## Full text: Volumen secundum. Opera geometrica. Opera astronomica. Varia de optica. (2)

Ex his manifeſtus eſt Orontii Finei error, qui circumfe-
rentiæ quadrantem æqualem minori duarum proportione me-
diarum inter inſcripti & circumſcripti quadrati latera prodi-
dit, circulum vero æqualem quadrato quod fieret à majori.

## 41. Theor . XII. Prop . XV.

S I inter productam circuli diametrum & circum-
ferentiam recta aptetur radio æqualis, & pro-
ducta circulum ſecet, occurr atque tangenti circulum
ad alterum diametri terminum: Intercipiet eapar-
tem tangentis arcu adjacente abſciſſo majorem.

Eſto deſcriptus circulus centro C, cujus diameter A B. Hæc autem producatur verſus A, interque ipſam & cir-
cumferentiam ponatur E D recta radio A C æqualis. Quæ
producta ſecet circumferentiam in F, occurratque tangenti
in G, ei nimirum quæ circulum contingit ad diametri ter-
minum B. Dico tangentem B G majorem eſſe arcu B F. Ducatur enim per centrum recta H L parallela E G, quæ
circumferentiæ occurrat in punctis H, M: tangenti vero B G
in L Et jungatur D H, quæ diametrum ſecet in K. Simi-
les itaque ſunt trianguli E D K, C H K, quoniam angu-
los ad K æquales habent, & angulum E æqualem angulo
C. Sed & latus E D æquale eſt lateri H C, ſuntque hæc
latera æqualibus angulis ſubtenſa. Ergo æquale etiam latus
D K lateri K H. Itaque C A ſecat bifariam ipſam D H,
itemque arcum D A H. Arcus igitur D H ſive huic æqua-
lis F M duplus eſt ad arcum A H. Ipſi autem A H æqua-
lis eſt arcus M B. Igitur arcus F B triplus erit ad arcum
A H. Porro quoniam H K ſinus eſt arcus H A, ejuſdem-
que tangenti æquatur L B, erunt duæ tertiæ H K & triens
L B ſimul majores arcu A H . Quare ſumptis omnium tri- plis erit dupla H K, hoc eſt, H D ſive G L una cum L B
major arcu A H triplo, hoceſt, arcu F B. Apparet igitur
totam G B arcu F B majorem eſſe.

TAB. XXXIX.
Fig. 7.
per 9. huj.

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