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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 SECHLONIBUS AAMLIII.
PROP. ZXTII.
De Recta Parabolam contingente.
 sumpto ubiris in Parabolae diametto puncto P, cui ordinatim-
applicetur Pa, diameter PA extra Parabolam continvetuF UE EaE
continuatio AF, ipsI AP diametro intercepta aequalis; recta Fa du-
cta Parabolam in puncto a continset. EE contra; si Parabolam in
a contingat recta a L, diametro produetae occurrens in F; Crit AF
(continuario) ipsi. AP (diametrO inter CCPE) aequalis.
Nam Tumpto, in eadem diametro, puncto quoris D, cui ordinatim applicetur
DO, qua ad rectam F a pertingat in T; Dieo punctum T vel idem esse cum
puncto a vel extra Parabolam cadere; hoc est, rectam DT vel xonalem esse
rectae DO (s nempe puncta D, P, coineulanc) vel (s alibi sumacur D) lon-
Bicrem.
i
1II
oto inat
hujulque quadracum?
Fsto enim (ob commodiorem calculum) P a == p.
PA = a (ideoque P F = 2 d,) PD = a, (ideoque
DA = a = a DF = 2 d F a, variacis nempe signis
1, -, prout supponitur punctum D intra vel Cu-
pra punctum P sumi.)
Fric igitur (proprex Parabolam) PA. D A::
Pag. DO9. Hoc est, d. d = a : : p2.   p = DO9.
Et (propier similia criangula) PF. DF:: Pa.
DY. hoc C 2d. 2a + a: : p.
4. a a = a
4a
=DT9
Fst isitur disterentia quadratorum DF9 = DOg. =
1+a
cit
442 P.
+= a
=DF.
2 + 4 da f a
4d.
Ouae quidem vel aliqua est, si puncta P, D, distene,
(Ticque proprerea a quantitas realis;) vel omnino nulla, si coincidant puncta
P, D; (cranescente quippe quantitate an adeoque ee ipsius mulciplicibus omni-
bus.) Hloc est Ouadrata D Lq DOq e proprerea eorum latera D T, DO,
vel aequalia sunc, si Pumacur punetum D idem atque P; vel illud majus elt, li
alibi sumatur D. Fx proxierea, cum rectae aF (quancumris urrinque producta)
Cingula puncta ipso a excepto, sinc exira parabolam; ca Parabolam in unico pun.
eto a concinsit. Ouod crat Demonstrandum.
Elque haec nostra demonstracio muleo expeditior, quam quae ab Apollonio
aliisque, (adhibico Cono, rariisque lemmatis praemistis) asteruneut.
Si vero propolicio haec non tuisset antehae excogicara; led a nobis jam quae-
renda: IWud Analytice sic fieri posset.
Supponamus rem quali jam factam; concingeniem aF, diametro producta oc.
currere in d: es quaerenda sit longitudo rectae PL.
Retineatur eadem quae prius fioura; eademque symbola, nis quod pro P F
(nondum cognica) substiciatur s, adeoque pro DF, f F a. Frunt isicur (ut
prius) P A. DA:: Pag. DO9 -
P+
serc
p2
=A p FE PF. DF:: Pa. DF. hoc est,
f. f= a:: p. eV p = DP, EF 
Ca j. ta C scusCtit
 p= DF9.
EAE item (PrOpIer cangencem) B Y = DO (hoc el, D F aequalis vel major
quam. DO; illud quidem A D, P, coincidanc; Hoc, Si secnS) _ D X 9 = DO4
Hoc est
2s
aip; ee Curcumque mulcipticando in af2 e
divi.