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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 360r, page id 00068196:0715
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Dubito: nun sinus smmant in A basin e i nanom, ea non itutitudin
duretdimensio circuli quia serans ad abtitusinem Hyp. secam ad baba ex conhoee
detragonisimum.
Ellus b.t sea eris plpeatrili cantes
si incaliqua tigumostingeret, ut
perpendicularis ad hasim et ad arcuri
ad altituonem summari posset, dantur.
quadralura circuli posset et summuri per...
pendicularis ad arcum, quia, hic dactis
dectaeurva  Planae aequalis superficies curva, invectigando, scilicet locum ejusmodi   applaatarum ad altitudine adnecta recto quadam, summaret perpendicu. D)
tem
in rectu
Ergo 25- 16 - 4
Ergo 2eb - 16b = X
monctum dividatr Hinc dueo regulam
alelarim
 a er duat horu, met
E BC - AB0
jam AB AC.
erguAD= AC AB
BC AB
distantias at AB. sed tanum
quioqud quanto quadratum avu consideratu omna rediuntur facillima componius quia illud qua
sed quorum quadra
ntratiles, quae
chalum, componitur ex quadratis basis et altitudinis ontrrimae
applicarentur ad quadrata annum basium miminarum separatum et ad quadrata
altioliduum minorum sparatuu idem est de oibus ductibus, ad circum applicatis.
coponunti enim ex visdem ductibus ad arcum et iisdem ductibus ad basm.
idio vu sinus ad varcum, ducti in radium adarcum, aequantur radeo in sinum ad
Generaliter inquirendum est
in proportoo ductus ratiorum pro pr in partes minimas, proportionales maxi-
3(00
Methodus data figura curva inveniendi r figuram a cum quadratura quam
fitas curvae pendeat. Hoc facillimum est. sed attale invenire figuras Et calculi
as est postea invinire figuras quadrabiles,  ideo curvas quoque in rectam reduci
biles. Huc Haberi pt jam figuraadius urva vg. A cujus quadm dcincusio pendet
a quadratura v.. altrius cujusdam hypertloeods . aut figurae  altius C
cujus fegum pendet ab ista quadratura
in rectaum puntabili, invenore spatium quadrabil
et et sa 5 cguntatione. Ideo quot nobis Hugenius dedit cuvas nrecta
commulabiles tot ego spatia quadrabilia dabo.
Iulvo et aliar methodum determinandi curnas infinilas 4
spatia quae pendent a curearum rectificave, et 944;
videndum in on coincidut priori.
 quolibet
e liba
quamlibet
rectam connintabile
q tostire etos srpr
ipse fltimduis, areu
cont ila ut data figura habert. possit curga
contra data quacunque cura
quod aliter quoque ac simplicius sic demonstratur: Esto tumgens carora m perpendiasari pter ad srcifcantali, dare duo curoas
AB BC.
BC.
sitem,s in quadratum, altitudimp Ergo ergo D = AC BC ducta in AB
lla rectam. Era
altitudinem, auctam radio in sinum ad basiu
m magnis.
tangentem per in ipso contactus puncto, inter duosaxes hargllulos alacta Al. Ancta perpendiculam. NIl nit diversas in rectu qua
CRL po Mp
cusunt
jam . AC
Ergo perpendicularis in rectam illam
inquadratur cularis in arcum–
generatm
 paralletos ab, ec interceset, eb  ducta in olistam sratio quadrabili
so modus
sta aed busin + perpendiculari in rectam
in quadratum rect basis,
demprlemsui
linen
Hinc illud quoque apparet summam ommum perpendicularium Xl. ad altitudinem, aequari omnibus hu inccurvam Patr si s. dici sit. Data qualibs
langente yn
dat
1250 ta applicantum ad arcum, ea idem est appli eomnonq idem est ac si eorum quadrata
100
105 57 - 450 (20
quoliens
10
s
sit
curvas diversis
 summari posse
a sempe sum
man possunt put
Atd
et omni
RL. quae seuu
ade En
momenta habeat
seu cylindo
eom revolutive
circa cb. facti
nod sali
memorabile
falsum.