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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 139, page id 898203430:0167
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=167
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OROIHATIONNM COMIC. LMMMBVS LIB. 1.
lum P 4 N ad quadratum 9 4, ve rectanouium sub. F O, BK ad quadra-
cum BIE; sed consequentia, nempe quadratum 14 aequale est quadra 0
B K, ergo de incecedencia, siue rectangulum P 4 N, rectangulo sub
HIO, BI aequale Crit. Ouod memenco.
Ee quoniom E B ad BF est ve 3O ad OE (viraque enim rario est et
quam recti ad transuertum) de BF ad BC CAt. vE O F ad OB (nem ob
cangencem AC, AC Cenrum F, est BF ad FG; vE 2 OF ad FB, _ per 2 ex 37. pri
convertionem rarionis BF ad BC ve OF ad OB) ex aequali erie HB ad u Conie.
BC ve 3O ad OB; rectangulum erxo sub extremis A B, B O, vel re-
etanculum FTOB cum quadrato OB aeguatur rectansulo sub mediis. 30.
BGs vel duobus simul Tub 3 O, BK, ee (ab 30, K G; sed rectanou-
tum sub 3O, BK aequale ostensum fuic superiis rectanoulo FIOK, ergo
rectangulum EIOB cum quadrato O. B xeguarur rectangulis simul, I OU,
e sub 3O, HC, sed rectangulum HOK. equatur duobus Cimul, nempe
HOB, ee sub HO, BK, erBo idem HOB cum quadrato OB aequale
est cribus simul (yb HO, OB, sub HO, BKC, de sub, 3O, H C, dem.
praigitur ex his communi rectangulo HI O B, remanet quadratum OB
aequale duobus simul sub HO, BK, ex sub 3O, R Ci sed recrangulum
sub. HIO, BK, demonstraum, tuic virimo aequale rectangulo P AI, er 50
quadratum idem OB aequale est duobus Cimul rectangulis P 4 N, d sub
3O, KC, rectanguum vero sub 3O, KC aequale est b rectangulo sub v67. huiusi
AO, TK, vel lub L K, KP, vel quadrato media K N: quare idem
quadracum OB aequatur rectangulo P 4. N vna cum quadrato K H, TiuC
vnico quadeato 15 4, Sive quadrato BO: adeoque ramus OB ad datam
Eyperbolam aequalis est ordinatae BC. vsque ad delcsiptam oppolitam
Sectionem NOA.
Ftucusque omnibus prxeostensis, concipiatur in singulis figuris alius qui
CUINGHC FAIUS OS ad Fyperbolam datam, _ ex S ordinata YZ OpPOSI-
tas Sectiones secans in F, Z, tangentes lacerales in V, Y, _ AZCM in X.
demonstrabimus enim ijldem penicus argumentis, quibus vs fuimus su
per secundam figuram, rectangulum R B ad ZST esse re quadratum
BO ad quadratum OZ, Sed rectangulum. R B O, siuc quadratum B O
octensum est in lingulis figuris aequase quadrato BO, erso de rectanguum
Z. S T quadiato O X aequale eric; his itaque addito communi quacrato
2S, exic rectangulum Z. S T cum quadrato XS, sive vrricum quadratuim
X T, aquile duobus Cimul quadratis OX, XS, siuc vnico quadrato O5: 26
propterea ramus OS ad FIyperbolam datam aequalis semiordinatae XI
Vique ad deseripeam OA. T, e sic de lingulis ramis e
Temiordinatis ad veranque partem ductis:
quire convexa huiulinodi Oppo.
titarum Seccionum lune
Limites
Ordinationis propotua
2. L. D. O. M.