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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 125, page id 898203430:0153
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ORDINATIONVM COMC. LINTTBVS LIB. L.
Amplius, ex puncto Hyperbolae  ordinetur ad axem FectA O9.
Et quum superius demonstratum (ic IIO ad BK esse re difterencia late
rum Flliplis ad cransuerlum ciuldem, vel, ex constructione, ve axis trans
veruS PH Oppolutarum Sectionum ad ipsaTUM FOCIUM, VeL VE RCCEANSU
lum PgN ad quacratum 99, quumque sic HIO ad BK ve rectangulum
Lub HIO, BR ad quadracum BK, eric rectansulum P9 N ad quadratum
O ve reccangulum sub HO, BK ad quadratum BK: Sed consequentia,
nempe quadratum 9 aequatur quadiaco BI, erco d anecedentia, (1-
ee rectangulum P g N aQUatE rCctanONO (uB FTO, BK. Ouod sCrUA.
Ec quoniam EIB ad BF eA ve 3O ad OE (nam veraque racio est rC-
eti ad Transuerum) de BF ad BG CA vE a OF ad O B Ob LANSENLEM, 2 ex COnUer.
AC, eric ex aequali HB ad BC vt 3D ad OB, rectangulum igitur (ub 1037. prim
AIB, BO, vel rectanculum FIOB cum quadrato OB aequale est rectan
gulo Tub 3O, BC, vel duobus simul sub 3O, B R, ee sub 3O, HC,;
led rectansulum sub 3O, BK aequatI RCCtanSUIO FTOK, ve paulo ance de-
monstranimus, ergo rectangulum FTOB cum quadrato OB aequatUE duo-
bus rectangulis, alcero HIOK, alcero vero sub 3O, I C; led rectanoulum
HOK aequale est duobus, nempe FIOB, _ sub HO, B K, ergo idem
rectangulum HIO B cum quadeato OB aequale est tribus rectangulis.
nempe HIOB, sub HO, BIE, de sub 3O, KG; dempro isitI COmUNI
rectansulo HOB, remanet quadratum OB aequale duobus simmil rectan-
sulis (ub HO, BR, de sub 3O, KC; sed rectangulum sub HO, BK
octensum postremo fuit aequale rectangulo PgN, ergo idem quadracum
OB equale est duobus simul rectanoulis P 9 H, _ suB 3O, H C; sed
Co
rectangulum sub 3O, IC aequatur b rectangulo sub AO, TK, vel rC- b 67. huius
ctangulo sub LK, RT, vel quadrato medixe R N; quare idem quadra-
tum OB xequatur rectansulo PgNV, vna cum quadrato (E NV, Sive vnico
quadrato K9, sive quadrato B O, ideoque ramus OB ad Fllipsim, ab
orisine per vercicem ductus, aequalis est lemior dinatie BO vlque ad oppoli.
tam Sectionem NO A.
His icaque demonstraris in singulis siguris, producantur huiulmodi op.
volitx Sectiones, donec conveniant cum verticali tangene ad D in pun-
eis 2, 6. icemque produciae lacerales tangentes G A, C, C, verticalem.
AC secent in 4, 5.
Ec quia rCCtINGUUm R7 O ad 6 4 2 est ve E quadeatum tansentis e 16. cerrit
7 A ad quadratum tansentis A 4; de rectansulum 8B7 ad 5D A eA VE ConiC.
idem quadracum 7 A ad A 4. eric compolie reccanoulum B7 O cum re-
ctangulo 8B7, sive quadratum BO ad rectangulum 6 4 2 cum rectan.
sulo sD4, live ad vnicum quadratum D2, ve idem quadratum 74 ad
A4, vel ve quadratum B O ad O D, Sed permutando quadratum B
aequale nuper ostensum est quadrato BO, erco _c. quadratum D2 qua-
drato DO aequale exiti ac ideo maximus ramus OD, ad Flliplun, aequalis
lemiordinaixe D2, ad Eyperbolam.
Sic postremo in omnibus figuris medius quicunque ramus OS, de Per
S Ordinetur recta laterales tangentes (ecans in T, Z, Sectiones in V, Y.
_ em in Z: eadem ratione ac supra demonstrabitur rectangulum 6D2
d