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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis (shelfmarks Leibn. Marg. 100:1/2, Stück 2; Leibn. Marg. 100:1/2)
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Cap. L. XXX
= Sphaera = 3 Cplindei = 3  = 3 10. FrEO s =. hoc et Superticies Sphae
SSplara = 0 Colindri = 10 = 2rC = 4 . hOc Cs Superticies Sphara est
Fota oCslindri. sSphaerae. . 4 C + 2.1. 4 3: : 6. 4: : 3. 2. Adeo ut C7.
Partes Cylindei interceptX panIS BaI varaIleliS SeIgnIAILETR TUNE COrrCLDOn-
dentium Sphaera Sectorum (su est, Cylindrus genitus convertione Parallelo.
Grammi LD da est 3 Seclorto Solidi BCB.) Nam Frustum Scurellae MDB
=3 Lubi Cplincrici DE; Ex ConuS C AB = Z Cylindri C B. ErgO SectOr CBM
Cylindri CD. Paricer Sctor CbM = Z Cylindri C d. Frso etiam Sector
= Sectori Sphaerae = Z CHI. = 2 = . ErBO a = 8. hoc elE partes Su-
perticierum Sphaerae de Cylinder absciltae planis Basi parallelis sune aequales: pucd
Superticies Bb = Superticiei Da =O CMIXD a. Hinc lequitur Superticies 5
Zonarum esse propotoaleo luis Alcicudinibus, ret scomentis AXiS SpHRTX inter.
CeDtis.
oCotindri Circumteripri. deylindri Intcripii: : CM 4. C P4: : 2. F. FT C.
lindeus Circumleripeus. St In(cripE: : CN. C P3:: 2V 2. +
Sulperticies Coniei Rhono CMHI Sphaera Inseripri cAt =M HL XOCM; e
Conici Rhombi Inleripi. o Coniei Rhombi Circumleripii:: C Fg. C 19: : Z. 2.
Et Conicus Rhombus Inicripcus. Con Rhom circum (C:: C F3. CC3:: F, 2 V 2
Secs Sphaerae =GFIxO CMI, e Sphara = ZHIGX D CM. ErgO sSphaTA.
Khombi Enser.:: GH. MH:: V2. L. FE Sphaera. Con Rhomb Inseripr::
Si F F C dimidium Friansuli tlopleuri Circulo tn-
Ceripei, e AD B dimidium Circum leripti rorentur circa
AB: producetur Conus Aquilaterus Sphaerae Inscriptus,
et alter Circumseripeus.
oConiFEO = ZOEGKHF, ee B Balis = ZOECK
(F G =) ZF F. ErGO ∞ = 2b. FrGO tOI 0 = 3b.
Hoc elt; tuperticies curra clt dupla baseos, adeoque
tota superficies est baleos cripla.
L. CDB = 30 = L. F. BD. ErgOH. D =-LB =-FC.
FrBODCD = 4 CF. = sSphaTR. ErGOSSpMTA.
b Coni Circumse:: CCD. (O BD =)  CD OCB::
. 3. ErgO sSptaera. tOC 0 Con Circum (C:: 4. 9
Et Sphaera. Con Circumle: : Z C B X S. 3 C BXEOE0:
4. 9. Adeo ut Conus Circumle. Sphaer. :: 9. 4. Soli-
ditate e Superticie. firgo Conus Circumser. Cylindeus Circumse. Sphaera::
9. 6. 4:. Solatcare limul e Superticie. Adeoque Archimedis ratio Sclquialiera
concinuatur in Cono s. guilatero, quod primus demonstravic . F asques in Appen.
dice ad Geomerrix Elementa.
Coni Circumsc. o Con Inter:: BDg. CF. 9: : 4. F. EC Conus Circumle.
Con Inter:: BD3. C F, 3: : 8. F
Si Sphaera cidem inseribantur et circum (eritrantur Ai quilaterus Conus, Cstin-
drus, et Conicus Rhombus: iplorum Superticies de Solidicates se invicem habie.
bune, ut numeri sequentes: Ouod eric maniteltum si binae qua que anre ostensarum
Rationum reducantur ad candem denominationem: Onde emersent 30 adhuc
alia Theoremata; ee quidem primaria eorum quae Torricelius demonttravit de So
lidis Spharalibus: Indeque Facile deducencur reliqua.
Superficies
Solidicaes Coni Aquilateri Circum le. Cy lindri Circumsc Rhombi Circumsc. Spha-
ra. Cylindri Interipii: Rhonibi Insc. Coni Insc. Sunt : . L. H8. 3L.Y L. 52. 12f2. 10. 8
Coroll. Sphaera. Rhonb Circumse. : : r. Y 2. Tolidicate sinul de superticie.
L G F B L 1.
xe est aequalis cuerae Superticiei Cylindri Cireum seripei
quadrupta Cui maximi circuli.
CBb = = Cytindri a D.
lindrus circum scripcus. SpI. . 3. 2. Soliditare simul ec Superticie.
Soliduas = 3 FTGX D CM.