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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 15
# Folio 2r, page id 00068110:0003
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latias patentem, quae non substitit ad aequationes eas in quibus una vel utraq
quantitas indesmila Radicalibus est involuta, sed absest ullo cequationum
apparatu, sangentem confestim ducere monstrabat, auestiones de Maximis
e Mimmis eodem citusilo draccabat; et speculationes de Quadraturis
facilius explicuit; Haec constant ex Epistola Penotoni ad Domimum
Collincum data Decembris diei 10 Anno 1672 8t inter C ollinii chartas
dipementer gaudeo Amici nostri Barovis dectiones
Mathemulicus extraneis plurimum placuisse. fd etiam
haud parum gaudeo quod intelligam, eos jam eadem qua
Ego Methodo in Sangentibus ducendis uti. Qualem Ego illoru
methodum q conjicio hoc Exemplo facilius disces. Recta CB
in Curva fuadis terminata ad AB in quovis dato Angulo
applicetur, du AB X, BC y; Et relatio inter X d y quavis
equatione daprimatur, scil. hac X - 2XX y + bXX -bbX + by - 2.
=0 qua Curva determinatur. Ad Jangentem ducendam
haec est Regula Multiplica terminos cequationis
per progressionem Arcihmeticam, secundum
dimensiones ipsius 2, scil...
X - 2XXy + bX X - b bx + byy -y =0
D
0
2
eosdem ettum per progressionem secundum dimensiones ipsius
X - 2XX yy + bXX - bbX + byy. -25 =0
pao productus fiet numerator, postercor per x divisus fiet
denomnator Fractionis, quae exprimit longituoinem DB
casus exttemitur Tangens co ducenda est. Gtag longitudo
2X X y + 26yy -3y.
3X X = 4Xy + 2bX = bb
hic est casus particularis, seu potius
Corollarium methodi Generalis quae sine Calculi molestia non
solum in sangentibus ducendis, ad curvas omnes sive illae Geome–
tricae sunt, sive mechanicae, sive quacungu ratione ad rectas
aut etiam ad alias Curvas referantur, sed etiam ad alia
magis recondita Problematum Genera circa Curvedines
Areas, Longitudines et centra Gravitatum Curvarum se
diffundit, negu haec Methodus (Sicut ea Auddenis de
Maximis
2
reperta cujus haec sunt verba
x multiplica seil.
DB est