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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 41, page id 898203430:0233
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DADNNATARVM POTENTINM LIMIT. LIB. II.
mul conticiune rectanoutum sub MO cum N ET in OB, vel in OFL, vel suB
aequalibus A B cum D C; in BC, ergo differentia incer rectangula HF
AHI, sive inter rectangula ABD, e A C, D est idem rectangulum sub
AB cum DC in BC: hoC est rectangulum ABD sub daca, e lecto leg-
MENEO, aquatuT rectangulo AGD sub aggregato insecti cum inter posO,
in incerpotirum, una cum rectangulo sub data AB cum incer poluo DC in
extremam porcem BCi diuili segmenti B D. Qnod erat demonstrandum.
ROPOSIEIO LAI
Ocus uhatarum potentium differentiam intet qua
dratum datae, (5 rectanculum coadditarum, quod sit
minus quadrato datae, est Locus planus, nempe con-
cauum peripheriae Circuli, cuins centrum sit punctum
bisecans datam, radius vero possit sesquiquartum qua
drati ejusdem datae. ee   cau
ttoi
IT data AB secta bitariam in C, quo Facto centro, ad inceriallum.
 radii C D potentis selquiquartum quadenti A B, hac Temicireulus
DE F. Dico huius peripheriam esse Locum propositum: hoc eR ordinaratm
quamcunque CFI inter puncta B, D, porse diferenciam inter guadracum.
darae AB, et rectangulum conddicarum AC, B, quod minus este quactt. 
to A B sic OAtendiEE.
Ouoniam enim, ex constructione, quadracum
OD ad AB eAt VE 5 ad 4 _E GUAcTAEUM AB
2d BC eA vE 4 ad s ( co quod (t AB secta bin
fariam in C) quadratum CD ad C B erit ve
quinque ad rnum, estque C B aequalis C A, )
ergo recta AD secta est 2 in B secundiim ex-
tremam, de mediam rationem, dc ideo recraN- FO A
Gulum AD B aequale eM quadrato data AB.
Insuper, quum recta AD secta sic in B secundum extremam, _ me-
diam rationem, e alterum ex eius segmentis BD sic diuisum in C vecun B per L cu
que eric disserentia incer rectangulum ADB, e rectangulum AC B b ip Praecedens
sum rectangulum sub AD cum BC in GD, sed A D aeQuatuL ipS FB
(quuum sInE CF, CD, _ CA, CB, de reliquae AF, BD aequales, de
AB communis) d reccanculum AD B aequale est quadrato A B, ve su
perius demonstrauimus, ergo differentia inter quadratum AB, de rECEA.
culum ACB es reccansulum sub L. B cum BC, nempe sub LC in CD.
cui aequatur quadeatum media proportionalis GHI in Semicirculo F F D.
Ordinata igitur CH Porest praedictam disserentiam: de hoc de singulis si-
milibus ordinatis _ec. Ouapropter concauum huius plani Loci D F. CAt L0-
cus propolux Ordinationis. Ouod crat ec.
eRC
C
t
b Prims
ropot. lib
13. Filem.