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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 SEC11ON1640
misto; adeoque eadem est cum alricudine Frianguli, si circuli sine triangulo recti,
(eric enim perpendiculum illud in ipso crianguli plano, adeoque ipsius etiam batI,
taliem productae, perpendicularis, ejus alricudinem metiens;) sin secus, minor
erit; tunc enim perpendiculum ad balin crianguli demilsum, erir ad Cioni basin
obliquum, adeoque majus perpendiculo alcirudinem Coni metiente.
Norandum tamen insuper est, Conum tormari polte, non modo s expolici Tri
ansuli recta parallelae, line circulorum Diametri, verum eriam si circulis (vel
quidem limilibus FPiplibus) alio quoris modo limiliter aptentur; (quod, A OpuS
lic, tacile est demonttracu; nos autem obiter tanCum mOnemUS:) Verum, eo casu,
Friansulum illud non necessario per Axem Coni incedet, neque ea omnia conse.
quentur simpromata qua hinc dependent.
Si vero, pro Circulis, Substimantur coridem Piourae rectilinex, (aliaere vel cur-
rilincae vel mistae, praeter circulos et Fsipses,) non quidem Conus, sed saltem
Prramis emerset: Cui et ea omnia facile accommoctari postune (mutatis mutan.
diS) qua de Cono (hoc clt, Pyramide rocunda) diximus. Pyramidis autem no-
men hic laciori sensu accipiendum volo, quam ut solis tiguris rectilineas bases Ha-
bencibus conveniac; ita nempe uc bales planas qualeunque admicta, (sieur et de
Prismace supra dictum est ad PrOP. 2.) ne scilicet lonsis verborum Ambasibus
ucendum ellet. Adeoque
PROP. V
De Pgramide
Dramidis voce (Tub qua e Conum comprehendo) intellieo Fieu-
ram Colidam ex intiniris planis circa cundem Axem rectilineum
ordinatim posicis contlatam; quorum omnium crasticies supponuntur
inricem aequales (nempe e alcitudnis tigurae Lolida,) diameeri vero
(vel homolosa latera, aut etiam recta quaeris similiter Dosicx) di-
Hantiis a vercice proportionales; adeoque ipsa plana in duplicata ra-
tione distanciarum a verrice, (sieut ex Prismatis nomine intelliso ejul-
modi planorum aporeoatum inricem aequalium.)
Si autem Prramis plano per verticem secetur; manifestum est plana
similia (Parallela) similiter Sccari; communes ergo sectiones (plano-
rum secantis ex sectorum) lunt infinitx rectae Arihmetice proportio-
nales, (nempe in subduplicata ratione fsurarum, hoc est, in ratione
distantiarum à vertice,) adeoque omnium aggresatum erit eriangu-
lum; DeT PFOD. 2.
Anem vero Prramidis (ut ex Prismatis) appello, Lincam a vertice
ductam, similium planorum parallelorum ominium centra conjunsen-
tem. Plana vero ad Axemordinatim positam appello, quae parallela, et
similia similiterque posita, centra habent in aXC.
Si vero, vel quod criangulum, unde formari supponitur Pyramis, non sic recti.
lineum, (sed curritineum, seu quocunque modo detormatum,) aur ob aliam
quamlibet racionem, Planorum, centra non sine in eadem recta; vel ipla plana
circa cundem axem non sint limiliter potira, (sed spirali puta, vel alio quoris
modo distorra;) modo incerim plana sine limilia e aequaliter cralta, debitamque
ad inricem rationem retineant; Ppramis laxata, distorta, vel deformata dici po-
icst. (Oux etiam de Prismate, aliisque fguris solidis, paricer incellisenda LuInE.)
T ineaque omnium centra conjunsens (li recta non () Avis distortus dici
porelt.