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# Title: [Johannis Wallisii SS. Th. D. Geometriae Professoris Saviliani Oxoniae, Tractatus Duo] Johannis Wallisii SS. Th. D. Geometriæ Professoris Saviliani Oxoniæ, Tractatus Duo (shelfmark Leibn. Marg. 103)
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Curvarum EvdorE.
Adeoque Sphaeroidis lati superkicies (convertione Ellipleos circa
minorem axem descripri) ad superticiem Sphaera circum scripca,
UE Omnes V: R = F= + a Y
R.=; ad coridem R. HOc Cst, uE
quadrilineum A T X R f3. 28. hyper DOIX SuOquC axi CONjUGAEO
incerjectum (cujus Pemilatus eraM(VeTTUM AR = V: PE - f12
ee AT = TI, TN = R;) aa A Ta rectangulum.
HIOc CA, Si, ab FEyperbolacujus semilatus cum rectum tum trans-
versum R H, Fllipseos semiaxi minori aequetur; ad conjucacum axem
ordinatim applicetur x T semiaxi Fllipseos ma ori aqualis; s
compleatur A T _ rectanenlum: Frit, ut A I n K quadrilineum,
ad ATn rectanculum; sic superficies Spharoidislati, ad circum-
Scriptae Sphaerae superficiem.
Vel sic, elegancius paulo, utrumque Cimus efferamus. Sint el-
lipseos axes conneati, AC F. maior, B C HI minor, ( BD (pa-
rallela C F) circumseri pri circuli quadranti F L occurrens in D:
es compleatur C BDF rectanculum. Sumatur, in D F conti-
nnata, FC aequalis C. F. Denique centro C verrice H, scribatur
HIC byperbola; es compleatur C F CI rectaneulum. Intellica-
tur antemtum axe A F sphaeroides obloncum, tum axe BE spha-
roides latum, ellipseos conversione describi. Frit, ut C F DE qua-
drilineum, ad inscripium rectanculum C F DB; sic Sphaeroidis ob-
lonsi superficies, ad superficiem inscripea Sphaerae: Aeque, ut C F C, FI
quadrilineum, ad recto nculum oircumscriptum CFC, L; sic superficies
sphaeroidis lati, ad circum scripiae sphaerae, superficiem. Addo etI
es partes parcibus respective sumptis proportionales esse, (num et de
Parcibus etiam procedie demonttracio: ) Hoc est, si in eadem rario-
ne, ordinacim applicaris recta incelligatur recta C F, qua spix-
FOideos _ COMPATAEA SphaerK AXes leCaNCUE pLAnO. DAtA VeIOFA
cione quam habet Sphaeroideos ad Spherae suxerticiem, vel erinm
iltius parres ad parces hujus; racionem irem ad circuli planum dari
nemonelcit. Sed de his hactenus.
Accedo ad Spiralem, quam e memorato loco (Schol. Drop. 38.
ralis lonci- arich. Infin.) consideravimus. Incelligarur, incra sviralem li-
neam inscribi, fgura ex similibus sectoribus consaca. Florum
AECUS, Proprer X qualia FadIOEUM AUBMENEA (VE C A = 1) arich.
metice proportionales esse oltendimus: Adeoque _ arcuum ho-
et
E18. 32
Sunea Spi-
indo.
Fi8. 33