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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 9, page id 898203430:0201
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DRDINATARVM POTENTINM LIMIV. LIB. II.
Eatam diametrum AC; eric, per praecedencem, quadratum C F ad qua.
dratuu D F. ve quadratum C. D cum quadrato semidiameeri coniusatae.
nempe cum quadrato DF, hoc est ve rnicum quadraum C F, ad qua-
deatum ejuldem semiconiusatae DF, ergo quadraca C F, C F sunE aequa-
lia: sed quadratum C F aeguatur duobus C D, DE, quorum D C ~-
quale est rectangulo A C B cum quadrato DB (ed quod sic AB lecta
bifariam in D, eique addita sic B C) _ quadratum DF. xquatu SubsCS-
quitertio quadrari AB, vel criplo quadrati DB, ergo de quadratum C F
aequale est rectangilo ACB cum quadrato D B vna cum eriplo ciuldem
DB, quae conticiune quadratum ricae AB; hoc est C F potest quadratm
data AB cum rectangulo Tub coaddicis A C B. Ec hoc lemper ec. Oud-
re concauum huius Flyperbolae es Locus propolica Ordinationis. Ouod dc.
PR OPOSITIO XIII.
Ocus Ordinatarum potentium summam ex rectan-
gulis sub data (s partibus, est LOcus planus, nempe
recta linea per interuallum data huic aequidistans.
CPT AB daca vicunque secta in partes AC, C B, sicque F. D datae AB pa.
rallela per interualum ipsi aequa-
lc. Dico hanc esse Locum propolicum
hoc est ordinatam CD posse suminam
rectangulorum ABC, BAC.
Patec hoc ex constructione, ee C
secunda secundi Elementorum.
PROPOSILIO XNV.
Ocus Ordinatarum potentium summam ex rectan
sulo sub superaddita in additam cum rectanculo sub
data in superadditam, est LOcus planus; nempe recta
anculum semirectum cum data constituens ad occursum
datae cum super addita.
NIT AB data, de AC superaddita, Factoque ad. A angulo LemIICC
LDCAD. DICO reCtaM AD eNC ZOCUM PFO.
Dolirum; hoc est ordinatam CD posse sum-
iam ex rectangulis AC B, C AB.
Manifestum itidem est hoc, tum quia C D
aequalis est CA (ob angulos semirectos ad A,
D) cum per secundum Proposcionem secundi
Elementorum.