Bibliotheca Polyglotta

1. A rectilineal figure is said to be inscribed in a rectilineal figure when the respective angles of the inscribed figure lie on the respective sides of that in which it is inscribed.

I. FIGVRA rectilinea in figura rectilinea inscribi dicitur, cum singuli eius figuræ, quæ inscribitur, anguli singula latera eius, in qua inscribitur, tangunt.

第一界
直線形。居他直線形內。而此形之各角。切他形之各邊。為形內切形。
此卷將論切形在圜之內、外。及作圜在形之內、外。故解形之切在形內、及切在形外者。先以直線形為例。如前圖丁戊己角形之丁、戊、己、三角。切甲乙丙角形之甲乙、乙丙、丙甲、三邊。則丁戊己為甲乙丙之形內切形。如後圖。癸子丑角形。難癸、子、兩角。切庚辛壬角形之庚辛、壬庚、兩邊。而丑角、不切辛壬邊。則癸子丑、不可謂庚辛壬之形內切形。

2. Similarly a figure is said to be circumscribed about a figure when the respective sides of the circumscribed figure pass through the respective angles of that about which it is circumscribed.

II. SIMILITER & figura circum figuram describi dicitur, cum singula eius, quæ circumscribitur, latera singulos eius figuræ angulos tetigerint, circum quam illa describitur.

第二界
一直線形。居他直線形外。而此形之各邊。切他形之各角。為形外切形。
(p. 一八八)如第一界圖、甲乙丙、為丁己戊之形外切形。　其餘各形。倣此二例。

3. A rectilineal figure is said to be inscribed in a circle when each angle of the inscribed figure lies on the circumference of the circle.

III. FIGVRA rectilinea in circulo inscribi dicitur, cum singuli eius figuræ, quæ inscribitur, anguli tetigerint circuli peripheriam.

第三界
直線形。之各角。切圜之界。為圜內切形。
甲乙丙形之三角。各切圜界於甲、於乙、於丙、是也。

4. A rectilineal figure is said to be circumscribed about a circle, when each side of the circumscribed figure touches the circumference of the circle.

IV. FIGVRA vero rectilinea circa circulum describi dicitur, cum singula latera eius, quæ circumscribitur, circuli peripheriam tangunt.

第四界
直線形之各邊。切圜之界。為圜外切形。
甲乙丙形之三邊、切圜界於丁、於己、於戊、是也。

5. Similarly a circle is said to be inscribed in a figure when the circumference of the circle touches each side of the figure in which it is inscribed.

V. SIMILITER & circulus in figura rectilinea inscribi dicitur, cum circuli peripheria singula latera tangit eius figuræ, cui inscribitur.

第五界
圜之界。切直線形之各邊。為形內切圜。
同第四界圖

6. A circle is said to be circumscribed about a figure when the circumference of the circle passes through each angle of the figure about which it is circumscribed.

VI. CIRCVLVS autem circum figuram describi dicitur, cum circuli peripheria singulos tangit eius figuræ, quam circumscribit, angulos.

第六界
圜之界。切直線形之各角。為形外切圜。
同第三界圖

7. A straight line is said to be fitted into a circle when its extremities are on the circumference of the circle.

VII. RECTA linea in circulo accommodari, seu coaptari dicitur, cum eius extrema in circuli peripheria fuerint.

第七界
直線之兩界。各抵圜界。為合圜線。
甲乙線兩界。各抵甲乙丙圜之界。為合圜線。若丙抵圜而丁不至。及戊之兩俱不至。不為合圜線。

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