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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 123, page id 898203430:0151
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=151
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ORDINATIOMTM CONTC. LIMITIBVS ETB. I.
ELI, erso e reccangulum P L. H ad quacratum L. A erit ve caciem late.
rum differentia ad transuertum FIliplis, sed ratio haec eadem ck, ex HIy.
Pochek, ac racio transuersi laceris P N Sectionum oppolitarum N9, PR
ad carum latus rectum; quum igitur rectangulum PLN ad quadratum
EA Sc ve cransuersum ad rectum ipsarum Sectionum, lXe necesaTIO ExAn
sibune per puncta A, C. Fc quum rectangula L. II, MHR aequalia sInE
quadraris mediatuum IEN, RP, LCCEX CA, CC iplas Sectiones contin-
FenE a ad A, C; sed exdem recLa contingun quoque ad A, C, Fllipsim a ex conuer
datam, ex constructione, atque alcera opposicaium est ad vnam, Filip(IS (0 37. primi
vero ad alteram partem rectae C A veranque Sectionem contingentis, de Conic.
hoc pariter de alia Sectione opposita; ergo ipsae Sectiones oppolitae, da
taque Elliplis in iildem tancum punctis A, C, sC MULIID CONInSUNE CON.
AICXO.
Insuper, in prima figura, quum positum sic punctum E terminum semi-
recti lateris BFT, incidere in punctum originis O, eric quadratum B HI,
vel BO aequale D rectangulo sub lemiordinata AH, vel AO in lemior-
dinatam TK in triangulo circum seripio AC C; sed est A O aequalis ipsi
LB, ergo quadratum B O aequale cAt rectangulo L. BI, vel LKI, vel
quadrato mediae umpta RN, ideoque ramus OB ad Fllipsim aequalis est
Temiordinax BO, vel HH vsque ad FIyperbolam AQN.
In secunda aurem figura, quum, ex constructione, sic FHI ad FIB VE EO
ad OK, erit converrendo, componendo, de permutando BF: ad F. IE ve
TIE ad EO, sed HIE maior eAt F O (quoniam ex Trpocheli, in hrac A.
sura oriso O dictat a verrice B per interuallum maius Cemirecto BIY)
ergo de B F ipla FK maior eric: quare punctum I, quod est centrum
oppolicarum Scctionum, incidic incer verticem B, d originem O, ideo-
que ordinata ex HE Fllipsim SecaE, Ve in 9: GuaprOPTEE SI iungatI O9
(quum (iC ex Hyporhesi F. O ad OK, ve disserentia lacerum ad cransuer
b26. huilo.
Tum, ac ideo FK adK O, ve crantuertum Fllip(S ad recum) ip(a O 9 c ex 23. lib
normalis exit c super Sectionem ad punctum 9, ac ideo guadratum O0 2. nORIX BI.
inBC. in
aequale est a rectansulo sub semiordinaris OA, KI in triansulo cir- apoil
cumseripio ACC, vel sub. LK, KI; sed ee quadratum sumpiae mediae d 27. huius
KN eidem aquatur rectangulo sub L. K, K L, ergo quadracum O9 egua
cur quadeato L IV. siue minimus ramus 09, ad Elliptm, aequalis lux le
miordinatae K N vsque ad Hyperbolam ON A, siue aequatis iptius Hy.
verbolae Cemiari.
Ex quoniam quadratum 09, siue duo simul quadrata OK, H9 aequi
lia sUII quadrato H NI, dePTO COIUNI GUAdFATOR 9 ReAHCE quadra
tum OR aequale rectangulo P gH; led rectangulum P9 N ad R BO est
ve quadracum OK ad OB (nam pars rectanguli PoN ad partem reccans
Buli R BO, hoc est rectangulum P PN ad R , O est vE e quadratu c ex 20. cex
Eangentis AI ad quadratuM tangemis A7, ee reliqua ad reliquam, Hoc eii Conic.
est rectangulum _ 9I ad 8B 7 eA vE P idem quadrat AI ad A 7.
vel ve quadratum OR ad OB) _ antecedentia, nempe rectangulum
PgNT, e quadracum OK sune xequalia, ergo de consequentia, sCilicCtrC
etangulum RBC hoc eAt quadratum BO. e quadratum O B aequalia
CTLINE
C ibidem.