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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
# Folio 991, page id 851387705:1011
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De Cochlea.
eR O P. VL
Cochlex solidicarem extribere.
Ntellisatur Cyludri Cochlex inscripri superticies
Curra, in Planum ABBa Parallelogrammum expan-
di: Aeque in eo recta AIIII, eadem quae tuerat, in sy.
perticie Cylindrica, curra Spiralis, cujus ductum se.
quicur Cochlea.
Incellisatur porro, secto per Arem Cylindro, in una
aliqua Cochlex revolurione, Sectio Facta DFF; (pura
Friangularis, Ouadrata, aliare qualibet, pro expolitx
Cochlea nacura; cujus Figurx magnitudinem datam
supponimus, ejusque Cenrrum graritaris M nocum.)
Cujus itaque Batin (in latere Cylindri inscripri po-
Ticam) oblique secer, secundum Obliquiraris angulum
HIAa, sCu AHIB
Si uaque incelligatur, super ABBa planum, in recta DF, ad anoutos reclos in-
Tiltere tigura data D F. I; acque (eildem ad planum angulis retentis) super AIIFI
rectam moreri, rerento eodem Obliquitaris Angulo: Manitettum clt, Prilma de
seripeum iri cujus Basis SC ipSa D E F, Lacus aurem ipA AHIH aequale, sed AITi
cudo quanta elt recta ABB. 
Adeoque (propter Pritmata, super aequales bases, alticudinibus proporrionalia,)
tancundem erit Prisma Scalenum DL FFIII, acque Prilma Rectum DEFBB: Nempe,
quancum elt quod Fic ex D F. P plano, in alcicudinem A B B ducto.
Incelligacur demum, planum illud A BBa, in superticiem Cylindricam (uei pri
ustuerat) curracum; manence linex ABB lonsicudine: Manence item ejuldem
ad DEF planum politione perpendiculari. Onde tiet, ut recta quam prius deleripse.
rac s punctum (ipli ABB aequalem) procracta jam in arcum majoris circuli similem
ipsi ABB, longior jam tucura sIC ( DFOPEeE Curraturam) quam prius fuerat. Idemque
de arcubus qui ab aliis deseribuncur ejuldem D P. F Dunctis, quae Lunt exIa D F. rC.
etam, incellisendum exit.
EF propterea majus erit Colidum sic curracum, quam fuerat Prisina. Onantum
nempe elt, quod tic ex arcu qui ab M (iplius DE F cenrro graricatis) deleribitur, in
iplam DF. F ducto. Per PrOD. 12. C aP. 5
Cumque hoc perinde valeat, in siu ABB, acque in sim AHHI: Si incelligatur DFH
tirura plana (quam in una aliqua Cochilex circulatione facir Planum pex AXem)
in rectam duei quae aequalis sic areui circulari quem deseriberer ejuldem D F. F Cen
erum praricatis M, secundum ductum arcus ABB lacum, (circulatione una vel plu
ribus, pertectis vel impertectis prour expolicx, Cochlea Circulariones elle contire.
ric:) habebuur (quicunque tuerir Obliquiracis Angulus) Cochlex magnicudo.
EV
ovidem (cum eadem urrobique valeat demonltratio) sive Cochilea Mas tuerii sire
Faemina. Ouod erat propolicum.
Sin porro Cylindri, cui adjacee Cochlea, magnicudinem, adjungere libeat: id sa
cile tier ob noram Cylincri magnicdinem: per SO prOP. 12. C aP. 5
SC HOLZV M
tueretur aliud Colidum, ex limili ductu ejuldem D P. P plani per curram AFIH
alicer constitutam; puta, sumpris BFT, BH, non quidem in iplarum AB, AB, ra
tione, sed in harum racione duplicaca, criplicata, tubduplicata, Cuberiplicata, alia(Ve
consticuta; vel etiam per AFI II curram quamlibet. Ouippe, non modo Prismis
Scalenum urcunque Inclinatum, sed de utcunque Distorrum, aequatur Prilinati RC
ctoxque alio: (Ouod in Tractaru de Conieis sectionibus, prop. 3, 4. ostendimus:
Acque Curracura Cylindrica urobique cancundem prastac. Verum de his, aliilque
Eimilibus, lcum ad praesens negorium non spectentu) non exic hic expaliandi locus
Dem valeres, quod ad solidi magnicudinem specta, h, provera Coctlea, substi-