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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)
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DE SECTTONIBOS PFOP. XXXIX.
sequenter distantia recta CMM ab Fperbola curra _O, convinue decreseit.
Duod crat secundo demonstrandum. 
3. Sit altignara diltantia qualibet quancumris exiguas puta 2a; Dieo FBy.
Perbolam AO rectamque CM eo produei polto, un earum distantia minor cracat
quam est altionata 2a. Sumatur enim linea recta aliquanro minor, par a cui
aequalem esse volumus rectam OM; d quaerendum sio puinctum II (cui ordinarim-
ponenda sc HOM) seu lonsicudo recx CiHI. Quoniam ixicur supponimus
a =OM = V== 1 -Y -, -I; eric (cransponendo)  1 = V  L a;
 
et (utrinque quadrando)
1= = 1 + a = 2 a V = 1. EF ( transpo.
nendo, acque, reduendo) ZaeN. 7. = _ + 7 L.  BC (quadrapd9)
2
4 a2 c2Y
a + sP + 24 5e Sloetr t) scriso ut
Adeoque (diridendo per L) exit - aP f. s. P  2a 51
4 a IF
Habetur ergo quanciras c3, (cujus radix c = CF,) adeoque punctum F, cui SI
Ordinatim. ponatur TTOM, erit OM= an (quod A Opus SE, Syntherice demon-
strari possi repecicis Analy seos restixiis,) adeoque minor quam distantia astignata
2a. Fdeoque distancia concinuatae rectae Ci M M, ab Hyperbola continuata AO,
tandem minor cradet distantia quavis allignata. Quod crat certio demonstran-
dims. e. Adeoque, constat. propolicum, rocuris 1loc
Pollet e hic ostendi. Ad eandem Lrverbolam nonnist duas Nompiotas Curin-
que unam) duoi pesse: se mutuo in centro secantes. Alia enim quaecunque in
et ad recsuilitam appropinquationem
non accedet. St tacile e dembratNIS
Tret. Aimptoras unias Tperbola esse etiam TEyperbolae oppositae Asymptotas.
Olod Timili tere propretu deonstrabuur ei quo ulus sum ad Corollarium
DrOP. 37. NSABUP) clodqI (ssiuisco
Negne illis rantum vinis FEyperbelis, Oppositis, sed e binis aliis pisce, conjuea-
sis  de quibus post dicetur) eadem conveniunt Asymprotae, e quidem solae.
Patet item, quod (si ab eodem puncto L ordinatim applicatae LZO, FO, utrin-
que continuentur ut Armptoris occurrant in I,) erunt, OM, O M, (utringue
Scmoca d aegualos. Cusi )erritt raM BL NE; FM, (Y = 1,) quan, HO, HO,
LFGCsi LMLIHCLSIO 1150, LL et VOND OHBCLG NI a
CY e L 1), erume e OM OiF Ct M -= HO) aequales.
Trem, St (ad eandem quanmvis Diameirum) Ordinatim ponantur rectae quol-
libet MOTIM (Asemptotis occurrentes in M FEyperbolae in O, diametro in LY,)
omnia rectandula MOM (seementis comprehensa) vel etiam rectaneila OMO
(sumptis O, O, in utroque crure Lyperbola) erunt tam inter se, quam quadrato
recta AM (ab asrmptota ad verticem ordinasint posita) aequalia. Nam ubieun.
que in diametro (incra Psyporbolam) sumatur punctum axplicarionis FI; rectan-
siltum MDM rst OM D, LHOC c  M, HO, in. HLM + HO; hoc elt
VE in1;) semper erit = V (hC muluipii
L. 1151
cando parebic;) noc elt A M q; esbenim (ex hypocheti) L. L: : C. N g. W M9::
CA4 (= 5). AN9 =
VEII OTAEMH ZjEIM OBARI 1SL  S ilic
 sit e
dud
sumptota vero, quae jam dicitur, eadem est quae ad prop. 36. luxponitur P an-
senis insinita, a Centro ducenda, quae not nils pose intinucam ditanium (Hoc est,
nunquam) Fyperbolam concinget.
atia de Alymipions, de Thectemaca e Problemaca quae dx jam diedis decuet
PosenE PPAIOTCB. JIG NSOU Sis) coucsOni
ci
elo cipeet  sespeoior