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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 932, page id 851387705:0952
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De Caleuto Cenor Gravitatis.
C ap. V.
Formatum; convertione scilicet FIyperbo
lae O A O fig. 216. circa conjugatum axem
sC.S. Oupue hoc, idem esse solidur
acque illud quod Forno constructum
iri modo doeuimus, ex dictis latis pa.
tet.
Cumque Solidi hujus fectio quaelibet
plano facta, sic alicui per Axem sectioni
recta, seu perpendicularis: F.sto Ca per
Arem sectio 0000; in qua oppolita
Fyperbola (Genitrices) AO, 20; qua-
rum Centrum, C; Axis conjugatus (qui
_ Solidi AXis CA) SCs; Asmptotarum
altera, CMI; AXIS Fran(verIUS, Aa =
2C A = T = 2 S; Axis InTETCEPTUS, AD
+
a Centro distancia, C D = C =
F a = 5 Y a; Ordinatim applicata ad
EIyperbola axem, DO ==h : Cujus qua-
dearum, B - 2 a + = 42 - = a + d 7
=Z; (quae tunt itaque, ut series
Primanorum aucta serie Secundanorum; aut eriam, ue Series Secundanorum mulcta.
ia serie Aqualium:) Adeoque 02 = S = = B: Ouod icaque est quacratum re.
Etx CD (distantiae d Centro) vel (huic aequalis) Os, ordinacim applicatae ad
Arem conjugatum. (Oux omnia olim demonstrarimus, Con. Sect. DrOD. 35, 4. L.)
Et, propterea, Tumpris C. S, hoc est DO = h, arichmetice proportiona libus; crunt
omnia rectarum sO, ordinarim applicararum ad Axem conjusatum, (spacium
OsCA complentium,) quadrata, toridem S2 f == B2, Tumpris B arichmerice.
proportionalibus: HOc est. Series sEqualium aucta serie Secundanorum.
Sed e sumpro M in ACymPtOta C. M, erit (Per prop. 30. ibidem,) ut L adZ,
sic quadracum C s Scu DO, hoc est h2, ad quadrarum sM. Adeoque quadrata
omnium SM (spacium M Ci s complenrium) tune cocidem = h2; tumpris C. d = b
arichmerice proportionalibus.
Maniseltum autem est, (ex constructione Colidi,) quae rectis Aa, Do, insictunt
erecta plana (solidum complentia) cocidem esse circulos; quorum diametri sunt
iplae Aa, Oo, rectae. Ouippe radii C. A, SO, circa Axem SC sconversi, totidem
deseribunt Circulos.
Incelligatur autem, sumpro, ubiris in sO recta, puncto m, recta per Centrum
Cm, cui crectum insistat Planum sectionem faciens, quam itaque compleant rectae
m (iptis in punctis insistentes:) Ouarum. quadrata (uipoce; in suis respectire
circulis, incer diamerri segmenta Om, mo, mediarum proporcionalium, seu ordi-
nacim applicatarum ad Circuli diametrum,) sunt coridem quadrata sO, dempris re-
spectiris quadraris sm; Peu m 2 =- dOg - 5mg.
Sitque L punctum mins. adeoque s m =0, 8 sO4 -- s mg = 5Og: FF
propterea, qua rectae C. S insistir sectio, cadem erit atque SO A Ci hyperbola.
Sit 2, punctumm in M, (nempe C meadem existente atque C. M a (ymptota; )
adeoque s m = dM e dm9 = S H9 = = B2: FL pr Opterea 5O9 - d m9 =
8 + = b. - , b. = 8 = m: ipsaeque m, coridem S, invicem aequales. A.
deoque, quae Asymprocae intillic lectio, est Pacalletoprammum Rectaneulum.
8
Solidum vero sic constructum cum varias admitrat sectiones plano factas; eas
Fig. 216. ut ordine exquiramus, considerabimus hoc idem solidum uc alia constructione