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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 984, page id 1815201908:1041
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NOVLA CXLENDRLCA
Demonstratio
ACa LinErBuI A _B, L. L ME quarum alcicudines F K, O F, aequales sinc A B.
M diamerris semicsteulorum AGB, I. RM, qui in sciplos ductiiplas, vein
Scholioro. ostentum elt, vngulas producune.
IBiamecris A B, F, ML in Xque mulcs, Sed plures ac lemperplures, equales partes
AI TP F. V.V V diuilis per divisionum puncta P, I; V, V ducancur normales ad
diamerros GC, GC: R O, RO, _ compleantur rectanguta, C, I, OT, R V, RV.
icem CIsCI, OV, OV, Cemicirculis inscripca. Rectangula (I, GII, RV, R V vna
cum semicirculis suis ducta in scipla, hoc es in rectangula iltis aequalia se similia C I.
CF, _ OV, OV producentintinica parallelepipeda, rngulis que ex lemicirculo-
rum ductibus generantur, in scripea, quorum bases erunt rectangula CIC, R VO.
hoc est quadrata IC, V. O; alcicudines vero erune xquales diamecrorum parces IL,
VV. Ouia ex constr. AI suncad TB, DEL V sunc ad V MI: suneque C I, OV me-
dix InEEF AP, TB, _ LV, V M, crunc quoque AI, ad CT, ve L V ad OV. de in-
nercendo CF ad AI, vE OV ad LV. SCd CKCONSEF. A T TUnCAd AB, VE L V 2d
LMI. erSOCxaquO CI sunc ad AB, ve OV ad ILM: ee pormucando C L (unE 2d
OV, ve AB ad LMI. ergo racio quadeacorum lingulorum CF ad quadraca sinou-
la OV duplicaca estracionis diamerrorum AB, F MI. Sed racio alcicudinum FI, 2d
alcicudines VV, eadem est ex constructione, quae diametrorum AB, L HI. Racio
isicur compolica exraciono guadracorum C. I ad quadeaca OV, et ex ratione al.
ticudinum Et ad altirudines V V, hoc est ratio parallelexipedorum singulorum vn-
sule AKB inscriprorum ad parallelepipeda lingula rngulae L. I M inlcripea, eri-
plicaca est rationis diametrorum AB, ILM. ergo singula parallelepipeda vngulae
A KB Engulis rngule P. TM proportionalia suINE. CrZO Per 12.5. elemenc. ve vnui vuou-
Ix ARB adrnum rngule P. PM, sic omnia simul ad simul omnia. Requi rnum
estadrnum in triplicara rarione diamcerorum, ve iam ostenum cst. Proo omnia li-
mulcumpea rngula AR B, Cunc ad omnia simul Cumpea vngulae I. Y M in criplica-
caracione diameerorum. Quare Ei prolequamue reliquam parcem discursus in pro-
vol. 45. X 17. exprelsi, legicime concluderur, ongulam quoque 2d rngulam in eripli.
cara exiltere diametrorum ratione. uod eraC demonstrandum.
DAR S