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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 962, page id 1815201908:1019
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962
TNGYLA, CYLIND R 1O A
quaenis FI in cylindri superticie extii
bons commutes mtellectiones cum
planis poncis puncta 6, l1, 1.
cotC aqualem elle line lL l.
Demonstratio.
Atam TF adC Pracium paralleru pla
CBM, Faciens cum plano CDB sC.
ctionem lK, cum plano CDL Mcctonen
RL, cum plano C LCB lectionem LV.
Duoniam isitur planUM CDP, CCCaC du0
plana parallela KFL, CBM, crunca lectio-
RCS RF, C B parallelae. Kurlum quia pla-
num C F C Blccac duo plana parallela R si l.
CBM, crunt sectiones IG, CB eriam pa-
rallela. Para llelae igitUr BSUINERF, I. C. DC-
inde quia plana parallela RF L, CBM sCCAE
planum LD C, crunt sectiones communes,
nimirum RP, ee axis cxlindei, aequidictan-
Ees. Fed eriam lacus F C axi eouidistat. ergo
RL, F C aeguidistanr. erg0 C+ FR L Paralle
logrammum elt. ergo FC X qUatUFK L. Iun-
sancur deinde CMI, RTI. Duoniam plana
Barallela IRHI; CBMI lecac planum
CL F LM. crunc commun ectiones T. I, C MIparallolX. Rursum quoniam plana
parallela RFFL, CBML lCCAEplAnUM CKD HIM, crun sectiOnCS RFL, CM p2-
rallele. ergo etiam L. I, R EI Cuncparallelae: lune aucem d FII. K I. supra oAtenlx pa-
xallelae ergORFTIL Paralleloorammum est. ergo HII aequalis cst, R L. sed eciam
octendi supra PC equari K C; Equarur igicur PC; HT J. Ouod erar demonstrandum.
Corollarium.
TOcahac propostionem prorsus esse viiuertalem; vera estenim, siue A B, diame.
cer sccirculi AD BC, sine quae daiti eixquidistatis, vepacec demonstrationem
consideranti.
PROPOS
191
x1O. 1X
Sro cylindeus cuius balim diuidac diamieter A B: ex CEHErOD erig a-
scurnormalirer C. D ad diametrum AB: per C vero ponatur in lu-
perticie cylindri C. F recta linca: deinde agaeur planum per AB, de pun-
ctum quoddam E, in recta CF, extribens sectionem ABKF. polica
denique in cylindri luperticie recta BHI, ducacur planum per C D, 8
quodlibet punctum HI in recta B II, tandem per D F. rectam e idem
punctum HI sectio RatD F. GII.
Dicorngulam exlindricam D BFCE K B aqualem esse Colida ma-
snicudini DHICE GFI.
Demon