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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 35, page id 898203430:0227
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ORDTNATARVM POTEHTIVM LIMET. LIS. I.
LEMMA V. PR O P. LIV.
I recta AB secta sit bifariam in C. (9 non bifariam in
D, rectanculum sub inaequalibus sermentis AD B
aequatur quadrato minoris sermenti DB, ona cum du-
plo rectanguli BDC ex eodem minori sermento in
reliquum C. D ex dimidio datae.
 Vmatur C E aequalis CD, de eric reliqua F A aequalis DB.
 Tari, rectansulu FDB cum qua
drato DB aequale es rectanoulo L BD,
vel rectanoulo ADB, sed F D B aequale
elt duplo rectanguli C D B C quIIm SIt
ID dupla CD) ergo rectangulum ADB
aequatur duplo rectonguli C D B cum
quadrato D B. Ouod cras demonstran.
dum.
A  c
PROPOSITTO IV.
Ocus Ordinatarum potentium differentiam inter re-
ctanculum sub inaequalibus parcibus inteerantibus
datae, (5 quadratum minoris seementi, est ad conca-
um semiellipsis prolatae, cuius minor axis sit dimidium
data, in qua est scementum minus, (5 qui sui recti
lateris sit dimidium.
OIT data A B secta bitariam in C, et non bifariam vecunque in D.
L. D PaCCL, quum si AD maior DB, rectangulum AD B maius eNC qua-
draco DB. His poliris: Si circa C B dimidium datae, catquam circa ii
norem arem. describatur Flliplis prolata C. E. B, cuus iple minor adis C B
Cui recti laceris sc dliimidium, aequalis
nempe datae AB. Dico huiuS peri-
Pheriam esse Locum Propolitum: hoc
CA Ordinatam DF Porse difterentiam
incer rectansulum A D B, e quiu
dratum DB:
Es enim, ob Fllipsim, rCCLanSII-
IUm CD B ad quadratum DF, VE
2Xis cransuersus CB ad suum rectum
BA. vel ve vuum ad duo, erBO rC.
etaH