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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 128, page id 175905688X:0150
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# Lines: 57 recognised, mean confidence 0.78
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ELOR EM ONDF DE BE AUN E
Jem libuerie, eaque indefinite productâ: ducantur linea DR,
LP, QT Parallelae ipsi BFI; Ita UE D R cadac intra BFL; L. P
autem supra BII, inter puncta X ee Y; QT vero ultra pun-
ctum Y. Fodem modo ducantur linex QD, R AF, SF, TR
parallela ip(I X Y PCu Z C; ita ut linea () D eranleat per li-
neam Z A, productam versis A; de S F per eandem inter pun-
Eta A X X; nec non linca TI per candem A X, productam ver-
sus L. Duibusita consticuris, (i per qam Propneui 2 di libri C oni-
corum Apollonii de scribatur FIyperbola, guxe tran(eat per pun-
Ctum Y, cujulque ACympeori line linca, quas resere quaelibet
constructio; manifectum est, per r2 Propuem ciuldem libri re-
etansula omnia, quae ad caldem lineas similiter sumuntur, sibi in-
vicem esexqualia. Ideoque demonstrandum Colum restat, A(YIM-
Protos, atque rectansulum uniuscujusque xquationis, rite elle
Constructa.
Fsto isicur secundum ultimam aequationem FIyperbola cor
Pructa, cransiens per punctum Y, cujulque A(ymPEOtI (IMED.
_ DO; de rectangulum, contentum (ub lineis DC, GY, sIE
aequale rectangulo dato df- L bc. Flinc si juxta constructionem
Fecerimus lineas A X ∞ ∞, X Y ∞Y, AB ∞c, BD vel XG b:
manifeltum est, B X vel DC ForC X - LC; G Z autem y. L b;
acque mulciplicando unam per alceram prodicurum bc-  bx- F
67- F xy, prorectansulolinearum DC, CY. quod aliunde quo.
QuC aequatur df- L bc. AC proinde, si utrinque commune autera-
cur rectangulum bc, relinguetur x y. f. cy- + b x ∞ df. quae est
aeguatio propolica. Fodem modo reliquarum omnium aeguatio-
num es constructionum demonstratio oltenderur.
Aqua
A
X) Ws
Rectam
AlymD
Xy
ABD
A(y Mi
Rect
X) +
AH DC.
Alsi
Rectune
ASym
RB
H) f.1)
AB 
Recle
Aeqt
19 +. brs
AP. H
AlyMp. AE,
Recli
X) L. 17 0C
AC VC
Asympr. S
Rectane. CH
ACD
Aiope