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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 309r, page id 00068194:0617
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Cum hactenus Analytis recentiores ad con-
construenda problemata per intersectiones linearum
non nisi ordinatis invicem parallelis utantur
tentavi an non constructiones interdum felicius
procedere possent adhibitis ordinatis convergentibus
ad idem punctum. Et
Et incipiamus a loco ad rectam. B.X L XV-
quae sit BV, referenda ad directricem BA. cujus data
sunt puncta A et B.  sumto quocunque
puncto V in recta locali BV, jungatur AV, et ex V in BA
agatur normalis VX. constat esse BX ad XV in
ratione constante quae sit B ad 1. jam AB
vrcetur a, et AX, X et AV, V. fiet BX, a +X
et VX qu= AVqu = AX qu. seu  erit
seu xe seu erit VX qu = vV - . Et fiet
 BX: XVX Et BX erit a + x Et fiet
aa + 2aX+XX, :, vD - XX = βB: 1
seu βB∞V, aa t2aX + (1 + BC) XX
quod si in direstrice sumamus aliud punctum
concurgus praeter A, e velut H et juncta HV
et BH sit h. et AH vel h a sit C
vocetur 2, fiet eodem modo fiet BX- AB A e xec h HX
3522Ch Cnhu et VX 22 ul quH
et  qu BX: qu. VX = th  h X e qu HX:, ZZ- qu HX = BB: 1
adnoque hh. h HX + qu H X  βBZZ a Bβqu HX
et  Et pro HX ponendo st H- AX = h- a -K - e - x
et fiit ber 2he +2ta + (ee- 2 CA + XX) , +BB) = (Ba
Et a valore ipsius βB, Z, sabtrahendo valorem
ipsuis βBWV, fiet nti het chx + (ec = ) (t BB)
aa tax (∞77 BBVV +
jam hh- 2be + ee aa 0, fai et 2h 20 24
BB (v)
in B ee reX B reBBX  β(o
seu sint ee + VvagZ = 2ex seu X = ee t vv - 12: 2e
et XX =  + 2CCVV= 2eCZZ + v + - 2VvZZ+ Z3: 4ee
quos ratores substituendo in valore ipsius BBpV, siet
A eeBBVV =  eeaa + 4a1 + 4a ebv - 4aeZZ + (1+ BB)  qu(ee + VV - 72)
seu (eeBBVV = 4eeaa + 4ae + 4 aevv- 4 a e32 + C+ + v +  57 +2eC vV L2eCZZ = 2V0Z3
conservemus e, quia eodem modo se habot ad h et ad a,
sed tollamus e = h- a firt at 1t BB vocemus r: C
osits quae dim
gueno ene  reBt ec,
ECevvi 3B)
o= (tanee) t Aaheet gaa ee (t gahe. quab et, qaavu vV antiov- Tah E + 4a ad et (.  V s.  ( non
fiet  ae = ah-aa, et fiet H ad
lutoy 
seu siet   e (2+ vorZWV) C + 2a Z + (a= tah - 2rp C) (271 VV) + 4 ah ee = 0
at adaa
quae admodum memorabilis est aequatio, quia sic 
n et V A non habentur nisi in 79 et vV. Et p
q= ras et oo =re Habebitur aequatio
illi similis quae solet esse ad Hyperbolam Et aequationes binae
qu
tahhv
sed
Et raciendo Z
ad Hyperbolas converti poterunt in binas ad rectas
ipro ordinatis sumantur non ipsae convergentes, se ea quae eas possunt
pergemus nunc ad Circulum, et ad sectiones conicas
bt. a
AH, e
AX, X
X a eC + vo- 2: 2C = AX
Xc YXqua v B xX
VXqu ZZ Hiqua
seu LX qu 2E eC + rex- XX
Ergu fiet rex = B + VV. 2Z
et juncta HV sit Z
patet so ideo cum
sit V Xqu = VV - XX
et rum et misus
VXqu = ZZ- HXqu
Seu VXqu = ZZ- Cet 2X - XX
Ergo aequatis binis valorulius
ipsius X, VXqu. fiet
2CX = ee + ov - 2Z
e existente basi trianguli
X  et X segment.
baseas per perpendicularem
ex vertice, Hinc datis catio–
naliter basi trianguli
et quadratis laterum, al
adbatlvea e
pe
reimens is
perpendicularem et
vertice sun ratiopalic
vel gencralius ea
 atio