit .41.
(nam duo triangula .Z.E.D. et .Z.S.*. ſunt inuicem ſimilia, cum .S.*. parallela ſit
ipſi .E.D.) vnde .S.*. proueniet nobis ex ſimilibus partibus .289. cum fracto, quod
reijciamus ob minorem laborem.

Producantur poſtea .V.*. et .E.D. vſque ad eorum concurſum in puncto .ω. quæ-
remusque; quanta ſit .E.ω. ex eadem regula, cum dixerimus, ſi .40. dat nobis .289. quid

366[Figure 366]

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