INyENl^ENDI ALTITUDINEM TOLl 6'c. ^% 



ADDITAMENTUM. 



Quoniam in dcmonlhando Icmmate noftro 

 ficilc c(l in prolixos ct fupcrfliios fc im* 

 niittcrc calculos , ncquc dcmonflratio 

 brcuis et fynthctica cuiuis (latim apnarcr, 

 monitus fiii , ad fubicuandam aliis dcmonflrationi» 

 opcram, vt meam apponercm •, id igitur faciam, 

 pofti.]uam memincro dc fequcntibus propofitionibuSj 

 quac in elcmcntis Gcomctriac dcmonftrari folent. 



I. Ciiordam arcus A-l-B habcri multiplican- 

 do chordam arcus A , per chordam complcnicnti ad 

 duos re(flos arcusB, vt et chordam arcusB, pcr chor- 

 dam complcmenti ad duos redos arcusA, lummam- 

 que produL^^orum diuidendo pcr diametrum. 



II. Sinum verfum alicujus arcus haberi , dinidcn- 

 do quadratum chordae ejuidcm arcus per diamctruin, 



III. T.ingcnrcm alicnjus arcus , cujus chorda 

 ponitnr A pro . adio R , ene ——^^r^i'^^^- 



IV. Productiim chordac alicuju^ arcus in chor- 

 dam complcmenti ad duos redos, cfle acqualc pro- 

 du(flo finus illius arcus in diametrum. 



Hifce in memoriam reuocatis , du(ftisquc ( jn 

 fig. i.)re(flisPl, PQ, PR, ct QI, t\-\z{perart.].).u^- 

 ncndo vbiouc IV pro radio , QI— [PQl'^iV=-PF-f- 

 pir^^^T^l^IV , vnde hiberur ( pcr art. 11. ) 

 LAl=rIM-lL-[2lV=.PQ^:-PQ^=.PI=-4-PQ.Piy 

 (+lV=-Pq=s 4.IV=-PI = )]4l\ K Kodem modo ob- 

 tinctur qnoquc LN= [ 2IV =.PR=-PR=.PI- _f-PR=, 

 Pl=.V(4lV=-PR=;.(4-l^=-Pl=Jj:4lVS ergo erit 



