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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 70, page id 898203430:0098
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70
VTNCEMTMS VINTAMI DB LOCIS SOLII
nam Eyperbolam secans in N, O, axem vero in M, ac ducta per ver-
licem B contingente PQ, d PS ipEi BF. Parallela, quae producta datam
Hyperbolam lecet in R, iunsatur RFi, _ F. 9. Quae producta ordinacam
LOiecet in T.
Fric itaque (ob concentricas Frperbolas, e cum eadem diametro
22. huius. Consusaca siul adscripras) ve PS ad SR, ita a HI F ad F B, vel, ex
constructione, ita BE ad PP, led permurando in parallelogrammo PF,
es PS aqualis ipA BF, er3O _ R S ip(I FF, de reliqua P R reliquae
BF aequalis erir, sed Curul aequidictane, CrgO R F, P B sUInE aequales,
br. huius. Sed RF per Focum semiapplicata aequatur b Lemirecto lateri datxe Lly per-
bolae, quare et B P, Suie BO eidem semireeto laceri aequalis exic.
Praterea, quum Ely perbolae H
HI, I. B Sinc Concentricae, ac (-
mul adscrip. X, Sicque iplarum
communis diameter coniugata AC,
_e PO. NO sinE ad F M ordina-
tim cuetae, eric rectansulum PBO
Ca. hu VS. ad NL. O vE C quadratum F. B 2d
35. huiu.
E M, vel in trIaIGUIO MF P, VE
Ouadratuu BO ad M T, sed
quoniam est BC aequalis semire
eto datae Fyperbola L. B, ve su
periis demonstracum fuic, de L
OT unsic tuuius terminum , dc
cemrum L, eric Ordinata M I X-
qualis d ipsi MI K alcicudini nOr-
malis LI: Guare _ rectangulIII
PB  ad NI. O erie ve gitadea-
tum BO ad quacratum M K. Sed permutando est rectangulum PBO
aequale quadrato B2. erco de rectangulum NLO, aequale est quadrato
MK, his isitur addico communi quadraio LMI, Het rectanoulum NI. O
cun quidrato I. M, Line vnicum quadratum N M aequale quadratis si.
mul AHE, ML, Siuc vnico L K: aC propterca, de semiordinata M N,
in delcripta Hyperbola NFTO aequalis est normali L IE super datam Hy
perbolam I. B; _ sic de lingulis normalibus, e semiordinatis. Ouares
concauum descripre Hyperb. Cs Limes Ordinac. propolux. Ouod erat, ec.
R
 A adlcripeis, quarum eadem sic lecunda diameter IrAHIUCrHS COMU
Gulu, secrangula lub cuusiber ordinatae partibus integrantibus a Sectiont
Dus comprehensis, aequo: esse quadraco seomenci ordinatae ejuldem in
Ter axem, e rectam iunsentem centrum Sectionum, ac terminum Pemi
recti per verricem incerioris ordinarim positi. ORenta enim est B O equalis
leru ecto laleri Sectionis L. A B, de recrangulum NL,O equale quadrato M P.
PROPO.
Inc seguitur in concentricis TIyperbolis per diverlos vertices simul