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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 31, page id 898203430:0223
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OADIATARVM POTENEIVM LIUT. LI. II.
Ouoniam enim quadratum CD duplum 
est quadrari C A C ex constructione) vel
rectanguli A C B, idem quadratum C Y
duobus rectangulis A C B aequale exic. FC
quum quadratum C. D ad E F sIC 2 VErC-
ctangulium ACB 3d AF B, vel ve duo
Tiul A C B ad duo simuI AF B, sique
permutando quadearum C D aequale
oltensum duobus rectansulis ACB, exie
de quadratum EF aequale duobus simul AFB, sed disterentia inter quadra-
tun data AB, C quadeata simul partium AC, CB aequatur duplo rectanguli
ACB, ergo ipla ditterentia, et quadraro C D aequalis eric. Similiter dif-
Ferentia incer Quadratum AB, _E QuadTaEA SIMUI PaTEiIM A E, E B XGUATIE
duplo rectanguli AF. B, ergo eadem disserentia, de quadrato P. F. xqualis
exit. Ouare ordinatae CD, F F, de alix huiulmodi porsune praedictas dit-
terencias; ac propcerea concauum deleriprae Flliplis est Locus propOlI
Ordinationis. Ouod etat eec.
P R OPOSITIO ZZMNVU.
Ocus Ordinatarum potentium differentiam inter qua
a dratum datae, (5 summam quadratorum additae, (9
superaddita, est ad concauum Ayperbolae, cuius cen-
erum sit punctum bisecans datam; anis addita, (5
vertex occursus datae cum addita, semiaxis transuer-
sus dimidium datae, semirectum vero ipsa data.
PTT data AB, de superaddita quaelibet A C, adeoque addita BC; ee
1 secra A B bitariam in D, CuM CenErO D, Seminxe trantuersO D B,
lemirecto rero aequali ipsI AB Rac FIy perbola BF. DicO HanC CNC Locum
propolum: Nimirum ordinatam C L porte disterentiam inter quadratum
datae AB, _ summam quadratorum A C, C B superadditae, de addica.
Nam quadeatum A C cum quadrato
C B. aequatur duobus rectangulis AC B
cum quadrato AB, Per 7. SCC. FlCM. ex
30 difterentia inter quadracum A B, de
duo Siul quadrata A C, CB aGUatUE
duobus simul rectangulis AC B, sed duo
AC B aequalia lunE quadratO C F C guIIm
Policus sic cransuersus axis, AB subduplus
THO reCtO, dC Propterea recrangulum.
ACB dimidium quadrati C F) ergo de quadratum C F aequiualet praedi-
eta difterencix inter quadratum darx AB, de quadrata simul additxe, e
Superaddisae B C, A C: & hoc de quacunque alia simili ordinata dc.
Mmate
Eoi priai