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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 301, page id 851387705:0321
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Comisantem sic Formatus, si tam expositi Frianguli Crura sint aqua-
lia, quam circulorum plana plano Frianguli recta, crit Conus Rectus,
(mtpote cujus Axis eA Basi perpendicularis, qui propterea Axis Rectus
dici COleE;) Si vero vel altera vel alterutra illarum conditionum desit,
(puta si vel expolitum Friangulum sic inaequierurum, rel plana circu-
lorum plano Frianguli oblique insistant,) erit Conus Scalenus, hoc est in-
clinatus vel obliquatus, (cujus nempe Aris Basi oblique insiltit, atque
Axis Obliquus dici Colet:) s vero Friangulum Distortum fuerit, het
et Conus Distortus, non rerus Conus.
Prout autem Friangulum potest (productis infra basin cruribus)
in infinicum concinuari; ita et Conus pari modo concinuandus (uppo-
nitur.
AEque Ctiam, SIEnE (continuatis, pos decurtationem, Frianguli Cr-
ribus supea verricem) aliud Formari potest nara noeuplu Friangulum
(quod Trianculum opposicum axpellamus, ita et Oxposcum conum formari
suxponendum eAt.
Pleraquie in propolitione (praecerquam quod Detinitiones Cinc) per se lacis
Patene, nec ulreriori egene Demonstratione. Unicum opus est, ut oltendam, nempe
Fiouram solidam sic formatam, (Ei Conum Distorcun eximas,) talem Conum esse
qualem desinit Apollonius: Vel, quod idem est, Parallelos circulos coni noltri pa.
rallelis Circulis coni Apollonii congruere. Ouod quidem rerum cAt.
Nam (propier parallelismum Circulorum, adeoque ee eorum Diametrorum in
eodem plano existencium, iltalque Diametros distantiis a rerriee proportionales,
Si lacus alterurrum, expolici Prianguli per axem, pura VB circumteratur secun.
dum circuli unius (puta Balis) Peripheriam, crantibic etiam per Peripherias re)i
guorum, Radiorum extremitares lambens (qui ubique funt distantiis a verrice
proporrionales et balis radio paralleli, adeoque, durante tora circumductione.
erianoulo quod Axe trianguli expolici, recta circumducta, e balis radio compre
hendiur, ubique accommodatur,) coramque tiguram describet: Ouxe elt Apollonii
constructio Coni. Conus isitur a nobis formacus idem est cum Apollonii Cono:
Ouod erat oltendendum.
Acque hinc etiam sequitur, A verrice ad quodvis superficiei Conicae punctum re
Etam duei posse
Recordandum incerim este, (quod supra univertaliter monvimus.) sient Jineis
criansuli; ica planis Coni, al. qualem cralticiem concedendam elle, quanta nempe
elt ∞ alcicudinis Coni: vel, quod idem cst, Circulorum axpellatione, exlindeu-
los numero intinitos, tancx quidem alticudinis, super circulis illis constiuos in-
celligendos esse; qui ivicur solidum ex intinicis cylindrulis cono vel inscriptum
vel circum seriptum supponuntur constituere; quod solidum idem esse cum cono,
eodem argumento concluditur quo uA Tuus de Frianonlo, PFOD. 2.
Coni aucem alsicudo, menturacur perpendieulo a Verrice ad planum Balis de-
misto: