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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 213r, page id 00067993:0427
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de simplici Cattu excerpendo, nempe Z. H = H L3 dc, ejus le
riei infinitae Cummo Facit Z(cu Z. Sed si ex hac iterum, simplici
Caltu terminos excerpamus, nempe: Z F f. 8 _c, ejus sericiinf-
niex Cumma erie Semicireutus, posito gradracum Diametri eAle 1. Cvo-
niam aurem eadem oper à d quadracura syperbolae Rricbmericatrabe.
cur placet cotam harmoniam oculis subjicere:
364 31 100EIA 169 196 225 256269 74 3SIO
81524 3548638099 120143 168195224255 288323360399
36iserss 1005 10 orisoero inssoso
cc.
c.
(cireulo ABCD cujus
agratur SDocencia inscripta
Hyperbola CBEHC, cu
ljus gractratum ABCD
Sicin Figura 5. Asymptoris AF, AE, sibi normalibus, Hyperbolae
curra deseripea OCHI, cujus vertex C, porentia vero Hyperbolae in-
Scripta sive qracratum, quod rectangulo sub ordinatâ quàcungue
EtL, in suam ab scistam AE, semper aeqrale est, sic ABCD: circa hoc
gradratum describacur Circulus, se ponatur Fyperbola ita conti-
nuacA a C VSg; ad FL UE SIE AE dupla iphius AB. Tunc posito AF esleuni-
CaTE, erit AB =, _c ejus quadratum ABCD erit Z, ee Circulus cujus poren
cia in scripea est ABCD, erit Z. f. X, FG _c. Hlyperbolae verolcujus po
cencia inscripra estidem qradrarum Z) porrio CBEHC quae logarictmi
racionis iplius AE. ad AB(sire binarii) repratentat, eric 3. L 40 L72 aC.
JOH.
XAB CLMHBIIEIP BE XHUSABGILMSAI OnEs MmIOd MMSAuT SDEL. 24
rocuei cunsespeab 13 P0nb c2. Ln SJY ~ _ WIHIGLSGLIMSSI MINIEEP
EAB DECY MMOMTD MIBEONET SIBCIEAES SMISIMP MMIOd MTUISAMMuS
DUON LSMNISTDKS SIIDIIOBO E PHIOLBLI ONSLMMIO ge StAEAB
Eso Bos ipouonlus qus uiodiSO3 sausBey uapiou supHI pos
SMUIu
BegC = unuSy sunSyasd noscundes csvonesydnu sivorier
OIIME CMOKSIBL W BnnguOS inSueVs sesurab secp n et Z
DeL inCOQVuMSuEBBS PE VDQV Comabgosin sopio
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WDHOHESGCITMLISIIOTES SIIBEIMU DUMS CTIINIONBLIMW SUONeS vivSyd
nxui n3y. 3∞ SbCi erespeab Mnno3 in Jun) =Dg ~HECIP1O. 3∞ CE17C
SNGHEIMIBE STASCIML IA SNGMUSVIXS
day qV sypiosqe 170
mvd
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TALS SIVOIEN LMIBIEME DE SesIUM MMEGDQV cMICIISGCMSAIS cmpS
=GEDSIPE VDQV CAMSG LTIS 1I35GO Pa QV aneISqe CeOdIBBN
ne eBsEP erecg me eresdiu sabunssa suones cusuns
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CEMEsPCAb MIAI WSPC: Nyal idnoper om oups, cenS uns
uy L3 D MEKyd) pun CXXGd iperabp, D CmOB Supdin y epuyL
In es E.ZCT umLORUME 13 Syeab Sd syegV SruIMe UpenF
CSPUI L3 ~ CeRXGdy CLINVOS LSIUI Ones sy ab CMISAC CequOS
LNIEVAB COSPBLIILBLV SHLIIZA .LINIOSEELLSGIE NEIXS SrRES
Posurprab Bned Corxoce suipunsord eyes inb csinsou porb cex
-UBAPS SOLIIISI LHIWIOSG LINdDEEMEISHVOI SIUNduTEUSqr
LINLEEKISGSHd ABMIE CIM ∞ : unOd FESONSISESIELESSIV SOVOI
eabie De esxujgo1d say unus absu seresyqud snus vey cs siai
SOBOGISEI LIMPUNOS) 73SICVSIOdUTSIEZ SOS eS CMPVONCMEnqqVE
WesG3S,V Vod iverI 3abonB SUNU iUIE ~ CHevOS Suny LSd
ZBIBIIOSG 3uESyaUs esHII BY pC uniosuan solb 1dO
eAt qradrapla rationis Circuli ad Gractratum. Archimedes quidem. Po.
rgona Circulo inscribens de circumteribens, quoniam major est in-
Scripeis ec minor circum seripeis, modum olédie, exhibendi limites incra
quos circulos cadac, sire extribendi appropingrationes: elle seilicet raci-
em circum ferentiae ad diamerum, majorem quamze adi leu quam 21
ec minorem quam 22 2d7. Hlanc Mechodi alii sunc prolecu, Pco.
lemaeus, Vicca, Mecius, sed maxime Ludolphus Colonienlis, qui octendie
ele circumterenciam uc 3. 14 759265358979323846 dc.
ad diametrum, ad 1. 00000000000000000000
Verum hujusmodi Approxinguaciones, ethi in Geometria practica
vriles, nihil camen exhibent, quod menci Catistaciat, avidae veritatis, nili
rogrestio calium numerorum in infinicum concinuandorii reperiacur.
Mulci quidem perfectum Tecragonilorum protessi Cunc, uc Cardinalis
Cutanus, Oroncius Finaus, solexhus Scalioe Thomas Gephyrander
Thomastlobbes, sed omnes Falso; caleulis enim Archimedis vethodie
Ludolphi, refellebaneur.
Scd quoniam video, multos non latis percepille, quid delidere.
cur: Sciendum est, Tecragonismum sive conversionem cireuli in aqua-
le quadracum, aliamre rectilineam Eguram (quae pendet à ratione
circuli ad gradratum diametri, vel circumferencix ad diametrum)
Posseincellisi qradcuplicem, nempe rel per calculum, vel per constru-
ctionem linearem; utrumq: vel accurate, vel propemodum. Quadracu-
per calculum accuratum voco Analysicam; eam verd quae per
Constructionem accuraTam sC, voco Geometricam: per calculum
proxe verum, habetur appropinquacio; per constructionem prope ve.
tam, Aechanismus. Axproxingrationem loneissimé produxic Ludol.
Phus; Mechanilmos exresios Vieta, Huxenius, aliique dedere.
Constructio Geomerrica accurata haberi porest, qua non cantum
Circulum inceorum, sed de gremlibet sectorem sive arcum metiri li-
Cedc, motu exacto acque ordinato, sed qui curris cranscendencibus
competat; quae per errorem aliogri Mechanicae censentur, cum 
nen aque sinc Ccometricae, ac rulsares: licet Algebraicae non sint, nec
ad aegraciones Algebraicas, seu certi pradus, reduei qreane; suas enim
seoprias, et Ei non Algebraicas, camen analycicas habent. Sed ista hic
prodisnicace exponinon poltune. Quadracura Analycica, CeU QVX Per
calculum accuracum Ec, icerum in cres porest dispesei; in Analycicam
Manteendencem, Alscbcaicau, de Arictmericat. Mnalycica trans.
cendens;