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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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lFOD. XI
ON ICT
PF. Pa:: DC, DO. hoc ct, 2d. p: : 2 d F 2Yde
que quadtacum D09 - 4  + 4d5 = 8 avde
43
B = DO. Fjul
a+6+2Vac
FI isicurquadratum rectae DO aequale quadraro ordiiacim applicatae puncto
D; adeoque recta DO ipsi ordinaum applicacae aequalis. Sed e puncto D ordi-
nacim ponitur recta DO (ex constructione,) eroo ordinatim applicata clt: pun-
etaque OO propcerea lune in ipta Parabola curra, adeoque OO recta Parabola
inscripta. Sed ee eam (acque eadem ratione ipsi parallelas inseriptas omnes) bi-
Secat recta a. Flt isitur (per det.) an diameter, eique ordinatim applicata XO,
(ordinacim inseripeae lemillis.) Ouod erar demonstrandum.
Monendum aurem hic est, quod cum (cam in Analysi quam in Syntheti) di-
cimus duarum rectarum DC, alteram quidem aequalem elle pG a p D, hoc cl
ditterencia rectarum DC, DD, Fieri quidem pocest uc quandoque DC (nempe
quoties recta OO diametrum AP non tran(iC,) quandoque DD (nempe ubi OO
tran(ic AP) major este: AdeOque DC BDD, nuINC DEF PO = pD, nuINC Per
PD =DC incerpretandum exic. Vecum hoc calculum non omnino percurbat;
quoniam ea quanciras in operacionis propreltu quadranda occurric: quo casu,
verumvIS contingat, eadem quadraca prodibunt. Nempe cum sic in Analysi
= d J. 2. p = DO, live exponacur 2 a = 9
2. d
Eirc3
2.4
=
24 P = DO (ur ubi OO non tantiC AP,)
Ep = DO (uc ubi cantie) uccoris modo erit 4 a +4 +. 4 a9
= DO9. Er paricer concingic in Demonstratione Syncheticea. Ouod monuillé
tusticie.
Poltene hie alia Theoremata mulca sigillarim ostendi, puca,
Quoalibet Curvae Parabolicae punctum alicujus Diametri verticem esse
Adeoque In qualibet Parabola infinitos esse Tertices, atque Diametros in-
sinitas numero.
Icem; Parabolae Diametros omnes este invicem Parallelas.
FE; Duamlibet rectam (in eodem plano) cuilibet Parabelae Diametro paralle-
lam, ejusdem Parabolae Diametrum étiam esse; eique in uno aliquo, e quidem
unico, puncto occurrere
Trem; Duamlibet in eodem plano rectam, per aliquod intra Parabolam punctum
transeuntem, Diametro non parallelam, in binis punctis Parabola occurrere: 
alicui Diametro Ordinatim positam esse.
FE; Dua vel alieur Parabolae Diamerro Ordinatim posita es
vel Diametrum
aliquam quocunque modo secat, vel quae Parabolam secat laut ipsi occurrit) in
binis punctis; nec illius Parabola Diametrum esse, nec ipsius Diumetro ulbr pa
rallelam.
Tlem; Duae Parabola Diametro alieim in vertice occurrit ordinarim applicatis
parallela, Parabolam in illo puncto contineere. I. ress . LsB.  setis es Ssilee
EC; Dua Parabolam contineit, Diumetri per contactus punctum transeuntis
Ordinatim applicaris parallelam esse: adeoque eidem Diametro Ordinarim positam.
His aurem, aliisque consimilibus, sigillacim demonstrandis, non immorandum
esse sentio; Cum ea vel in progreltu praecedentium Demonstrationum Paris jam
oltensa linc; vel ex eildem principis lacile demonstrari pottint. taii suve
iovic
P R O P. XXV. (ALEITIEIOS WSC, 
Effectiones Geometricae.bf ACZCHC:SESI
Z praecedentibus, non erit disticile Ccometricas LRectiones cot-
Aligere. Putam
Datae Parabolae Diametrum invenre. Nam recta, quaslibet duas inseripras
Parallelas bilecans, est Diameter.
Iiem, Per datum quodvis in eodem plano punctum, rectam ducere quae sit
Parabolae