f6% Opuscula. 
Deraonftratio. A punais C,£, GdTr. ducantur OT, EP, GQ, 
^c. perpendiculares ad TM, Faciie apparet trianguia omnia ^i^/t 
CjBK, CDK &c, fimiliaeire. Quod fi iatus IB cum omnibus fuis 
homoiogis jBK , KD &c. in unam rummam conferantur , erit fane 
haec fumma IS . Latus vero Al , & omnia eius homologa in unata 
fummam conferentur hoc modo; cum quifque appuifus factus vel 
ad J5 , veiadC, vei ad D cb^f. compleat unum tnangulum & prz- 
ter triangula compieta his appuifibus fuperfit trianguium ultimum 
HRG , erit numerus omnium trianguiorum ■=.m-\' i . Es his trian- 
guiis primum AIB ^ & uitimum H^Ghabent iatera ho noioga Al ^ 
HRy in ceteris omnibus latera his homoioga funt CiC, EP &c, 
quae iineac fingulac xquaies funt OT , & in unam fummam coilatac 
{untm — 1 Or, ideoque fi latus & omnia eiushomoioga con- 
ferantur in unam fummam, erit hsec fumma = AI HR -f^ 
m — I Or , erit ergo 
JB=x AI: 1S 
Al-h HR-j- m—i OT. 
Theorema XV. 
Slglobus a certo pundo ^ (Fig.VIII) poft certum numerum 
appuifuum tandem perveniatad pundumH, vel 5* ,* eorum ve- 
ro, quos dixi, appuifuum primus fiat in pundo ^iateris TM, aiii 
vero omnes ordinati fint , fiantque in C , D, ^ j (^T^f. , ac duda fit 
AI perpendicuiaris ad TM, & pariter duda fit HR , vei i'i2^perpen. 
dicuiaris ad latus, in quo fit appuifus uitimus, fitque numerus 
appulfuum — m . 
Dico primum : fi numerus fuerit impar, ( quo pofito appul- 
fus uitimus neceffariofiet, vel in TM, velin OiV, puta in A"} & 
portioilia, in qua fit appulfus ultimus, appciietur -KO , erit 
1B=lAI: IT-hRO ^m—^ON 
1 
AI-^HR-^ m— I Or. : 
2 
Dico fecundo : fi numerus w fuerit par ( quo pofito appulfus ul- 
timus neceifario fiet , vei in Or , vel in MN, pura in L ) & portio 
ilia, in qua fit appuiiusuiLimus , appclietur <^ , erit 
IB — 
