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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 58r, page id 00068200:0117
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Linea
De dimensione curvae conicae, inprimis Elliptiae
et Hyperbolicae.
it entud lonieae AC paste A aAB
n est
Curvae conicae sunt parabola, Hyperbola, et Ellipsis sub qua circulus
comprehenditur. Et circuli quidem arcum dimensus est Archimedes
ex data spa plani circularis quadratura; nostro autem seculo detecta
demensio cujvae Parabolicae, ex data quadratura Hyperbolae; sed ipsius
curvae Hyperbolicae atque Ellipticae dimensionem frustra omnes hactenus
tentavere etiam maximi Geometrae tentavere. Et sane longe major
est difficultas, quam ut v per vulgatas methodos superari possit.
Itaque nostram analysin experiri placuit, cui vix quicquam hactenus
in accessum deprebendi, et quae plane ab Algebra aac methodo indivisi
bilium  aliisque publice notis hactenus artibus differt, etsi illis
subinde velit gradilus velut instrumentis utatur
sit ergo curva (onica AC cujus axis AB. vertex A, axis AB. cui occurrat, curvae ordinata cB
occurrat curvae tangens CT, et tangenti perpendicularis cP. Constat secundum
generales expressiones meas (posito abscissam AB esse X. et ordinatam BC, y
yfar ye aqual rax = et latus rectum a, latus
transversum 4) fore yy aequal. ZaX + a XX. ubi quidem
in parabola est ipsa, q infinita, unde terminus  xx evanescit in circulo
 (sive + vel =) significat -. et a est aequal. q. unde fit 2aX - XX.
in Ellipsi itidem + significat -. sed a et q sunt inaequales; in Hyperbola
significat +. Ex hac autem aequatione calculo etiam generali sequitur
fore BP aequal. a + a X. Jam ex vertiae A educatur ad axem
normalis AD aequalis lateri recto a et  pnctum D
ducatur DE parallela axi, cui PC producta si opus occurrat in E et
compleatur rectangulum ADEH. jam DE trans feratur in BF in directum
ipsi ordinatae BC. et idem ad aliud quodvis curvae punctum, quale fuit
ipsum C. fieri intelligatur, denique per omnia puncta F. transeat
nova curva AF constat ex aliqui demonstratis spatium ABFA
aequale esse rectang uto sub AD et recta  aequalis sit ipsi curvae AC.
itaque ad inveniendam curvae longitudinem opus est tantum dimensione
spatii ABFA.
Hujus spatii ut natura cognosca
vide intus sched. 2
absolutam