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

VERA CIRCULI proportionalia, & ex prædictis ſatis facile colligi poteſt
trapezium A I L P eſſe dimidium polygoni A B D L P & trapezium A I O P eſſe dimidium polygoni A B E I O P
& triangulum A I P eſſe dimidium trapezii A B I P: & proinde terminos duplicando, polygonum A B D L P, po-
lygonum A B E I O P & trapezium A B I P ſunt continuè
proportionalia, quod demonſtrare oportuit.

Ducantur rectæ C G, K N, ſegmentum tangentes in
punctis E, O, & rectis D L, D B, L P, occurrentes in
punctis C, G, K, N, ut compleatur polygonum
A B C G K N P.

## 69.PROP. V. THEOREMA.

Dico trapezium A B I P & polygonum A B E I O P
ſimul, eße ad polygonum A B E I O P, ut
duplum polygoni A B E I O P ad poly-
gonum A B C G K N P.

### 69.1.

TAB. XLIII.
Fig. 1. 2. 3.

Ex hujus tertia manifeſtum eſt triangulum A B I & tra-
pezium A B E I ſimul, eſſe ad trapezium A B E I,
ut duplum trapezii A B E Iad polygonum A B C G I: & ex prædictis facile concludi poteſt triangulum A B I eſſe di-
midium trapezii A B I P, & trapezium A B E I eſſe dimi-
dium polygoni A B E I O P, & polygonum A B C G I
eſſe dimidium polygoni A B C G K N P; & proinde termi-
nos duplicando, trapezium A B I P & polygonum A B E I O P
ſimul, erunt ad polygonum A B E I O P ut duplum polygo-
ni A B E I O P ad polygonum A B C G K N P, quod
demonſtrandum erat.

Hinc facile colligi poteſt polygonum A B C G K N P
eſſe medium harmonicum inter polygona A B E I O P,
A B D L P, quod hic admonuiſſe ſufficiat, in ſequentibus
enim demonſtrabitur.

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