66 DE SFPERFICIEBVS 



GK , C M , CN pamllebe AB , nec non O N parallela 

 CB, hisqiie pnieparatib, dicantur Al — x.lG—j, EG 

 — z , GL=:fl'.v , LGz=4y , EG-DC—dz , eriint C S =-^ 

 ddx, SQp^lddy, et reda PR parallela CO , T>K-ydz. 

 Et quia DPO ( hyp- ) ad fuperlicicm perpendicularis crt , 

 dicantur CN == w, ONmw, et CO^p. His poiitis 

 AA fmiiha CSQ^, CNO, nec non DPR et DCO, 

 praebent ddx-=z-=^\ ddyz=i''^. Sint hneolacGC, 

 H C proiediones cknieutorum ED , FD hneae breuif- 

 fimae inter duo punda E et F in planum horizontis, 

 et radius ofcuh curuae GCH in G, dicatur r, et ha- 

 bebimiis generahter rdxddy-rdjddx—d.O, in qua 

 fi in locum elcmentouim ddx^ddj fubftituantur -— * 

 et "— , proucniet nrdxddz H- mrdyddz — zds"^ , 

 exiftcntc G C rr ^.f , quare ddz r= ^rTdl^^irfd^ \ propterea 



ficnt ddx ~- ^Td^H- w rdy 1 ^f day— Srax-i-mTa^- ^^^^^^ 

 gcncraha funt pro omni fuperficie in qua pinnum tan- 

 gens anguUim rcdam continct cum plano trianguh EDF ; 

 fcd fi idem planum tangens fuperficicm in D anguhira 

 quemcunquc oWiquum formare debcat cum.plano rrian- 

 mh EDF , cuius fuuis fit =zg , et cofinus — h , erunt 



^ , , — 771 dsf . j 



quidem, vt paulo ante, rfrf.vzr ^777^.^^^^,, et aay^ 

 —^.'1--^ , fcd aefhmatio elementi ddz aha inuenie- 

 tur , ncmpe ddz — j^^^^J,%^,Yr ; ad abbreuiandum , 

 fiant "e.=zgz ^hp',Y zz.gp-hz, ct du—mdv-^ndXy 

 erunt t\%o ddx—^^ ., ddy — ,7^^, aaz^f^^^. 



Sit dz=zAdy-\-Bdx ae ]uatio difFerentiahs fnper- 

 ficiei propoHtae, in qua A,B fignifiouit magnirudines 



TTt 



