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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 91, page id 898203430:0283
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VARTAR: DISPOSTTIONVM LHHT. LIBER HI.
P R OBL. V.
P lL. AAAVII
Vier duas datas lineas mediam Tlarmonicam as
snare.
InE datae rectae AB, BC, inter quaS OpOrECaC MeaLM HLarmOnICaIM
a invenire.
Concipiantur iplae in directum in A C, quam CIICA tanquam araHL
trum describatur Circulus A D C F, aeque ex B ad circumteren.
riam vlque applicetur BD Circuli radio aequalis, producaturque ad alte
ram peripheria parrem in F. Di.
CO D E esse harmonice medium.
inter datas AB, BC.
Ouum SiE enim BD aequalis ra
dio, aequabitur dimidio Cummx ex
tremarum AB, BC; quare BD
eric media Arichmetica, Si vero ex
B agatur BF ad AC perpendicu-
laris, ipla erit media Ccometrica.
inter ealdem AB, BC. Sed LC-
ctangulum DBF aequale est rectangulo ABC, vel quadrato perpendicu-
laris BF, ersotres BD, BF, B P. erunt in eadem concinua ratione (3C0-
metrica; ac D B est media Arithmetica, de BF Geometrica inter A B,
BC, quare per superius Corollarium mulcipliciter demonstratum certia
BF. erit media Harmonica inter caldem datas AB, BC. Ouod exat Fa-
ciendum.
Aidc Datet, seclansu sub extremis quibulcunque datis requale
Le rcerangulo sub mediis Arichmerica, ae Hlarmonied let Caler
quoniam rectanoulum A B C sub extremis aequale cA rectangulo D B I
sub mediis dict S: quapropter maior extremarum ad mediam Arichmericam
est ve media Harmonica ad minorem extremarum, cd quod in Circulo sic
AB ad BD ve E B ad B C, ob aequalicarem rectangulorum A B C,
DBE.
Horum omnium demonstratio lusgeri de suod lecus.
2 22
PHOBL.