Iisdem poſitis ducantur rectæ F E, L E, hyperbolam tan-
11TAB. XLIII.
fig. 4. gentes in punctis F, L, ut compleatur trapezium A F E L,
quod dico eſſe medium harmonicum inter parallelogramma
P D M L, F D M K. triangulum A F L, trapezium A F G L,
& medium harmonicum inter parallelogramma P D M L,
F D M K, ſunt continuè proportionalia, quoniam triangu-
lum A F L eſt medium arithmeticum & trapezium A F G L
medium geometricum inter eadem parallelogramma, ut pa-
tet ex hujus 13; ſed triangulum A F L, trapezium A F G L,
& trapezium A F E L ſunt continuè proportionalia ex hujus
1; & proinde trapezium A F E L eſt medium harmonicum
inter parallelogramma P D M L, F D M K, quod demon-
ftrare oportuit.
11TAB. XLIII.
fig. 4. gentes in punctis F, L, ut compleatur trapezium A F E L,
quod dico eſſe medium harmonicum inter parallelogramma
P D M L, F D M K. triangulum A F L, trapezium A F G L,
& medium harmonicum inter parallelogramma P D M L,
F D M K, ſunt continuè proportionalia, quoniam triangu-
lum A F L eſt medium arithmeticum & trapezium A F G L
medium geometricum inter eadem parallelogramma, ut pa-
tet ex hujus 13; ſed triangulum A F L, trapezium A F G L,
& trapezium A F E L ſunt continuè proportionalia ex hujus
1; & proinde trapezium A F E L eſt medium harmonicum
inter parallelogramma P D M L, F D M K, quod demon-
ftrare oportuit.
Sit quadratum circulo circumſcriptum 4000000000000000;
erit ergo eidem inſcriptum 2000000000000000, inter quæ
quadrata ſit medium geometricum 2828427124746190
octagonum nempe intra circulum: deinde inter octago-
num intra circulum & quadratum extra ſit medium har-
monicum, quod levi labore invenitur dividendoduplum
quadrati octagoni intra circulum ſeu duplum rectanguli à
quadratis intra & extra circulum per ſummam quadrati &
octagoni intra; eritque inventum medium harmonicum, octa-
gonum circumſcriptum, nempe 3313708498984760. conti-
nuetur hæc ſeries convergens polygonorum complicatorum
donec prima medietas notarum ſit eadem in utroque
erit ergo eidem inſcriptum 2000000000000000, inter quæ
quadrata ſit medium geometricum 2828427124746190
octagonum nempe intra circulum: deinde inter octago-
num intra circulum & quadratum extra ſit medium har-
monicum, quod levi labore invenitur dividendoduplum
quadrati octagoni intra circulum ſeu duplum rectanguli à
quadratis intra & extra circulum per ſummam quadrati &
octagoni intra; eritque inventum medium harmonicum, octa-
gonum circumſcriptum, nempe 3313708498984760. conti-
nuetur hæc ſeries convergens polygonorum complicatorum
donec prima medietas notarum ſit eadem in utroque