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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 153, page id 898203430:0181
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CHBINATIONVMCOMO, LMMITTOVSLIB. P.
Sectiones OpPOLIEX ES, OR; has contingere datas ad puncta A, C, ac-
que iplis else insccipeas, carundem que convexa esle Limites propoliiOs.
Ex puncto C, in Eyperbola AB, sic concingens C M coniugato axi
DL OccuEreNS in MI, acque ex A suPer tanSeNEEM AF sic perpendicularis
A N, de ex contact A ducatu AP ipEi OL. parallela, quae OrdinaEX IF
Occurrat in P. Constur punctum P cadere vlera produccam IF, quum
huic aequalis (I OG, quae, ex Fypochesi, minor est O A, vel IP,
ed quod sic minima.
Tam, quum OG sic rammus minimus ex origine O, _ AF C trianculum
oppolicis Sectionibus circumleriptum super A C ex origine ordinatam,
Tcque in eo semiordinata TFI ex rami sublimitare, erit quadratum OC,
vel TF aequale 2 rectangulo sub OA in IHI, vel recrangulo sub DI in 227. huius.
TII, ideoque TF. est media proportionalis inter PP, IHI, aeque ip(i me-
dixe TF addica est in directum, de aequalis YO, ergO recranguIuM PP HI
aequatuT b rectangulo O PF, sed rectangulum PP FF ad quadratum P A B 19. huius
hrabet rationem composicam ex ratione IP ad P A, vel ex ratione aequa- 2d num. 2.
lium O A ad OI5 d ex ratione FTP ad P A, vel HI ad TF ( ob simili-
cudinem eriangulorum ET P A, TITF) ex his aurem rationibus consatur
ratio recranguli sub AO, HIT, vel quadrati e rami minimi OC7, vel re- c27. huius:
ccanguli MOLC in triansulo rectansulo MCO,) ad recrangulum L. IO,
vel consicitur ratio linea MO ad F. P, (ob communem alticudinem OY)
ergo rectangulum IPTI, vel ipEi aequale O P F ad quadracum PA eA vt
linea MO ad FI, vet re d linea NO ad OL, sed NO ad OI est ve C
d ex Co
summa laterum D B, BY Sectionum AB, CD, ad iplarum rectum l4- 0 ex Schot
tus B P, acque idem rectangulum OPF. ad quadratum semiordinata ex 27. Dulus 20
P in Fyperbola ES eAt, ex FIypotheli, ve eadem summa ad idem rectum,
ercO rectangulum O P F. ad quadratum P A est ve idem O P F. ad quadratum
semiordinatae ex P in Fyperbola F S: ergo haec necessario trantIE peF A.
Fit quia rectangulum PLFI, ve superius octendimus, aequatur quadrato Fex conurn
PE, FECEA AHF EIyperbolam quoque S AP continget Fad A.
Sit praeterea alius quicunque ramus ex origine O ad FTyperbolam AB, ConIC.
DEXter ad DUNCTA A, C, ductus, qualis est OB, e per B sic Ordinata TV
datas Sectiones secans in B, D, deseriptas vero in P, V, de coniugato axi inL
Ec quoniam ramus OC aequatur ordinatae IP, ex constructione, erie
quadracum OC, Tue duo simul OT, TC aequalia quadrato LE Cine re-
ceangulo C F. cum quadrato TC, dempro isitur communi quadrato LC
eric quadeatum OI aequalo rectangulo O(F.
Inluper quoniam rectae AF, CP verunque Sectionum oppasitarum par
cansum ad eadem puncta A, C, ve superius ostensum fuit, iplaque con-
tactuum puncta iunsit recta AC, cui aequidistan O F, V T, cangenes
AF, C I quancum E opus producas in HI, Z, & Sectiones iplas lecan
res in O, I, C, E, _ in V, D, B, T, eric quadeatum tangentis AFI
ad quadratum FaNSeNEIS AZ, vel quadratum OL ad OL vE B TOLIM FC- 8 20, cerriy
crangulum OHE ad tOtum VZT Cin Sectionibus AT, CV) de ve pars ConiC
ad partem, nempe ve rectansulum IEFI C. ad rectansulum DZ B (in SC.
etionibus AB, CD) ee ve reliqua ad reliquum, hoc est ve rectangulum
2C. L
27. HWIUSC
nVIo 3
1037. Primi