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Clavius, Christoph, Johannes de Sacrobosco, and Giovanni Battista Ciotti. Christophori[i] Clavii Bambergensis Ex Societate Iesv in Sphaeram Ioannis De Sacro Bosco Commentarivs. Venetiis: Ciottus, 1603. Print.
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Full text: Clavius, Christoph: Christophori[i] Clavii Bambergensis Ex Societate Iesv In Sphaeram Ioannis De Sacro Bosco Commentarivs

Other titles:
In Sphaeram Ioannis de Sacro Bosco Commentarius
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https://dlc.mpg.de/image/88386665X/5/
Ioan. de Sacro Boſco.

74. THEOR 4. PROPOS. 4.

A rea cuiuslibet circuli æqualis eſt rectangulo comprehenſo ſub ſe-
midiametro, & dimidiata circunferentia circuli.

E sto circulus A B C, cuius ſemidiameter D B: Rectangulum autem

[figure]

D B E F, comprehenſum ſub D B, ſemidiametro circuli, & B E, recta, quæ æ-
qualis ſit dimidiatæ circun ferentiæ circuli. Dico aream circuli. A B C, æqualem
eſſe rectangulo D B E F, Producatur enim B E, in continuum. ponatur\'que E G,
æqualis ipſi B E, ut ſit B G, recta æqualis toti circunferentiæ circuli. Coniun-
gantur denique puncta D, G, recta D G. Quoniam igitur (per 1. propoſ. Archi-
medis de Dimenſione circuli) circulus A B C, æqualis eſt triangulo D B G: Eſt au
tem triangulũ D B G, rectangulo D B E F, æquale, ut in ſcholio propoſ. 41. lib. 1.
Eucl. demonſtrauimus. quòd baſis trianguli dupla ſit baſis rectanguli; (Id quod
ətiam ex demonſtratione antecedentis propoſ. liquet, ubi oſtendimns, triangulum
D E F, æquale eſſe rectangulo D E H I: (erit quoque circulus A B C, rectangu-
lo D B E F, æqualis, Area ergo cuiuslibet circuli æqualis eſt rectangulo, &c. quod
oſtendendum erat.

75. THEOR. 5. PROPOS. 5.

I n omni triangulo rectangulo, ſi ab uno acutorum angulorum ut-
cunque ad latus oppoſitum linea recta ducatur, erit maior proportiò hu-
ius lateris ad eius ſegmentum, quod prope angulum rectum existit, quam
anguli acuti prædicti ad eius partem dicto ſegmento lateris oppoſi-
tam.

S it triangulum rectangulum A B C, cuius angulus C, ſit rectus; duca-

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