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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 893, page id 851387705:0913
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PFOD. XXVITI. De Calculo Centri Cravitatis.
x sine series Iudicem habens ; Posro seriei rectarum MX Indice N. P.
S; Basisque Paraboloeidis, aequalis iph M L cerminali; ejusque 2]-
citudo, ad lonsicudinem arcus Sectoris contermini, ut F adS F F.
Postuntque pari modo ex aliis irem Figuris (puta FIrperbelicis, Fllipti.
cis aliisre mille modis rariatis,) alia spiralium genera Conrolu-
tione fieri; atque in eas unde construuntur erolri. Ouarum qui-
dem Fisurarum Spiralium mentura, ex illarum figurarum menturis
dexendent, quarum Conrolutione Aunt.
R.
Sunt uriquo Fieurx Spirales, non modo quxe ex Conrolutis Parabolis, R
Led et quae ex aliis fisuris Conrolutis oriuntur; Figurarum illarum,
ex quarum Convolutione hune Dimidia.
Ft quidem non modo Curra Spiralis Archimedea, est aequalis CurrX Pa- R.
rabolica spollonianae correspondenti; sed e alia spirales quaelibet,
aequales illis respectire sire curris sire rectis quarum Conrolutione
trunt.
Adeoque cognita Figurxe Spiralis Magnicudine, vel Currae Spiralis lon. H.
sicudine; cognolcitur similiter vel magnitudo iltius Agura cujus
Conrolutione Hc, vel longitudo linea: Et rice rerla.
Et quidem Spiralis illa cujus rectae M P crescunt in angulorum ANY
ratione duplicata, non modo rationem habet coonitam ad Secto-
rem conterminum; sed ipsius Currae Rectam aequalem astignare li-
cet, camque in data ratione SCCarC.
Ouod ipsum aliis item spiralibus innumeris continsit.
Sed e Figura Spiralis (ex Parabolocide conroluta) astienari potest,
qua ad Sectorem conterminum rationem quamris datam habeat;
faltem Minoris ad Majus, numeris explicabilem: Et Parabolocides
similiter, eidem correspondens: Ve ec cuiris Parabolocidi respon-
dens Spiralis.
O.
B
N.
Potestque haec Sxiralium doctrina, ad alia mulca spiralium genera am. R.
Pliari.
ETSviralis RadtiI M F, M P, crelcant, non quidem in ratione Angulorum ANY.
A.
LD A MT, (ut in Spirali Archimedea) Sed in corundem ratione duplicata, puta FiB. 199.
ut a2: Frunt Sectores similes (figuram Spiralem componentes) ut a  (uipote in 200.
duplicata ratione arcuum Tuorum:) Adeoque, corundem asgresacum ad aggresa-
cum coridem maximo aequalium; hoc elt, rigura Spiralis, ad Sectorem contermi.
nUm; uc L 2d5 (= 4 F E,) Per DrOD. L. hujus.
Si Ractii M P, M T, sinc in anxuloruM AM P, TeU PM P, ratione criplicata;
hoc estu ut a3; adeoque Sectores similes, ut a5: erunt simul omnes ad iocidem
maximo aequales; hoc ct, Figura Spiralis ad concerminum dectorem; ut L ad 7.
per eandem rhujus.
Fq universaliter, s RadiiM T, creleant in Angulorum PM P, ratione Sim
pla, Duplicata, Friplicata, Ouadeuplicata, ec. Fisura Spiralis, ad Sectorem con-
Terminum, exIE uEF, 2d 3, 5, 7, 9, eC. CZOn, uV Fdd 3, 47 5, 6, c. quod per
incuriam seripium tuerat in Srithm. Insin. SCh Ol. PFOP. 45.) Propter Sectores Simi-
Les in Radiorum ratione duplicata.
Ex Smilicer; si creseant Ractii in Angulorum ratione Subduplieata, subcripli.
cara, Subquacruplicata, eec. adeoque Sectores in ratione simpla, Duplicata Sub-
eriplicata, Subduplicara, ec. Fisura Spiralis ad Sectorem conterminum eries uE L
ad 2 = C7 3  1, 2 F L, aC. Bel uE L a1 2, 3, 2, dec. vel L ad 2. ; 3ad 5; 4 ad
_C.
St cetcam Kadii in Anoutorum ral Suplicata Subcriplieata, Triplicata sub-
quadeuplicata, etc. adeoque Sectores, in ratione Ouacruplicata suberiplicata, Fri
plicaca subemplicata, dec. (uipore in duplicaca ratione ractiorum;) exit Figura
Puuuu 3
Spiralis