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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1038, page id 1815201908:1095
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SPH A ROID F
ARS SF X T A
De Spharoide.
Cplinar C Sphaera nonnullas proporiiones earumqe parcium conati sumus huer sque
expulare; ex quia adrem nostram non parum facit mareria Sphaeroidica e Conoi-
dica curus reductio almaenitudines cubicas à circuli quadratura maxime depen-
det, hinceam intactam praetermittere nefas videtur: conabimur itaque hoc parno
cractatu proprietates Sphaeroidis magis obuias ac necessarias investreare ac demon-
dirare.
DEFINITIO PRIMA.
VEmiellipleos alter axium ita incelligatur consticurus ve circa cum
immorum ipsa Cemielliplis in orbem agacur donec in cundem locum
redeat a quo moveri experat; Colidum ex hac reuolucione Formarum
Sphaeroides vocetur.
DEFTNTTIOSEENNDA.
Arem Sphaeroidis voco lineam que in ciuldem Formarione immota
mansic; estq simul axis ellipseos que conoides genuit.
DEFINITIO TERTIA.
Centrum Spheroideos dicatur punctum quod in formatione cenerum
Fuic ellipleos, simulque est cencrum omnium figurarum quae per iptum
cran(cunE.
Scholion.
Tocaru dienum videtur duplex esse Sphaeroides, unum quod formatur suxer axe maiore et
lipseos, alterum quod sit sub minore, quod quoniam lenticularis forma ficuram exhibet, à
Geometris videtur praetermissum qui oualem ficuram cum elliprica confundere consuenerunt:
quae isitur sequensibus propositionibus ad ducemus, verique sphaeroidi, es ouali es lenticulari
communia esse volumus.
DE FINITIO OVARTA.
Similes elliples dicaneur que axes habent proporcionales.
PROPOSITIO CV. LEMM A.
Elipum cuius aris A C contineat circulus ABC, contingens in 
Lse C, ductâ deinde quovis FC, que occurrat axi in HI, ponatur que
cunque IK ordinarim ad axem AC. sccanS FO in L. Deniqueper H
ponatur FI F. ordinatim ad axem AC, _ per P recta M I ordinarim ad
AC, _e duCatUTMI HIBOccurrens rectX IR inO.
Dico SHI quadrarum ad F HI quadrarum cam rarionem obcinere
quam POY rectansclum ad IL. R.
Demon.