56S Opuscula. 
Dernonftratio . ApundisC, G cb*^-. ducantur CK, EP, GQ^ 
(^c, perpendiculares ad TM. Facile apparet rrianguU oninia JBI^ 
CBK^ CDK&c» fimiliaefle. Quod fi iatus IB cua?. omnibus iuis 
bomologis KD&c. in unam fummam conferantur , erit fane 
hnec iumma 1»^ . Latus vero -4/, &omnia ejus iiomologa in unam 
fummam conferentur hioc modo : cum quifque appuilus factus vel 
ad 5 , vel ad C, vel ad D c^f. compleat unum tnangulunj , & prae- 
ter triangula completa hisappulfibus fuperfit triangulum uliimum 
HRG , erit numerus omnium triangulorum = ^ -h- i . Ex liis trian- 
gulis primum ^IB , & ultimum HRG liabent iatera homoioga 
HR^ in ceteris omnibus latera his iiomoioga funt CJC, EP &c. 
qu3eh'neaE finguix aequales funtOT, & in unam fummam coll^itx 
funt »2 — . I Or, ideoque fi iatus AI^ & omn'a ejus homoioga con- 
ferantur in unam fumraam , eric h^cc fumma =^ AI -h HR h- 
— I Or, eritergo 
IB— AIi IS 
AI-hHR-^m — i OT. 
Theorema XV. 
Slglobusacerto pundo^ (Fig.VIII. ) poft certum numeruni 
appulfuum tandem perveniatadpundum J/, veiiyi didorum 
vero appulfuum primus fiat in pundo B lateris TM, alii vero 
•omnes ordinati fint, fiantque in C, D, E c^r. , ac duda fit^I 
perpendicularis adTM, & pariter ducta {\:HR, vel ^O^perpen- 
dicularis ad latus, in quo fit appulfus uitimus, fitque numerus 
appulfuum = m . 
Dicoprimum: fi numerus;« fuerit impar, (auo pofito appul- 
fusultimus necefiario fiet, vei inTM, vei in ON, puta initT) & 
portioillaj inqua fitappulfus uitimus, appelletur jRO , erit 
IB=^ AI: IT -i- RO OM 
1 
AI -h HR -t- w '-^ OT 
1 
Dico fecundo : fi numerus m fuerit par ( quo pofito appulfus ul- 
timus neceffario fiet, vei in OT, vel in MN, puta in I) & portio 
illa, in qua fit appuifus ultimus appelletur QN, eric 
IB^ 
