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PROBLEMA XV.

Seäorum circuli areas invenire.

Q Ua ratione inveniatur area semicirculi , quadrantis, sertu-quadrantisjScsimilium proportionalium partium, patete*dictis Probi, 7. nunc quomodo aliarum partium areas invenire'postimus,dicendum restat, & primo agendum de Sectore,fig. lx. Si igitur partio circuli sit Sector, qualis est figura A B C D ,

üeoßis, incomprehensa duabus femidiametris A B, A D, & arcu ECD; ejusarea invenitur, si nota sit in certa mensura, v. g, in palmis, tam se-midiameter, quamarcus totus: sienimfernidiarnetefducaturin'seruissem arcus, eritproducturn area sectoris in mensuris quadra-tis. Sit semidiameter A B fexpalmoram,arcus B C 0 1 Z, & semis-lisarcus, nempeB C 6 : multiplica 6 per 6 y erie productum zL-area»rpsius Sectoris. Demonstrationem insii apponam.

Quod si neque semidiameter, neque arcus sectoris sintnots,-mensuranda est semidiameter mensura aliqua nota,&secundumeandem mensuram' indaganda est circumferentia totiuseirculf,per Regulas positas supra Problem. 9. Mensuranda praeterea'estchorda B D'. Exfcrnidiamecroenirn LL chorda notis, in veniri pö’-testarcus B C D primo in gradibus,Lc deinde in mensuris,qnibusfnensurataestremidiameter, tandemquecxsemidiametro&se-miarcu indaganda area.

Sic aucemex semidiametro Ä B, & chorda B’ D, notis incer-ta mensura, v. g, in palmis stnveniesarcum B C D,. in gradibus, sidicas: ut semidiameter A B sex palmorum ad chordam B D ro>palmorum v. g. ita sinus totus rooooo partium adaliud; numerumenim procreatus dabit rectam BD cognitam in partibus sinustotius; medietas aute rectae B D cognitae in partibus sinus totius,erit sinos se missis arcus B C D > ac proinde sinus rectus arcus B C,vel D C, i deoque ex rabula sinuum femissis arcus B CD in gradi-bus nota erit jq.ua habita, totus arcus BC D non ignorabitur.

HabitoarcuB C D noto in gradibus, sic idem notus fiet irfmensura semidiametri A B, scilicetinpalmis,Tofaeircurnferen-tiar circuli a semidiametro Ä B fex palmorum descripti, jam notafacta tst io aslumpta mensura, nempe in palmis, per RegulamProblematis N oni $• si ergo sia t, u t grad us 3 % 0 ad totam eir c umfe-

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