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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 99, page id 898203430:0291
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NARIAR. DISPOSTTIONDM LIMIE. EIB. III.
Ato AB secerur bitariam in C, de dimi.
  dium C. B = siC sCCCTUE in L, UE reCtan-
sulum Cub BC. in sUI SEGMENEUM CD, 2d
quodrarum reliqui Pegmenei BLD SiC, ut unum
ad quacHOE. DicO, Dunctum D quaelitum lolrere, hoc est segmen-
Eum Majus AD esse medium haemonicum inter dacam AB, ee lep
MITCTEUI MInUS BI
Ex reliquo dimidio C A eata A B, SUIMAEUE A F aequalis DB.
Jam, quum CiE, ex conttructione, rectangulum (ub BC. in C. 1 ad
quadratum DB, ut 1, 2d 4, erie rectangulum lub duplo BC. in dy.
Dlum C. D, sive sub A B in P D, aequale quadrato ejusdem DB; +C
ideo eOcA AB ad BD eric, ue BD ad D L; sed A I. aequatur DB,
ergo etiam AB ad BB eAt, vE A F ad A. D.
Si isitur in eribus rectis AB, L B, DB, est uc data A B primus
terminus ad cereium BD, ita A F. primus excessuS ad F D secundum;
erit medius terminus HB medius harmonicus inter primum AB, dc
certium BD; (ex detinicione a Pappo allara) sed medius F B, CX
constructione, aequacur ipsi AD; quore haec ipla quoque AD, scili-
cet leomentum majus datae AB, est medium harmonicum inter da-
eam AB, e Termencum minus BD. Secta cst igitur data a B in D
secundum mediam, de exrremamracionem harmonicam. Quod erat
taciendum.
PROBL. XII.
DROV. XAXRVII
 PET PEOF
uivi
Atam rectam terminatam A B sic inaequaliter secare, ut
quadratum sermenti majoris sit medium barmonicum
inser quadrarun tocius data, e quadracum sermenti mi-
ROrIS.
Nempe sic, ut quadrarum torius ad quadrarum segmenti mi-
noris sit, ut differentia inter quadrata totius; es seemen-
ei majoris ad differentiam inter quadrata seementorum.
Vel denique secare datam AB, secundum mediam, es extre-
mam rationem harmonicam quadratorum.
D vero solvere conabimur, per novam quamdam lineam, Guata
Vereres Cieomerrae incer 1000s lineares ponere non conremplit
lEnI.
FI.N 2
du