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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 SECTIONIBUS PFOPXXXIV
Dueatur recta 2 A =F, e (in ejuscleni continuatione) AFI =d: REque ad
rectam AII ponantur (ad OppOSitaS partes) duxe rectae inricem parallelae; AS =-1
et HIB= a, (Talcem cancx line longitudinis AS, HB, ut AE ASXHB = Id :)
Sicque anculus S AH = AH B quisibet acurus, (modo major sit complemento
ansuli inclinationis in Flyperbola exposita.) Juncta rero aS producatur ut cum
recta BFI producta cocat in S; e juncta B A producatur ut occurrat ipAi aS in
V; ue compleacur erlareutum VBS; quod esto Friangulum. per axem in Cono
construendo.
Deinde super rectis AFI, BFLS, duo plana ita erizantur, ue comunis eorum
sectio HIO, faciat ad rectam HB angulos rectos, ad rectam rero AHI angulum
AFIO aequalem ansulo inclinationis in FIyperbola propolica.
Hoc enim omnino tieri poste constac: Si enim recta quaelibet HO perpendi
culariter intistens plano Frianguli V BS (adeoque angulos faciens vero (que OTHA,
OTTB, rectos) circumrolratur circa rectam BHIS uc axem (invariato 2youlo
OHLB,) donec ad licum plani perveniat in Hla, Faciacque in plano trianeuli angu-
lum coFTA acutum, qui minor erie ansulo inclinationis in Hyperbola, (est enum
ex constructione, angulus AHIB istius inclinationis complemento major;) ne-
cesse est ut, in crantiu, aliquando fecerit angulum inclinationis angulo aequalem:
(tactus enim cAt cransicus ab angulo recto, adeoque debiro majori, rel salrem aequali
ad ansulum debito minorem;) adeoque cunc tuerit in sicu debiro ut sic duorum
Planorum pront requiritur concurrentium communis sectio.
In plano aurem BOS sic potico seribi intelligatur cireulus, diametrum habens
BFS, qui sic balis cohi; aliique huic paralleli diamecros habentes BDS, conum
complentes, (Per prOP. 5.) qui plano AHO sectus exhibebie Fyperbotat (Per
PrOP. 7.) cujus ordinarim applicatx omnes (quarum TIO est una) ad diamecrum
AHI angulum facient aequalem ansulo inclinacionis ordinarim apolicatarum in Ly.
perbola, expolica act diameirum suam; sed e cisdemi sunc relpcctiro aequales (ut
Parebit ex demonttratione prop. 17, et 20.) ideoque lingulae singulis consruunt
adeoque e Fyperbola expolica Hyperbola sectione coni tactae. Ouod crat tacien-
dum. Adeoque Hyperbola a nobis detinita eadem est cum ea quam detinic ApoI.
Jonius. Ouod erar demonstrandum .t por e ts olto sil
Sed de eadem opera doenimus Conum construere eique datam Fyperholam ila
aptare, ut data ipsius diameter sit ciameter. ex reneratione: Aeque eciam Theore-
matice verum elle LEuperbole diametrum. quamlibet fieri posse, in aliquo saltem
ConO, Diametrum ex generatione.
Fet 203 31t 5HIOC IsBIGB DEC.).
14 AS 1II
sserloc st Cr rSCI
oisitraaci n
I ad eandem diametrum duxe FTyperbola OppOsito situ DOnan-
tur, collutnem habentes diametrum cransvertam, idemque la-
tus rectum; lintque ad il
lam diametrum orcinatim.
applicatae unius, ordinatim.
applicatis alterius parallelxe:
dicentur illa Lyperbolae-oppo-
sitae; carumque rertices, can
dem diametrum eranlverlam
terminantes, Vertices Oppositi:
Punctumque inter ODpoltOS
vertices mecuum es utrique
EIyperbolae centrum com-
MunC.
 aurem Hyperbolae Opposi
ix respondeno tly petbolis Oppo.
sucorum conorum eodem plano le.
atorum.
eROP.
mondous oi. - D R O DI IHXXIV. 2
De Diametro transversa  Fyperbolis oppositis.
eresis c
puci ) uert ogiel