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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 61, page id 898203430:0253
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VARIAH: DISPOSTTIOHNM LIMIT. LIBEK, III.
Ad dilucidandum quoque Corollarium Propositionis terriae huius, binae se-
quentes Proposiriones addere non erit inconcruum, es ex abundanti idem
Corollarium peculiari demonstratione comprobare.
aOPO511II XII.
N Circuli Cd Ollipsis quadrante. Manimum inscripto-
rum paralloderammorum in eodem anoulo a semidia-
mocis facto constitutorum, id est, cuius vtrunque
latus possit dimidium quadratorum ex semidiametris,
quibus ipsa latera adharent.
STO Circuli, vel FIliplis quadrans ABC, Cuns centrum B, teti-
diametri vero BA, BC, qua secta in D, ita ve guaoracum C B du-
Dlum sit quadrati B D, ordinataque DP. ip(I A B parallela compleatur pa-
Talleloorammum BF. Dico id esse huiulmodi inlcripeorum maximum.
Prodycamur semidiametri ad alteram parcem in B. C, BH, AIque ex
E agatur concingens IL. productis diametris occurrens in l, L.
Jam, quum ex Hypochesi
quadracum C. B duplum AI
quadrati B D exIE rECTAHBU.
Ium CDC aequale quadrato
BD; Sed ips C,DC aequa
tur a rectangulum LDB ob
tansentem IL, atque ex primo
Conicorum ergo ee rectan-
sulum L. DB quadrato BV
aequale est, nempe L. D, I
B sunt aequales, adeoque, et
LF, F. P aquales, quare parallelogrammum BF est maximum inseripri
Bilium erianculo B LL; ac ideo ed amplius paralleloorammum B P crie
maximum inscripribilium quadranci Circuli, vel Flipsis A B C. Ouod
erac demonstrandum.
Ouod aurem dum radius BC porest duplum quadrati BD, alter quoque
radius A B possic duplum quadrari lateris BF, ve in superiori propolicione
expositum fuie, constabie ex hoc, quod quadrarum AB ad DF, vel ad
BF est ve rectangulum C B C, vel ve quadratum B C ad rectangulum
E D C; Ced quadratum B C duplum est rectanouli C D C (eo quod
aequale sic quadrato BD cum rectangulo CD C, licque insuver quadratum
CB duplum BD) ergo ee quadrarum AB duplum erie quadrato AF.
primi
Conie.