Bibliotheca Polyglotta

Euclid: Elementa

eng

And it is manifest that, when the centre of the circle falls within the triangle, the angle BAC, being in a segment greater than the semicircle, is less than a right angle; when the centre falls on the straight line BC, the angle BAC, being in a semicircle, is right; and when the centre of the circle falls outside the triangle, the angle BAC, being in a segment less than the semicircle, is greater than a right angle. [III. 31]

lat Clavius

HINC manifestum est, si centrum intra triangulum cadat,¹ omnes angulos esse acutos, quoniam omnes sunt in maiori segmento circuli: si vero sit in latere BC,² angulum BAC, ei lateri oppositum, esse rectum, quod sit in semicirculo: si denique cadat extra triangulum,³ angulum oppositum BAC, obtusum esse, cum sit in minori segmento circuli.

1. 31. tertij. 2. 31. tertij. 3. 31. tertij.

kin 幾何原本 p. 196

一系。若圜心在三角形內。卽三角形為銳角形。何者。每角在圜大分之上故。若在一邊之上。卽為直角形。若在形外。卽為鈍角形。

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