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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 14
# Folio 81r, page id 00067976:0161
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de
reliquo etsi quotres cunqus libet ad huc circumflicaretur et AB adsus
saepius essent repetendae tamen non ascenderet altius. quotrescunque AB toties necmt
quotres CB curva est conica. nempe hac Ellipsis
si ad hibendo ejusmodi periodum punctum C. non maneat fixum, sed procedat recta B
sint vestigiis parallela habebitur quidem perrodus, sed tunc lucn habemus aliquid
compositum ex solis AB et BC alorequile simplicibus, dato aequale. quia mulatur
Quaeramus langentem curvae paulo ante exhibitae sit AB aequ. 7. et BCaequ V
ipsa AC
Jaim 3Z + v aequ d. Et 36Z + dv aequ. 0. jam  Sco aegu da
21c0
Jam L Ergo fei dqe aequ   p ex x +y ay: et ab ogo a dX +7 dq - a dx
SXX+ yy AZ
et fiet: +3xBAC + 37 y aequ. _ XZ ax + yZ du = a 7 ax
e sive fiet:
dx iqu 32+37V
aZ = xZ + 3xV
Videamus an ex motu describente tangentem invenire liceat
Ay
sit: fitum ABEC tensa in 1B.E, ita ut ibi unum membrum vel articulus in isque omniu
calena AIGIFI (B. EC
medius a caeteris distinctus appareat reliqui sunt in linea recta. Jam clavum infigentes
in puncto cB ut ibi calena sit firma apprehendam, manu c F. idque tam
bique Calenam manu fendentes, tamdia moveamus donec, punctum
1E perveniat in 2E, sitque sintus 1B. eE et C in eadem recta quo sacti
extrahentes clavum ex 1B eum similiter infigamus in 2F et cum
B. 2FG eodem modo procedamus ut pracessimus cum 1E1BiF dones
1B perveniat in 2B,  F manente 1G perveniat in 3G sintque 2F. 2B et C
itam in eadem recta. Quo posito patet 1B,E2F3G etc. esse
polygonum curvae, Ergo perpendiculares ad hujus polygoni
latera sunt curvae fangentes. Quoniam autem aliunde scimus
Tangentem Ellipsio habere cundem angulas aequale ad duas rectas
ex focis rnctas necesse est AaF. B, et C1B2F angulos esse aequiles
quod quomodo ex natura trapezii demonstran possel, esset
A2F 1BCV
quomodo semper ex
Vodendum
dispiciendum
datis focis et flexione Caleuo, aliquid certi crca
angulum tangentim ad Tangentem, duci possit
idque ideo potissimum, ut inveniatur regressus
seu modus investi inveniendi constructionem Curvae
ex data Tangentium proprietate
Examinandum esset, quomodo tate quid possit
forte tum
in transcendentibus habere locum.
loco rectilinearum
licebit fingere cuvas calenas
et ita habebitur quoque requssus seu proprietas langentium