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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 112, page id 898203430:0304
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VINCKNTU VIVIN
In criansulo ieaque
N A C secto Dec BNI,
BD Parallelas lacerious
L6C. CatI; quum HICAL
aequalis DC, elt quoque
AB equalis BHI; dc C MI
aequalis NM; ec obid in
criangulo C BN, ceiam
CL aequatur LH, ec Vtra-
vis harum minor ipsa bI
cui Cumatur l0 aguo.
lIS.
Jam, ob rulsaram Parabolae proprictatem quadr. tans. B M ad qua-
dracum canseneis BI, vel quadearum C. M ad quadracum LCF est, ut
linea CM ad IFT, vel, ue linea PI ad IFI; guare linea F I ad ICY
est, uF ICE ad IFI, et per convertionem rarionis IE ad F C est, ut
IC ad CEFI (sumpeis duplis ancecedentium IV, ICE) OV adICF
DE F C+ ad EFI; ec dividendo O (+2d CEF eA, DE F FI ad FTCE, sed
OCE aequatUr ipII E F; ergO CEiAM R V ad E CE CA, UE F II adTIC,.
Ouoniam isitur in his eribus rectis PE, PII, F CF, prima P P. 2d
certiam F CE est, ue prima differentia R. TI ad secundam IICF; erie
harum erium media EFI media BATMONICA INEeF eXFRCMAS H H, L CF.
Ouod crat demonstrandum.
SCHOL IV M
REquitur hinc, quod (tribus dacis magnicudinibus in quavis con-
tinua geometrica ratione) semper summa differenciorum estme-
dia harmonica, inter Cummam maximae magnicudinum, cum media,
de maximam differentiarum.
Superius enim oltentum est, in cribus dacisIl, IC, ITI in con-
cinua ratione seomerrica, iplam LII, quae est summa difterencia-
rum carumdem erium esse modiam harmonieam InCeF R, E (qua CON-
Aac ex lE maxima erium dacarum, e ex LF, vel ex huic aequali
ICE media carumdem crium proporcionalium) et inFer P CF, qua est
maxima disterenciarum carumdem erium concinue proporcionalium
IE, IC, IFI. EE CCONTTA.
I.
SCH OL IV M
+
PRguitutCCTaM, GuoIIBUS CLIS MABMHLDAMIDUS IM COMIMVALd.
aD tione harmonica) dimidium differenciae inter primam, ec tertia,
semper es media seomerrica incer summam ejuldem dimidii cum ter-
tia, de differenciam inter have lummam, ee mediam harm OHICA.
ln